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Stress or strain: which one is more fundamental?
In between stress and strain, which one is the more fundamental physical quantity? Or is it the case that each is defined independent of the other and so nothing can be said about their order? Is this the case?
To begin with these questions, consider the fact that first we have to apply a force to an object and it is only then that the object is observed to have been deformed or strained. Accordingly, one may say that forces produce strains, and therefore, it seems that stress has to be more fundamental. If so, how come stress cannot be measured directly? This is the paradox I would like to address here.
Of course, to begin with, my position is that you can never directly measure stress.
I have read somewhere an argument (and forgot exactly where!) that even in photoelasticity what you really measure is strain. The argument, essentially, is this: Birefringence arises because the molecular chains in the photoelastic polymer get stretched. (In case of crystals, "stress-induced" birefringence arises if the deformation is inherently anisotropic.) So, what is important here is the relative positions of atoms in the chain--not whether the atoms were carrying any load or not.
The above argument, of course, is sound. Yet, it does not quite settle the issue by itself. This issue is somewhat (but not fully) similar to the hen and eggs situation. To settle the issue, we have to go beyond photoelasticity mechanisms and examine it from the viewpoint of the theoretical structure of the mechanics of solids/fluids.
What is clearly undisputed is the primacy of displacements. (Definition: Displacement is the total movement of a point with respect to a fixed coordinate frame.) Displacements can be measured directly and do not need other physical quantities to be measured. Hence, they are primary.
Further, what can also be thought of directly is deformation. (Definition: Deformation is the relative movement of a point with respect to another point in the body.)
Now, displacement can be related to deformation via the relative deformation tensor, a tensor of second order. (As usual, in the simplest analysis, one assumes infinitesimally small deformations.) Now, if you split the relative deformation tensor into its symmetric and anti-symmetric parts, and ignore the anti-symmetric part (representing rotations), what you get is the strain tensor. This is the primary way strain is defined.
For homogeneous linear elastic isotropic materials, strains and stresses are directly related. So, we should expect to find a similar theoretical structure for the concept of stress too. In a way, this does turn out to be the case--but not quite fully. Let's see how.
Stress also is a second rank tensor and it also is symmetrical--it drops out the torques/couples part. (This is in analogy with the dropping of the rotation part while defining strain.) This fact about the stress tensor is usually taught in the introductory courses as the result of having moments balance out over the infinitesimal element. But the real reason is that this way we can maintain the similarity of the theoretical structure. The fact is, one could keep moment-balance (as required for static equilibrium) and yet choose not to drop out the torques-related part. However, a discussion on the so-called couple stresses would be a digression here.
In short, since both are second order symmetric tensors, stress and strain tensors do seem completely similar.
But are they?
There is that "displacement<->the gradient tensor<->deformation" relation on the strain side. What is its parallel on the stress side?
Here, even in the simplest case of the linear elastic (etc.) solids, it is difficult to believe that a conceptual parallel could be derived independently. One could, of course, argue from an abstract viewpoint that such derivation is possible "mathematically". But remember: deformation is by definition a point phenomenon, whereas force is by definition related to the momentum of an object. For field quantities, force necessarily arises only in the context of a geometric element of nonzero side--e.g. area (as in stress components), or line (as in surface tension). You always need a geometric entity like area or line element (even if it is infinitesimally small) before quantities like stress or flux can at all be defined.
Deformation, in contrast, can be defined at a point. We don't have to refer to a geometric element in order to define what this concept means.
It is this particular difference which makes it impossible to have a direct analog of deformation on the force/stress side.
Consequently, any quantity on the force/stress side must always be defined in reference to some or the other external assumptions as to how the quantity ought to vary across the relevant geometrical element. The simplest assumption of this nature is to say that stress must conceptually remain analogous to strain.
The rest then follows.
Sometimes, it is said that it is very obvious that strain must be more fundamental because in the usual stress-strain diagrams, it is strain that is taken on the x-axis, i.e. as the independent variable.
However, note that this "argument" is very superfluous. To plot stress-strain in the usual manner does not need all the above kind of thought. One need only observe that the constitutive law of metals is nonlinear and metal specimens experience necking so that there is a drop in the graph of engineering stress once the point of ultimate tensile strength is reached. In such a situation, taking strain on the x-axis avoids the possibility of having a multi-valued "function." Thus, the choice to take strains on the x-axis is more of a simpler convenience that happens to be in accord with the more fundamental reasoning discussed above.
As an aside: the difference about a quantity defined at at point by itself (e.g. displacement of a point) and a quantity that requires an infinitesimal volume, area, or line for its definition (e.g. stress, strain, electric field vector) is a fundamental one. It marks the conceptual difference between particles and fields. It therefore plays a crucial role in many other matters such as flux-conservative laws and wave-particle duality.)
Acknowledgment: It was the discussion on Henry Tan's blog about whether stresses can ever be measured directly or not that provided the spark to write this post.
If there are deeply thought out and interesting possibilities running counter to the arguments presented above, I would like to know about them.
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Ajit, though your question
Ajit, though your question is somewhat philosophical, I know what you're getting at and often think along the same lines as what you have written.
I agree that force and stress can never be directly measured. They are abstract quantities posited within theories that seek to explain motions and deformations. Even the most primitive measurement of force - Atwood's machine - requires us to accept a theory that the heavier body will fall and the lighter one will rise. All we can observe directly are the motions. Our theories don't define the heavier body as the one that falls, they state that the heavier body does fall (and exhibits many other behaviors that have nothing to do with Atwood's machine).
Personally, I have tried to define what I mean by a "fundamental quantity". I define it as a quantity that can be observed without recourse to any physical theory. For example, force is not fundamental because we have to transduce it into displacement or motion in order to observe it, and the transducer's operation can only be understood if we accept a certain theory about its operation. One can carry this to extremes and say that it is only a theory that when we perceive something to have moved, such motion is discernable to any other observer. On those grounds, even motion is not fundamental.
I also reflected on why I even care about the issue. The best answer I can give is that understanding the theoretical status of the different quantities makes us better able to apply the theory correctly. I go into more detail on my own page here.
Interesting debate:
Ajit and Grant,
Allow my student inputs here.
<< What is its parallel on the stress side?
Like Displacement -> Deformation on the strain side, we have Force -> Pressure (stress) on the stress side. And if we consider instantaneous (true) strain measure, we can eliminate the multi-valued functions even if we plot strain in Y axis (I guess, you can shed light into this). Also Force (and hence stress) we measure is with respect to some reference value and it is not exact. But strain measure is exact.
But I go with the Strain (or deformation). Because we could explain the linear behavior of materials with Stress (S-N curves), and both linear and non linear with Strain life calculations.
When we consider Force as an action that causes deformation, we are carving out a system to cover only the specific entity we wanted to analyze, and think that force is primary. But energy is needed and pre-exist before we could actually think of force.
One can store energy (in a cantilever beam) by pushing it down, as energy is transferred from us, and when we see it, we consider only that force as the action, and deformation as the result. When we release it, we have the deformation as the action, force (if any thing restraining or connected to) is the result. But according to Mathematicians, we have energy defined in terms of stress and strain, and both may be independent variables. And zero is not null.
One question I would like to ask others is that, I heard about stress singularities, but did not come across strain singularities -- which means we take strain as a fundamental measure (leaving out energy from the discussion).
Is stress singular at crack tip?
I enjoyed reading this thread of discussion, as well as an earlier thread started by Hanry Tan on whether stress is a measurable quantity. Thank you, Ajit, for writing so clearly about the issues.
Gopinath raised the question about stress singularity. I assume that he had singularity at crack tip in mind. Here are some notes:
- The singular stress field is an outcome of a mathematical model. The crack is assumed to be a mathematical plane, the crack front is assumed to be a mathematical line, and the material is assumed to be linearly elastic. Of course, none of these assumptions are correct. Thus, the stress is really non-singular at crack tip.
- What is interesting is that Irwin made this wrong solution useful for us. I have tried to summarize his idea elsewhere (G. Bao and Z. Suo, " Remarks on crack-bridging concepts," Applied Mechanics Review. 45, 355-366 (1992)).
- If we take the stress singularity at its face value, then strain is also singular. The stress is linear in strain, to be consistent with the model, however wrong it might be.
- If we relax the assumptions of the model, allowing the material to deform plastically, and allowing the crack tip to blunt, the stress becomes bounded, and the strain remians very high, possibly still singular. This was the work of McMkeeking (JMPS, 1977).
Stress vs. True Strain Plot:
Dr. Suo
Thanks for sharing your thoughts here. I accept that when I talk about stress singularity, I had crack-tip in mind, and that when I mention singularity, I knew before hand, that stress cannot go beyond its yield stress and the material at that point (where it exceeds sys) yields to make stress a reasonable value. Also by the term singular, I stick to only mathematical definition rather than its physical existence. Analogy is to see the fraction S=A/B, when B -> 0, even though B!=0. So whatever I discussed, it is subject to your quote: "The singular stress field is an outcome of a mathematical model".
If in a plot of stress vs. strain, if I see that the curve goes fairly horizontal, I stop there, and cry stress is singular, and if the plot goes fairly vertical, I cry strain is singular. And I am tempted to say, that in the plots I have seen so far, stress to be singular in all stress vs (engr) strain curves, and I have not seen much of stress vs (true) strain curves to comment. [These are added after original post (to be specific, ln(1+e) - what happens when 1+e is growing). I should not have said singular in the above statements -- My bad..sometimes when we look back at the comments we made, we laugh at ourselves.]
The last reference in your reply, work of McMkeeking (JMPS, 1977), Is that a hypothetical study to allow deformation of material only if load is applied? Because at one point, we want the material to deform without even adding any more load to it. Does his work show strain a singular property? Thats very interesting.
I am yet to read your article. I will read it sometime soon.
More on Strain Singularity
Continuing from where Prof. Suo left off, here are my thoughts specifically on the strain singularity at a crack tip, kindly correct me if I am mistaken in my conclusions:
1. From LEFM, with a stress singularity emerging at the end of the mathematical analysis, this implies that there must be a strain singularity as well, as Prof. Suo points out above.
2. For deformation plasticity, using the HRR approach, the strain is singular in elastic-plastic materials as well (but the order of the singularity is determined by the hardening exponent in the Ramberg-Osgood law)
3. McMeeking's work has looked at crack tip stresses and strains in ductile materials (with incremental plasticity) for a BLUNTING crack tip using FE analyses. The blunting of the tip nullifies the stress singularity, but the singular behavior of plastic strain is still observed.
4. Finally, on a related but slightly different note, Prof. C.T. Sun's recent papers (2005, 2006) argue that even CZMs do not eliminate crack tip singularity (for LEFM, this argument is good for stress and strain) unless the correct traction-separation laws are employed.
I am interested in these issues and would appreciate any comments.
Thanks for updating:
Thanks for sharing your thoughts on this.
I learnt a new stuff today from Dr. Suo's and your comments.
Cohesive zone and stress singularity
Dear Dhruv: The following concerns your point 4.
- Sometimes, a singularity is deliberatly left at the crack tip, even when a cohesive zone is used. The singularity models a short-range interaction, and the cohesive zone models a long-range interaction. For example, in a ceramic-matrix composite, the toughness of the matrix (atomic bonds) can be modeled by a singularity, and the bridging fibers can be modeled by a cohesive zone.
- When the traction-separation starts at zero traction at zero separation, and goes up smoothly, the cohesive zone will not eliminate the singularity. However, one can model the material as two half spaces joined on an entire plane by a set of nonlinear springs. Then, singularity will not appear.
- The above issues were discussed in Z. Suo, S. Ho and X. Gong, "
Notch ductile-to-brittle transition due to localized inelastic band," ASME J. Engng. Mater. Tech.
319-326 (1993).
RE: Cohesive zone and stress singularity
Dear Prof. Suo,
Thank you very much for your insight and direction: I will read your paper in earnest.
Dear Zhigang,
As to this discussion, I have exactly the same thinking about CZM as your said above. So, I totally agree with you. I don't konw the details of Prof. Sun's papers but suspect that statement. ( I should read them soon).
I did model the fracture of braided composites by uisng CZM with FEA. In this case, no "clear" and "clean" crack can be observed or defined (due to bridging and ... as you mentioned above. So, I think we'd better use "fracture" to replace "crack" to leave "crack" as something sharp). Therefore, we resorted to CZM.
However, how to implement CZM with FEA in an efficient manner comes as another big issue. Actually, many versions exist with different names. However, the center is the same: assume a strain potential energy function and implement it as conventional continuum elemenet. With this approach, the CZM is treated as a continuum complient layer. We (Prof. Waas from UMich and I) refer to this as the Continnum Cohesive Zone Model (CCZM).
Prof. Waas and I proposed our own version of implementation. We called it Discrete Cohesive Zone Model (DCZM). The center is the nonlinear spring as you said above. With this approach, the CZM is treated as a spring foundation. Besides its simplicity, the most amazing thing is that it is NOT sensitive to the FEA mesh size. Therefore, it should be very attractive to engineers, who do not want to be invovled too much to arrange the proper mesh size.
I have two papers on this topic. One is addressing the methodology and the other is about the application to braided composites. I appreciate it if you would like to read them and critisize.
1. Xie D and Waas AM, Discrete cohesive zone model for mixed-mode fracture using finite element analysis, Engineering Fracture Mechanics, 73(2006): 1783-1796.
2. Xie D, Salvi AG, Sun C, Waas AM, Caliskan A, Discrete cohesive zone model to study static fracture in a plate of textile braided carbon fiber composites, Journal of Composite Materials, 40(2006): 2025-2046.
In short, I consider CZM as a promising tool in fracture mechanics.
Yes, it should be stress:
Yes, it should be Force -> Stress, instead of Pressure. Thanks for correcting me.
stress vs. strain. Maxwell stress vs. electrostriction
This thread of discussion goes to the core of mechanics. Here I'd like to mention a specific phenomenon that speaks to aspects under discussion.
Consider a parallel-plate capacitor, i.e., a layer of a vacuum between two metal plates. When a votage is applied between the two metal plates, the two plates attract each other. We know about the attraction because we need to apply a force to keep the two plates apart. Without the applied force, the two plates will fly toward each other.
We also know that the two plates have electric charges of oposite signs. We know that because we can measure how much current flows through the external circuit. It all seems to make sense. A positive charge attracts a negative charge.
Now, replace the vacuum by a solid dielectric. If the dielectric is an elastomer, upon the application of the voltage, the elastomer will become thinner. In this case, no external force need to be applied to maintain equilibrium. Many people would like to say that the voltage applies a compressive stress to the elastomer. Indeed, they even give a name to the stress: they call it the Maxwell stress.
If the dielectric is some other materials, upon the application of the voltage, the dielectric may either become thinner or thicker. In the literature, you can find experimental data of how much thinner or thicker a given material will become. If a material indeed becomes thicker, would you be willing to say that the voltage applies a tensile stress to the dielectric? Slick people do not say that. They give a different name to the phenomenon. They call it electrostriction!
My coworkers and I find the practice unacceptible. In both cases, thinner or thicker, if no external force is applied, we would simply say that the stress in the dielectric is zero. After all, thinner or thicker is just an observation of strain, and says nothing about stress. For example, we would never call thermal expansion a tensile stress.
In a recent paper, entitled a nonliner field theory of deformable dielectrics, we have formulated a theory consistent with this simple point of view. We believe that we have resolved a long-standing basic issue in electromechanics. We really like the paper, and hope you will, too.
stress and strain in dielectrics
Your statement of zero stress in deformed dielectrics (thinner or thicker) made me think again. At first, I cannot accept it. Then, I thought of thermal expansion, where no stress is generated if the material is free of any constraint. To make the analogy, there must be a quantity in your theory of deformable dielectrics taking the place of temperature as a state variable for thermal expansion. I will have to read your paper again to see if such a quantity exists and then to see what material properties are in analogy to the coefficient of thermal expansion.
Another interesting situation to be considered is as follows. If the electrodes (e.g., two parallel metal plates) are separated from the dielectrics by two layers of vacuum such that no direct contact between the electrode plates and the deformable dielectrics. Upon the application of voltage, the electrodes would attract each other. To prevent contact between the electrodes and the dielectrics, an external force must be applied to the electrodes, similar to the case with no dielectrics in between. In such a situation, would the dielectrics still deform? What would the theory predict? Is there any experimental evidence? Of course, we are not talking about piezoelectric materials or any other materials with intrinsic electro-mechanical coupling (i.e, apparent microstructural change under an electrical field).
Re: stress and strain in dielectrics
- Another state variable is electric displacement.
- If an external force is applied, stress is force divided by area. This stress exists in the dielectric. In our theory, as well as in Maxwell's original theory for vacuum, the same stress also exists in the vaccum.
- The behavior of the multilayer can be calculated once a material law for the dielectric is prescribed. In a follow-up paper, we prescribed a material law. We showed that the Maxwell stress emerges from a very special material law.
Re: Re: stress and strain in dielectrics
- The electric displacement is linearly related to strain for piezoelectric materials due to intrinsic electromechanical coupling (i.e., constitutive relation in continuum mechanics). For nonpiezoelectric materials, a higher-order electromechanical coupling gives nonlinear relationship between electrical displacement and strain (e.g., electrostriction), which also can be characterized in terms of constitutive behavior of the material although the intrinsic EM coupling mechanism is less obvious to me. What are the differences between these conventional electromechanical theories and the newly developed nonlinear theory?
- With vacuum layers in between, the external force is applied directly onto the electrodes (parallel plates), and this force (mechanical) is balanced by the electrostatic force between the charged plates. Thus, stress exists in the electrodes (a different topic). I am not sure how one applies force onto a layer of vacuum and what it means by stress in vacuum. In the situation I described above, no contact between the electrodes and dielectrics thus no external force is applied directly to the dielectrics, unless the vacuum layer is capable of transferring any force from the plates to the dielectrics. It is hard for me to understand this.
- Does this material law contain any coupling coefficients between mechanical (strain or stress) and electrical (electrical displacement or electrical field intesnity) in addition to elastic modulus and dielectric permititivities? Or, the coupling is simply through a combination of pure elastic and pure dielectric properties.
stress in vacuum
1. There is always electromechanical coupling.
Primary school physics told us that ther are electrostatic forces between charged plates, whatever material in between, there will be deformation (except for rigid material, which does not exist.) The electrostatic energy turns into strain energy. So in this sense, there is always electromechanical coupling.
2. Again from highschool physics, one tends to think that the electrostatic interaction between the electrodes are far-riching (and instantaneous) , especially when there is nothing or vaccum in between. A little bit more electromagnetics tells us that such an interaction actually propagates as a wave through a medium, and it can be blocked or shielded. For EM wave or electrostatic field, the vacuum is one special type of material, just as steel for strain field. In all situition we are interested, the result of such an interaction is the same as that of the stress we are familiar with. So why don't we just call it stress? Vacuum is special only because it has 0 stiffness, but that does not prevent us from having stress, as stress is no longer stiffnes times strain. (You can think about the thermal strain of a rigid material as an analogy.)
3. The coupling is inevitable, unless for fake materials like rigidbody or so.
stress or strain? STRAIN!
The discussion reminds me of childhood: who is stronger elephant or whale?
Seriously, the stress is a superfluous concept because the theory of elasticity can be formulated without even noting it. The concept of stress, however, can be useful occasionally...
Dear Ajit, Nonlinear
Dear Ajit,
Nonlinear elasticity does not require stresses either: a nonlinear potential is constructed whose variation provides the equilibrium conditions without stresses. I believe that theories including structural evolution (plasticity, damage, etc) can also be formulated without stresses after some effort...
Free-body diagram in the presence of electric field
Dear Ajit and Rui:
Thank you so much for raising all kinds of concerns and objections. Similar thoughts occured to us when we started to work on the problem. By now I believe that we have resolved these issues to our own satisfaction. Our object has been to formulate a theory that can describe observable phenomena. Within our theory, here is how we analyze the free-body diagrams.
Case 1, a parallel-capacitor with a vacuum gap. When a voltage is applied between the two electrodes, you have to apply a pair of forces to the two electrodes to maintain equilibrium. In this case, our theory (and Maxwell's theory) says that the vacuum is in a state of stress. If you regard the top electrode as a free body, the force you applied will balance the force due to the stress in the vacuum.
Case 2, a parallel-capacitor with a solid dielectric. When a voltage is applied between the two electrodes, you do not need to apply a pair of forces to the two electrodes to maintain equilibrium. Let's say you don't apply forces. If you regard the top electrode as a free body, because you don't apply a force to the electrode, there is no stress in the dielectric. In this case, our theory says the stress in the dielectric is zero.
My class notes on deformation and polarization contain additional examples.
Dear Dr Ajit R.
Dear Dr Ajit R. Jadhav,
Thank you for the initiation of this thread of very interesting
discussions. I think you have exactly pointed out the attitude we adopted in
developing the nonlinear field theory of deformable dielectrics: working with the
measurable quantities.
For a parallel capacitor with vacuum or elastomer in between,
it's the force applied on it that we can measure instead of the stress inside.
Based on this force, we define stress as force over area.
Many other theories on electroelastics tends to
differentiate various stresses in dielectrics, e.g. Maxwell stress, mechanical
stress, and thermal stress et al. While we refrain to say these theories are
wrong; however, we can't see any physical significance in differentiating the
I think this may, to some extend, answer Dr R Huang's question "What are the differences between these conventional electromechanical theories and the newly developed nonlinear theory?"
Something you probably misinterpreted
Hi Jadhav,
In your Case 2-Y:
We (and many people as well) define strain as the deformation caused by whatever field, stress is not a must for the existence of a strain. For no phylosophical reason, simply because it is measurable. In absense of any knowledge of the material inside, strain is the easiest quantity to measure. Our naked eye (or with some modern aid) is a quite good tool. From the limited number of textbooks I have read, free contraction due to a drop in temperature is named "thermal strain", with the simple relation (for 1D)
ε = σ/E + α ΔT
Please let me know ff you have an alternative way of defining a measurable strain which excludes a thermal expansion.
BTW, we agree three is no stress inside the elastomer in this case, simply using the "ultimate test"
In your Case 2-NY:
I think you are refering to the case when the electrodes have rigid supports. Your interpretation agrees with our theory.
Let me try to rephrase your conclusion to resolve any residue concern:
Whether or not we have stress is being determined by the boundary conditions, (which includes loading and support), as this special example is statically determinant. This is a result from Newton's law, our first principal.
But how this stress relates to the strain and the electric field depends on the material behavior. Just like Hooke's Law, you can think of it as secondary if you like.
Dear Jadhav,
I totally agree with your strain definition. (Although I assumed that human eyes are capable of detecting displacement gradient.)
However, according to this definition, I think strain is merely a geometric (or kinematic) concept, not mechanical, nor thermal or chemical.
In your wooden peg example, we still think there is strain, using the same definition as you proposed: the (symmetric part of) gradient of displacement is not 0.
I don't think force is a necessity for strain to exist, nor is stress.
We do accept that there can be multiple models for a same phenomenon, so we are free to define strain in a measurable and self-consisitent way, in which we demand every nonzero gradient
of displacement (excluding rigid body rotation) implies strain. Strain is strain, we never call it mechanical strain.
On the contrary, the context of the equation I quote clearly states that it is free thermal expansion (plus a uniaxial tension). On the other hand, if someone wants to define some nonphysical (but might be useful practically though) term of "thermal stress", then he ought to presume a constraint.
We really dont need a quantity like strain
Dear Jadhav,
You are right, we really don't need a quantity like strain. In fact, through out our paper, we really did not use it.
We did not define strain either. The geometric quantity we used is deformation gradient, or gradient of coordinates.
I learned from textbooks (which you might not agree with) that the symmetricalized deforamtion gradient is a measure of strain.
There is nothing initiative we have done in terms of the definition of strain.
There are infinite ways of defining strain. Personally, I think as long as it is self-consistent, the definition is fine.
Our definition and derivation are self-consistent, and I don't see any clearly committed logical mistake.
We are just trying to define thing in a simple enough way so that at least we ouselves could understand.
Before saying concept-stealing, could you please give us a definition of strain which you think is the standard?
Why thermal expansion is not a strain?
Dear Jadhav,
From the definition you described here, which is exactly what we have used and I have been stating, I can not see any reason why the free thermal expansion of a block is not a strain.
BTW, previously when saying self-consistency would be enough, I meant your definition of strain. 'Cause I was curious to know if there is any alternative but self-consistent definition of strain that excludes thermal expansion.
Strain or no strain, that is the question.
Dear Ajit and Wei:
I'm a little lost in the conversation between you. Not sure if you are still talking about our JMPS paper on deformable dielectrics. If you are, or at least talking about things related to the paper, maybe the following notes are helpful.
- In Section 2, we formulated a theory without talking about strain. This theory is not a field theory, but a more premitive theory, applicable for situations where a field theory is not really helpful. For example, if the body is just a molecule or a cell, perhaps the body is too heterogeneous for a continuum theory to be of much value. Even for such a system, however, we can still talk about force, and about elongation. Section 2 is merely a restatement of thermodynamics of an electromechanical system, reminding us what may be measured, and what are work conjugates.
- In Sections 4 and 5, we formulated a field theory. Strain is invoked, between Equations (5.4) and (5.5).
Re: Zhigang
Dear Zhigang,
We are not talking about the paper.
Ajit disagrees that a free thermal expansion (or similar deformation caused by electric field in our paper) can be called "strain".
I am trying to talk him out of this.
This might help
Hi Ajit,
The following simple example might help to clarify:
A rod (of unknown material) of initial length 1m is under tension. We can measure the force and thus calculate the stress, no problem.
But at the same time, the temperature increases by 20°C. As a consequence of both the force and the temperature change, the rod extends by 5%.
For simplicity, there is no constraint involved.
What is the strain?
If you agree that the strain is 5%. Then let us repeat the same experiment, but reduce the force to 0 (or almost 0), now the rod extends by 2%.
This 2% is what we usually called thermal expansion or thermal strain, you don't agree that it should be called "strain"? What is the difference between the 5% and 2%?
If you disagree that even the 5% can be called strain, then what is the strain in this case?
(Remember that the material is unkown and might be nonlinear, so please don't try to define strain with youngs modulous.)
Hope this helps.
Is thermal strain a "true" strain?
I'll jump in here without having read the entire exchange - so please pardon any repetation of previously discussed issues on my part.
You wrote
" A rod ... is under tension. We
can measure the force ... , no problem. ..... there is no constraint involved."
There are some issues here :
1) If there are no constraints and the forces are balanced, there is no way you can tell whether a tensile force has been applied. So you cannot measure that force and there is a problem :)
2) If the forces are unbalanced then, of course, the rod will move/deform in the direction of the larger force.
The only way you can tell whether the rod is in a state of tension is to measure the deformation with respect to a reference placement. The same is true for a temperature change you need a reference temperature and a reference placement.
Strain is defined independently of what causes it but needs knowledge of at least two placements.
Yes, you are right
Yes, you are right. We need some proper constraint to remove rigid body motion.
You got exactly the point I want to make, strain is defined independently of what causes it, but needs only displacement.
Thank you!
Stress in a vacuum between parallel plates
There was some discussion in this thread about the concept of stress in a vacuum between two parallel plates. I believe Zhigang's theory is a continuum theory which implies that stress is considered a point quantity.
In that case, an analogy may be made with the mechanical theory of a material with voids - think foams, poroelasticity, etc. We use an effective theory for such situations assuming that the scales are sufficiently separated that the continuum assumption can be made. However, even for such materials the stresses and displacements inside the voids are not well defined quantities at the microscale even though they are well defined at the effective scale.
Stress in vacuum is a theory due to Maxwell
- When an electric field is present in an vacuum, a stress field may be assigned to the vacuum. This stress field is known as the Maxwell stress, which was derived in his Treatise on Electricity and Magnetism. The Maxwell stress has been used to calculate forces and torgues on conductors in the vacuum.
- We now believe that the Maxwell stress has NO theretical significance in solid dielectrics. Rather, the effect of electric field on stress in the dielectrics is derivable from a free-energy function, as a part of material law.
- For very special materials, such as a vacuum (if you consider it as a material), our theory recovers the Maxwell stress.
Why is Zhigang's theory an effective theory?
I feel that your theory is an effective theory because of you develop it with a two-component example, i.e., two plates and a vacuum/dielectric in between. Could you explain (just briefly) how you would develop the theory with just a dielectric (i.e., one component) in an electromagnetic field?
JMPS and APL papers on deformable dielectrics
Dear Biswajit:
I'm not sure what you are asking. I'm sending you pdf files of two papers by email.
- Zhigang Suo, Xuanhe Zhao and William H. Greene, A nonlinear field theory of deformable dielectrics. Journal of the Mechanics and Physics of Solids. http://dx.doi.org/10.1016/j.jmps.2007.05.021
- Xuanhe Zhao, Z. Suo, A method to analyze electromechanical stability of dielectric elastomers. Applied Physics Letters 91, 061921 (2007).
The JMPS paper gives a full 3D formulation. The APL gives an example of application, and perhaps is easier to read.
Stress observability and the relaxation modulus
I have skimmed the posts in this thread with great interest although I have not contributed in a month or so. Last night I was reading Lakes's textbook on viscoelastic solids, and then I started to fall asleep (no fault of the book, I was tired.) While in a semiconscious stupor I realized the following two things:
1. It is possible to relate stress directly to objectively observable quantities other than strain. There used to be a brand of special paper on the market that would change color when you squeezed it. I don't know how it worked (tiny crushable capsules of dye?) and I've never seen it in the US (I saw it in Japan). They used it to map the contact stress in bolted joints. Probably there is a kind of material that would change color with no motion required - a chemical reaction that requires stress to activate it. So...while it still may not be possible to directly observe stress, it can be observed through means other than strain. One can envision a constitutive equation for the paper directly relating stress to color.
2. Without this "stress paper" or a similar material, the relaxation modulus in viscoelasticty is unobservable, or at least has an uncertainty principle attached to it. The relaxation modulus is defined as the time history of stress when a step strain is applied to a body and held. But how is the stress measured? Only by measuring the deflection of another body, like a load cell, that the viscoelastic body is pulling on. But such a deflection cannot occur without violating the definition of relaxation modulus as the stress when strain is held constant. In practice, the load cell is very stiff compared to the viscoelastic material, so the strain is small compared to the initial step strain. In such a case the error introduced ought to be negligible, but it can never go away completely unless stress is measured in a way that requires no deflection to be observed.
Stress and strain are duals
I read through the posts with great interests and could not help but to register a user name for comments.</p> <p>In my opinion, the virtual work principle is probably one of the most fundamental rules in the framework of mechanics. Stress and strain are duals in the sense of energy or work. Definitions are arbitrary and the only rule one need to obey is the correctness of energy calculation for each pair of stress and strain definition. The ABAQUS theory manual has a section describing different definitions of strain and stress.
In the sense of energy calculation, the stress definition can be deduced from the strain definition, and vice versa. There is no certainty which one should come first. When deformation method is used, it is convenient to define strains or general strains --- this is the approach adopted in many FEM analyses. Nevertheless, when force method is used, for example in finite element limit analysis following equilibrium approach, only stresses are defined explicitly. The dual of each equilibrium constraint (see www.gams.com for more details) may have physical means and can be used to plot deformation field.
If one would like consider more fundamental than the abstract level of mechanics, then I would think strain in general means indicates the state of an object when compared to its reference state. Meanwhile, stress in general means indicates the interaction between two objects. The change of states is resulted from stress or force – does this means force (or stress) is more fundamental? – I do not know.
When material's property is concerned, the constitutive relationship describes how the strain is to be altered as a response to the stress.
As to the measurement, stress is usually measured based on the assumption of repeated (note: not necessarily linear) correlations between stress and strain, both in general means, and mechanical-electronic transformations. It is helpful to consider what "calibration" of a modern measurement instrument really means. I find it difficult to tell which component is more fundamental from the way of measurement. For example, when strain gauge is concerned, can we say resistance is more fundamental than strain?
Force itself can be an ambiguous notion
Thank you very much for putting things in perspective. What you said is good if you have no doubt what a force is. In a previous entry to this thread, I was pointing to an important case where force itself is an ambiguous notion.
work conjugacy
just a note related to the comment
In my opinion, the virtual work principle is probably one of the most fundamental rules in the framework of mechanics. Stress and strain are duals in the sense of energy or work. Definitions are arbitrary and the only rule one need to obey is the correctness of energy calculation for each pair of stress and strain definition. The ABAQUS theory manual has a section describing different definitions of strain and stress.
(and perhaps a bit of an aside for this thread)
Hill's "Invariance in Solid Mechanics" article in Advances in Applied Mechanics (I believe it was 1978) is the definitive source on this sometimes subtle topic. In my opinion, much for the student of continuum mechanics to learn from.
Different forces in different theories
I agree there is no rational basis for saying that energy is any
more fundamental than force. I will continue to believe this until
someone shows me a problem that can be solved by energy methods but
cannot be solved (even in principle) by force methods.
However, I don't agree that stress and strain are abstracted from the same empirical
observations. I do not know of any method for directly measuring a
force or a stress. But I can easily observe motions with reference to a
stationary scale, from which you can calculate your favorite
deformation or strain tensor.
Ajit, continuing with your bat and ball example, we can calculate the force on the ball by any number of different theories of increasing complexity (analytical dynamics, linear elasticity, nonlinear elastodynamics, etc.) and we will get a different answer for each theory. In some sense, the answers are not even commensurable, because point forces do not exist in continuum theories; they have to be accepted as stress resultants. So I can't agree with you that the the static and dynamic situations are equivalent. The forces that appear in static theories (i.e. theories with no concept of inertia) are fundamentally different from the forces that appear in dynamic theories. Because of this, I claim that forces are theoretical constructs with no basis in mere observation. Or maybe it's the converse, and I believe that since forces are theoretical constructs, forces defined in two different theories cannot be equivalent. In any case, it is fun to think about, for a while anyway
Incidentally, I had speculated in comment 5151 that there is a
material that will change color but not shape under stress. Ajit
claims that a color change has never been observed without a
geometric change. I still think such a material is plausible, but
even if one exists, it would not change the substance of our
discussion. We would simply be replacing strain by color.
Reply to Ajit - force, motion, energy, momentum
I am enjoying this discussion immensely. When I bring these points
up to my casual acquaintances, they slowly migrate to the other side
of the room.
Manually hit the ball with a striker, and the ball moves. It is
obvious that a force has been operative here. But how do we know
this? Answer: by measuring the motion of the ball and concluding
that it has suffered acceleration (for a very short period of time).
In order to conclude this, don't you have to accept the theory that
motions are caused by forces and not, for instance, the thoughts of
God? All I am saying is that I can measure displacements directly,
with no need to accept any kind of mechanical theory. And on that
basis I claim that motion is more fundamental than force.
This is a plain dynamical situation. (2) Let a horizontal spring
remain touching against the ball. Holding both the base of the
spring and the ball, compress the spring. Is there a force operative
here? Strictly speaking, within the purview of mechanics theory
alone, as yet, we do not know! Not by our dynamical definition of
force anyway. Now, suddenly release the hand holding the ball. The
ball flies, exactly as in (1). Now, reconsider the question: has
there been a force operative here? Yes. Why? Because the ball has
experienced acceleration (for a very short period of time).
Since the motion of the ball is identical in the two cases, there is
a certain equivalence to the two situations. (I take equivalence to
mean: equal valence or "powers," i.e., the ability to produce equal
consequences in an appropriate context.)
I agree that a force acted in both situations. However, as you have
posed the problem, we need two different theories to calculate the
force: analytical dynamics to calculate the force from the motion of
the ball, and elasticity to calculate the force that can be exerted
by the spring.
If I could calculate the force by each theory and get the same answer, I could agree that force seems to have some underlying significance independent of any particular theory. But I do not believe you would get the exact same answer, even if you had exact measurements. For example, if you calculated the force from the spring, you would really get a time-varying quantity. You could then only say that the impulse was the same, and I'm not even sure about that.
Another way to pose the thought experiment is within a single theory
that can handle both situations- for instance, elastodynamics. In
that case, we truly have the same force, but we have a priori
decided that we are observing two special cases of a general theory,
so there is no way to use these observations to tie two notions of
force together - there is only one notion of force, that found in
I will concede that the same kind of hairsplitting logic could also be applied to the motion - we have to assume the scale didn't grow or move, etc. But I can accept that more easily than I can accept the theory relating force to motion.
You say that you can measure motions but not stresses. My question
is: But how about experimentally measuring the motions of interior
points? You will have to take a cut, either physically or in
thought. If so, then just do the identical for stresses also. The
only difference would be that in the case of strains, you will
measure displacements of the parts while they were still held
adjacent to each other in the forced configuration; in the case of
stresses, you will measure accelerations of the cut away parts after
they have been released and allowed to fly (as per the stresses
operative across the cut).
But I still need a theory that relates accelerations to stresses. I
don't need a theory to measure the deformations.
The question which I then raise is this: Can you think of any
physical situation / process / transaction / interaction etc.
wherein energy gets transferred but not momentum?
I need a theory in order to be able to talk about energy and
momentum. So I'll choose the theory of classical thermodynamics. I
can transfer energy to steam by heating it up, without imparting any
momentum. (Classical thermodynamics doesn't posit any relationship
between energy and the momentum of the steam particles.)
You may argue that classical thermodynamics is a limited theory, but
so is every other known theory. A stronger objection is that
classical thermo is not only limited but has been superseded by a
better theory, statistical thermodynamics, in which internal energy
is related to the momentum of the constituent particles. In that case, I would have to think harder.
strain is the basic mesurable physical quantity
This is an interesting topic. Without reading the long contributions by so many experts here, let me just point out that in Physics 101, there are (only) three basic physical quantities, length, time and mass. Strain is the change of length and therefore a basic physical quantity that can be measured. Stress is derived from strain through a formula. As such, for a given strain (which is the deformation of a body) one can get any stress value depending on what formula is used, e.g. linear elastic, visco-elastic, plastic. NIST has the standard to measure length, not stress !!! In the class of Experimental Stress Analysis, one in fact does "experimentally determines the strain".
Bill Y.J. Chao
Re: strain is the basic mesurable physical quantity
I'm not sure I agree that there are only those three physical quantities. In particular, temperature, electric current, and luminous intensity come to mind. It is certainly the case that stress can be represented by length, time and mass (ie: mass / length / time^2), but I am not sure I believe those are all that is needed in all of physics or even all of mechanics.
That being said, I believe your genral point is correct—straiin is the fundamental quantity. At least that is the one we observe. No one has ever observed a force. We hypothesise forces to explain the motions we observe.
What a profound debate
struggle between theory and application
stress-strain curve for cube concrete specimen with ansys
I have modelled one cube concrete specimen in ansys . I want to plot stress-strain curve (static analysis , nonlinear solution ) .
can you help me(why stress-strain curve is linear)
can u give me link to henry tans blog regarding this topic
Nithesh P
concept of yield point
The concept of yield point is very loosely defined so far..this manuscript brings a fresh look to this old debatable question.


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The U.S. birth rate dipped in 2011 to the lowest ever recorded, led by a plunge in births to immigrant women since the onset of the Great Recession.
The overall U.S. birth rate, which is the annual number of births per 1,000 women in the prime childbearing ages of 15 to 44, declined 8% from 2007 to 2010. The birth rate for U.S.-born women decreased 6% during these years, but the birth rate for foreign-born women plunged 14%—more than it had declined over the entire 1990-2007 period.1 The birth rate for Mexican immigrant women fell even more, by 23%.
Final 2011 data are not available, but according to preliminary data from the National Center for Health Statistics, the overall birth rate in 2011 was 63.2 per 1,000 women of childbearing age. That rate is the lowest since at least 1920, the earliest year for which there are reliable numbers.2 The overall U.S. birth rate peaked most recently in the Baby Boom years, reaching 122.7 in 1957, nearly double today's rate. The birth rate sagged through the mid-1970s but stabilized at 65-70 births per 1,000 women for most years after that before falling again after 2007, the beginning of the Great Recession.
In addition to the birth rate decline, the number of U.S. births, which had been rising since 2002, fell abruptly after 2007—a decrease also led by immigrant women. From 2007 to 2010, the overall number of births declined 7%, pulled down by a 13% drop in births to immigrants and a relatively modest 5% decline in births to U.S.-born women.
Despite the recent decline, foreign-born mothers continue to give birth to a disproportionate share of the nation's newborns, as they have for at least the past two decades. The 23% share of all births to foreign-born mothers in 2010 was higher than the 13% immigrant share of the U.S. population, and higher than the 17% share of women ages 15-44 who are immigrants. The 2010 birth rate for foreign-born women (87.8) was nearly 50% higher than the rate for U.S.-born women (58.9).
Total U.S. births in 2010 were 4.0 million—roughly 3.1 million to U.S.-born women and 930,000 to immigrant women. In 2011, according to preliminary data, there were 3.95 million total births.
The recent downturn in births to immigrant women reversed a trend in which foreign-born mothers accounted for a rising share of U.S. births. In 2007, births to foreign-born mothers accounted for 25% of U.S. births, compared with 16% in 1990. That share decreased to 23% in 2010.
The fall in the number of births to immigrant women is explained by behavior (falling birth rates), rather than population composition (change in the number of women of childbearing age), according to a Pew Research analysis. Despite a recent drop in unauthorized immigration from Mexico, the largest source country for U.S. immigrants, the Pew Research analysis found no decline in the number of foreign-born women of childbearing age.3
This report does not address the reasons that women had fewer births after 2007, but a previous Pew Research analysis4 concluded that the recent fertility decline is closely linked to economic distress. States with the largest economic declines from 2007 to 2008, as shown by six major indicators, were most likely to experience relatively large fertility declines from 2008 to 2009, the analysis found.
Both foreign- and U.S.-born Hispanic women had larger birth rate declines from 2007 to 2010 than did other groups. Hispanics also had larger percentage declines in household wealth than white, black or Asian households from 2005 to 2009.5 Poverty and unemployment also grew more sharply for Latinos than for non-Latinos after the Great Recession began, and most Hispanics say that the economic downturn was harder on them than on other groups.6
Looking back a century, data about very young children provide evidence about earlier trends.7 The share of U.S.-born children younger than age 2 with foreign-born mothers was about as high during the wave of immigration in the early 1900s (21%) as it is now. By 1960, after four decades of restrictions on immigration, that share had plummeted to a low of only 4%. It inched up to 6% by 1970 before rising rapidly as immigration levels increased due mainly to federal legislation passed in 1965.
Population projections from the Pew Research Center indicate that immigrants will continue to play a large role in U.S. population growth. The projections indicate that immigrants arriving since 2005 and their descendants will account for fully 82% of U.S. population growth by 2050.8 Even if the lower immigration influx of recent years continues, new immigrants and their descendants are still projected to account for most of the nation's population increase by mid-century.
Among this report's other major findings:
- A majority of births to U.S.-born women (66%) in 2010 were to white mothers (although that share was smaller than in 1990, when it was 72%), while the majority of births to foreign-born women (56%) were to Hispanic mothers.
- Teen mothers account for a higher share of births to U.S.-born women (11% in 2010) than to foreign-born women (5%), in part because of the age profile of immigrants.
- Mothers ages 35 and older account for a higher share of births to immigrants (21% in 2010) than to the U.S. born (13%). In fact, immigrants accounted for fully 33% of births to women ages 35 and older in 2010.
About This Report
This report uses data for 1990 to 2010 from the National Center for Health Statistics and the Census Bureau to analyze and compare fertility patterns of foreign-born and U.S.-born women. The report consists of an overview and section on overall trends; births by the race, ethnicity and national origin of mothers; births by age of mothers; and births by marital status of mothers. Appendix A provides details on methodology and data analysis. Appendix B includes additional tables.
This report was written by Gretchen Livingston, senior demographer, and D'Vera Cohn, senior writer, of the Pew Research Center's Social & Demographic Trends project. Editorial guidance was provided by Paul Taylor, executive vice president of the Pew Research Center and director of its Social & Demographic Trends project. Guidance also was provided by Jeffrey Passel, senior demographer, and Kim Parker, senior researcher, both of the Pew Research Center. Charts were prepared by Eileen Patten and Seth Motel, research assistants. Number-checking was done by Motel and Patten. The report was copy-edited by Marcia Kramer.
All references to whites, blacks and Asians are to the non-Hispanic components of those populations. Asians also include Pacific Islanders.
"U.S. born" and "native born" refer to people born in the 50 states or District of Columbia. "Foreign born" and "immigrant" are used interchangeably. In keeping with the practice of the National Center for Health Statistics, women born in Puerto Rico or other U.S. territories are included with the foreign born. See Methodology for more details.
Unless otherwise specified, "teens" refers to those ages 10 to 19.
In references to marital status, "married" includes those who are separated.


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All investments involve some sort of risk, whether it's market risk, interest risk, inflation risk liquidity risk, tax risk. An individualized asset allocation strategy seeks to mitigate the risks of any one asset class though diversification and balance.
Individual Strategy
When done properly, an investor's allocation of assets will reflect his desired goals, priorities, investment preferences and his tolerance for risk. Asset allocation is an individualized strategy, so there really is no perfect mix of assets. Each individual's strategy is built on the careful consideration of the key elements of their financial profile:
Investment Objectives: What it is the investor hopes to achieve using his investment dollars – improve current lifestyle; achieve capital growth; fund a specific goal, such as a college education
Risk Tolerance: This reflects the investor's comfort level with market fluctuations that can result in losses. Inflation risk and interest risk need to be considered as well.
Investment Preferences: An investor may prefer one asset class over another based on a certain bias or interest towards the characteristics of that class.
Time Horizon: The length of time an investor is willing to commit to achieving his objectives.
Taxation: Investing in a mix of asset classes will have varying tax consequences.
An Evolving Strategy
A sound asset allocation strategy includes periodic reviews.
About the only certainty when it comes to the financial markets is that they will change, and so will your financial situation. Through market gains and losses, a portfolio can become unbalanced and it may be important to make adjustments to your allocation. As people move through life's stages their needs, preferences, priorities and risk tolerance change and so too must their asset allocation strategy.
Asset allocation, which is driven by complex mathematical models, should not be confused with the much simpler concept of diversification.
Learn more about asset allocation by contacting us today.


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George H. W. Bush's State of the Union Address, Envisioning One Thousand Points of Light
Given on Tuesday, January 29, 1991
Mr. President, Mr. Speaker, members of the United States Congress. I come to this house of the people to speak to you and all Americans, certain we stand at a defining hour.
Halfway around the world, we are engaged in a great struggle in the skies and on the seas and sands. We know why we're there. We are Americans—part of something larger than ourselves.
For two centuries we've done the hard work of freedom. And tonight we lead the world in facing down a threat to decency and humanity.
What is at stake is more than one small country, it is a big idea—a new world order, where diverse nations are drawn together in common cause to achieve the universal aspirations of mankind: peace and security, freedom, and the rule of law. Such is a world worthy of our struggle, and worthy of our children's future.
The community of nations has resolutely gathered to condemn and repel lawless aggression. Saddam Hussein's unprovoked invasion—his ruthless, systematic rape of a peaceful neighbor—violated everything the community of nations holds dear. The world has said this aggression would not stand, and it will not stand.
Together, we have resisted the trap of appeasement, cynicism and isolation that gives temptation to tyrants. The world has answered Saddam's invasion with 12 United Nations resolutions, starting with a demand for Iraq's immediate and unconditional withdrawal, and backed up by forces from 28 countries of six continents. With few exceptions, the world now stands as one.
The end of the cold war has been a victory for all humanity. A year and a half ago, in Germany, I said our goal was a Europe whole and free. Tonight, Germany is united. Europe has become whole and free, and America's leadership was instrumental in making it possible.
The principle that has guided us is simple: our objective is to help the Baltic peoples achieve their aspirations, not to punish the Soviet Union. In our recent discussions with the Soviet leadership we have been given representations, which, if fulfilled, would result in the withdrawal of some Soviet forces, a reopening of dialogue with the republics, and a move away from violence.
We will watch carefully as the situation develops. And we will maintain our contact with the Soviet leadership to encourage continued commitment to democratization and reform.
If it is possible, I want to continue to build a lasting basis for U.S.-Soviet cooperation, for a more peaceful future for all mankind.
The triumph of democratic ideas in Eastern Europe and Latin America, and the continuing struggle for freedom elsewhere around the world all confirm the wisdom of our nation's founders.
Tonight, we work to achieve another victory, a victory over tyranny and savage aggression.
We in this Union enter the last decade of the 20th Century thankful for all our blessings, steadfast in our purpose, aware of our difficulties and responsive to our duties at home and around the world.
For two centuries, America has served the world as an inspiring example of freedom and democracy. For generations, America has led the struggle to preserve and extend the blessings of liberty. And today, in a rapidly changing world, American leadership is indispensable. Americans know that leadership brings burdens, and requires sacrifice.
But we also know why the hopes of humanity turn to us. We are Americans; we have a unique responsibility to do the hard work of freedom. And when we do, freedom works.
The conviction and courage we see in the Persian Gulf today is simply the American character in action. The indomitable spirit that is contributing to this victory for world peace and justice is the same spirit that gives us the power and the potential to meet our challenges at home.
We are resolute and resourceful. If we can selflessly confront evil for the sake of good in a land so far away, then surely we can make this land all it should be.
If anyone tells you America's best days are behind her, they're looking the wrong way.
Tonight, I come before this house, and the American people, with an appeal for renewal. This is not merely a call for new government initiatives, it is a call for new initiative in government, in our communities, and from every American—to prepare for the next American century.
America has always led by example. So who among us will set this example? Which of our citizens will lead us in this next American century? Everyone who steps forward today, to get one addict off drugs; to convince one troubled teen-ager not to give up on life; to comfort one AIDS patient; to help one hungry child.
We have within our reach the promise of renewed America. We can find meaning and reward by serving some purpose higher than ourselves—a shining purpose, the illumination of a thousand points of light. It is expressed by all who know the irresistible force of a child's hand, of a friend who stands by you and stays there—a volunteer's generous gesture, an idea that is simply right.
The problems before us may be different, but the key to solving them remains the same: it is the individual—the individual who steps forward. And the state of our Union is the union of each of us, one to the other: the sum of our friendships, marriages, families and communities.
We all have something to give. So if you know how to read, find someone who can't. If you've got a hammer, find a nail. If you're not hungry, not lonely, not in trouble—seek out someone who is.
Join the community of conscience. Do the hard work of freedom. That will define the state of our Union.
Since the birth of our nation, "we the people" has been the source of our strength. What government can do alone is limited, but the potential of the American people knows no limits.
We are a nation of rock-solid realism and clear-eyed idealism. We are Americans. We are the nation that believes in the future. We are the nation that can shape the future.
And we've begun to do just that, by strengthening the power and choice of individuals and families.
Together, these last two years, we've put dollars for child care directly in the hands of parents instead of bureaucracies, unshackled the potential of Americans with diabilities, applied the creativity of the marketplace in the service of the environment, for clean air, and made homeownership possible for more Americans.
The strength of a democracy is not in bureaucracy, it is in the people and their communities. In everything we do, let us unleash the potential of our most precious resource—our citizens. We must return to families, communities, counties, cities, states and institutions of every kind, the power to chart their own destiny, and the freedom and opportunity provided by strong economic growth. That's what America is all about.
I know, tonight, in some regions of our country, people are in genuine economic distress. I hear them.
Earlier this month Kathy Blackwell of Massachusetts wrote me about what can happen when the economy slows down, saying, "My heart is aching, and I think that you should know—your people out here are hurting badly."
I understand. And I'm not unrealistic about the future. But there are reasons to be optimistic about our economy.
First, we don't have to fight double-digit inflation. Second, most industries won't have to make big cuts in production because they don't have big inventories piled up. And third, our exports are running solid and strong. In fact, American businesses are exporting at a record rate.
So let's put these times in perspective. Together, since 1981, we've created almost 20 million jobs, cut inflation in half and cut interest rates in half.
Yes, the largest peacetime economic expansion in history has been temporarily interrupted. But our economy is still over twice as large as our closest competitor.
We will get this recession behind us and return to growth soon. We will get on our way to a new record of expansion, and achieve the competitive strength that will carry us into the next American century.
We should focus our efforts today on encouraging economic growth, investing in the future and giving power and opportunity to the individual.
We must begin with control of federal spending. That's why I'm submitting a budget that holds the growth in spending to less than the rate of inflation. And that's why, amid all the sound and fury of last year's budget debate, we put into law new, enforceable spending caps so that future spending debates will mean a battle of ideas, not a bidding war.
Though controversial, the budget agreement finally put the federal government on a pay-as-you-go basis, and cut the growth of debt by nearly $500 billion. And that frees funds for saving and job-creating investment.
Now, let's do more. My budget again includes tax-free family savings accounts; penalty-free withdrawals from I. R. A.'s for first-time homebuyers; and, to increase jobs and growth, a reduced tax for long-term capital gains.
I know their are differences among us about the impact and the effects of a capital gains incentive. So tonight I am asking the congressional leaders and the Federal Reserve to cooperate with us in a study, led by Chairman Alan Greenspan, to sort out our technical differences so that we can avoid a return to unproductive partisan bickering.
But just as our efforts will bring economic growth now and in the future, they must also be matched by long-term investments for the next American century.
That requires a forward-looking plan of action, and that's exactly what we will be sending to the Congress. We have prepared a detailed series of proposals, that include:
- A budget that promotes investment in America's future—in children, education, infrastructure, space and high technology.
- Legislation to achieve excellence in education, building on the partnership forged with the 50 governors at the education summit, enabling parents to choose their children's schools and helping to make America No. 1 in math and science.
- A blueprint for a new national highway system, a critical investment in our transportation infrastructure.
- A research and development agenda that includes record levels of federal investment and a permanent tax credit to strengthen private R and D and create jobs.
- A comprehensive national energy strategy that calls for energy conservation and efficiency, increased development and greater use of alternative fuels.
- A banking reform plan to bring America's financial system into the 21st century, so that our banks remain safe and secure and can continue to make job-creating loans for our factories, businesses, and homebuyers. I do think there has been too much pessimism. Sound banks should be making more sound loans, now. And interest rates should be lower, now.
In addition to these proposals, we must recognize that our economic strength depends upon being competitive in world markets. We must continue to expand America's exports. A successful Uruguay round of world trade negotiations will create more real jobs, and more real growth, for all nations. You and I know that if the playing field is level, America's workers and farmers can outwork and outproduce anyone, anytime, anywhere.
And with the Mexican free trade agreement and our Enterprise for the Americas Initiative we can help our partners strengthen their economies and move toward a free trade zone throughout this entire hemisphere.
The budget also includes a plan of action right here at home to put more power and opportunity in the hands of the individual. That means new incentives to create jobs in our inner cities by encouraging investment through enterprise zones. It also means tenant control and ownership of public housing. Freedom and the power to choose should not be the privilege of wealth. They are the birthright of every American.
Civil rights are also crucial to protecting equal opportunity. Every one of us has a responsibility to speak out against racism, bigotry, and hate. We will continue our vigorous enforcement of existing statutes, and I will once again press the Congress to strengthen the laws against employment discrimination without resorting to the use of unfair preferences.
We're determined to protect another fundamental civil right: freedom from crime and the fear that stalks our cities. The Attorney General will soon convene a crime summit of the nation's law-enforcement officials. And to help us support them we need a tough crime control legislation, and we need it now.
As we fight crime, we will fully implement our national strategy for combatting drug abuse. Recent data show we are making progress, but much remains to be done. We will not rest until the day of the dealer is over, forever.
Good health care is every American's right and every American's responsibility. So we are proposing an aggression program of new prevention initiatives—for infants, for children, for adults, and for the elderly—to promote a healthier America and to help keep costs from spiraling.
It's time to give people more choice in government by reviving the ideal of the citizen politician who comes not to stay, but to serve. One of the reasons there is so much support for term limitations is that the American people are increasingly concerned about big-money influence in politics. We must look beyond the next election, to the next generation. The time has come to put the national interest ahead of the special interest—and totally eliminate political action committees.
That would truly put more competition in elections and more power in the hands of individuals. And where power cannot be put directly into the hands of the individual, it should be moved closer to the people—away from Washington.
The federal government too often treats government programs as if they are of Washington, by Washington, and for Washington. Once established, federal programs seem to become immortal.
It's time for a more dynamic program life cycle. Some programs should increase. Some should decrease. Some should be terminated. And some should be consolidated and turned over to the states.
My budget includes a list of programs for potential turnover totaling more than $20 billion. Working with Congress and the governors, I propose we select at least $15 billion in such programs and turn them over to the states in a single consolidated grant, fully funded, for flexible management by the states.
The value of this turnover approach is straightforward. It allows the federal government to reduce overhead. It allows states to manage more flexibly and more efficiently. It moves power and decision-making closer to the people. And it reinforces a theme of this administration: appreciation and encouragement of the innovative power of "states as laboratories."
This nation was founded by leaders who understood that power belongs in the hands of the people. They planned for the future. And so must we—here and around the world.
As Americans, we know there are times when we must step forward and accept our responsibility to lead the world away from the dark chaos of dictators, toward the bright promise of a better day.
Almost 50 years ago, we began a long struggle against aggressive totalitarianism. Now we face another defining hour for America and the world.
There is no one more devoted, more committed to the hard work of freedom, than every soldier and sailor, every marine, airman and coastguardsman—every man and every woman now serving in the Persian Gulf.
Each of them has volunteered to provide for this nation's defense. And now they bravely struggle to earn for America and for the world and for future generations, a just and lasting peace.
Our commitment to them must be equal of their commitment to our country. They are truly America's finest.
The war in the Gulf is not a war we wanted. We worked hard to avoid war. For more than five months we, along with the Arab League, the European Community and the United Nations, tried every diplomatic avenue. UN secretary general Perez de Cuellar; presidents Gorbachev, Mitterand, Ozal, Mubarak, and Bendjedid; kings Fahd and Hassan; prime minsters Major and Andreotti—just to name a few—all worked for a solution. But time and again Saddam Hussein flatly rejected the path of diplomacy and peace.
The world well knows how this conflict began, and when: it began on August 2nd, when Saddam invaded and sacked a small, defenseless neighbor. And I am certain of how it will end. So that peace can prevail, we will prevail.
Tonight I'm pleased to report that we are on course. Iraq's capacity to sustain war is being destroyed. Our investment, our training, our planning—all are paying off. Time will not be Saddam's salvation.
Our purpose in the Persian Gulf remains constant: to drive Iraq out from Kuwait, to restore Kuwait's legitimate government, and to insure the stability and security of this critical region.
Let me make clear what I mean by the region's stability and security. We do not seek the destruction of Iraq, its culture or its people. Rather, we seek an Iraq that uses its great resources not to destroy, not to serve the ambitions of a tyrant, but to build a better life for itself and its neighbors. We seek a Persian Gulf where conflict is no longer the rule, where the strong are neither tempted nor able to intimidate the weak.
Most Americans know instinctively why we are in the Gulf. They know we had to stop Saddam now, not later. They know this brutal dictator will do anything, will use any weapon, will commit any outrage, no matter how many innocents must suffer.
They know we must make sure that control of the world's oil resources does not fall into his hands only to finance further aggression. They know that we need to build a new, enduring peace—based not on arms races and confrontation, but on shared principles and the rule of law.
And we all realize that our responsibility to be the catalyst for peace in the region does not end with the successful conclusion of this war.
Democracy brings the undeniable value of thoughtful dissent, and we have heard some dissenting voices here at home, some reckless, most responsible. But the fact that all the voices have the right to speak out is one of the reasons we've been united in principle and purpose for 200 years.
Our progress in this great struggle is the result of years of vigilance and a steadfast commitment to a strong defense. Now, with remarkable technological advances like the Patriot missile, we can defend the ballistic missile attacks aimed at innocent civilians.
Looking forward, I have directed that the S.D.I. program be refocused on providing protection from limited ballistic missile strikes, whatever their source. Let us pursue an S.D.I. program that can deal with any future threat to the United States, to our forces overseas and to our friends and allies.
The quality of American technology, thanks to the American worker, has enabled us to successfully deal with difficult military conditions, and help minimize the loss of life. We have given our men and women the very best. And they deserve it.
We all have a special place in our hearts for the families of men and women serving in the Gulf. They are represented here tonight, by Mrs. Norman Schwarzkopf. We are all very grateful to General Schwarzkopf and to all those serving with him. And I might also recognize one who came with Mrs. Schwarzkopf: Alma Powell, the wife of the distinguished Chairman of the Joint Chiefs. And to the families, let me say, our forces in the Gulf will not stay there one day longer than is necessary to complete their mission.
The courage and success of the R.A.F. pilots—of the Kuwaiti, Saudi, French, Canadians, Italians, the pilots of Qatar and Bahrain—all are proof that for the first time since World War II, the international community is united. The leadership of the United Nations, once only a hoped-for ideal, is now confirming its founders' vision.
I am heartened that we are not being asked to bear alone the financial burden of this struggle. Last year, our friends and allies provided the bulk of the economic costs of Desert Shield, and having now received commitments of over $40 billion for the first three months of 1991, I am confident they will do no less as we move through Desert Storm.
But the world has to wonder what the dictator of Iraq is thinking. If he thinks that by targeting innocent civilians in Israel and Saudi Arabia, that he will gain an advantage—he is dead wrong. If he thinks that he will advance his cause through tragic and despicable environmental terrorism—he is dead wrong. And if he thinks that by abusing coalition P.O.W.s, he will benefit—he is dead wrong.
We will succeed in the Gulf. And when we do, the world community will have sent an enduring warning to any dictator or despot, present or future, who contemplates outlaw aggression.
The world can therefore seize this opportunity to fulfill the long-held promise of a new world order—where brutality will go unrewarded, and aggression will meet collective resistance.
Yes, the United States bears a major share of leadership in this effort. Among the nations of the world, only the United States of America has had both the moral standing, and the means to back it up. We are the only nation on this earth that could assemble the forces of peace.
This is the burden of leadership—and the strength that has made America the beacon of freedom in a searching world.
This nation has never found glory in war. Our people have never wanted to abandon the blessings of home and work, for distant lands and deadly conflict. If we fight in anger, it is only because we have to fight at all. And all of us yearn for a world where we will never have to fight again.
Each of us will measure, within ourselves, the value of this great struggle. Any cost in lives is beyond our power to measure. But the cost of closing our eyes to aggression is beyond mankind's power to imagine.
This we do know: Our cause is just. Our cause is moral. Our cause is right.
Let future generations understand the burden and the blessings of freedom. Let them say, we stood where duty required us to stand.
Let them know that together, we affirmed America, and the world, as a community of conscience.
The winds of change are with us now. The forces of freedom are united. We move toward the next century, more confident than ever, that we have the will at home and abroad, to do what must be done—the hard work of freedom.
May God bless the United States of America.


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What is a Subluxation
When a vertebrae becomes misaligned or moves out of its normal position, this is referred to in the chiropractic profession as a subluxation. Subluxations can be caused by a wide range of issues ranging from a minor slip or bump to a car accident or any sudden trauma. When a vertebrae is subluxated, it begins to put pressure on nerves, blood vessels and everything around it. This pressure comes with a price. The subluxation interrupts the natural pathways that the messages sent from the brain need to be clear in order to be completed properly.
As time goes by and a subluxation remains untreated, the spine and surrounding features such as discs can begin to degenerate. This degeneration becomes more difficult to reverse as time goes by as the surrounding muscles, nerves and bones begin to adjust to the new shape. The body is an amazing machine. It will start to accommodate these changes by compensating in other areas. The longer this goes on, the more difficult it is and the longer it takes to get back to near perfect position.