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Phase transformation analysis from the point of view of the theory of nonelasticity with cross-links

In the presented report the basses of the theory of nonelasticity with cross-links are formulated, which theory is a result of developing the ideas of Novozilov's statistical theory of nonelasticity. All postulates of the new case of the theory are analyzed and discussed in details. The questions of thermodynamically consistency of the theory and selection of active flow surfaces are discussed. The initial boundary value problem for this theory is formulated as weak Cauchy of the corresponding subspace of the Banach's space. The theorem of existence of initial boundary value problem solution and its uniqueness is formulated, the limitations on the theory parameters are represented. At the first part of report the principle of construction and implementations of constitutive equations are presented. For the illustration of model properties for one theory cases a rheological model for the constitutive low is given. The detailed analytically analyses for simple cases of loading are given. As one of the results the analytically investigations are limitation on the material constants, depending of its behavior under the cyclical loading. The methods of detecting the material parameters, by the experimental data are given. The stress-strain diagrams represented results of computation for complex cyclic loading paths. The good correspondence between the experimental data and computer simulation is shown. The description of effects of super elasticity and shape memory effects is given. The rules for computing jumps of material parameters in the points of phase transactions are given. The effects of depend the flow limit and material constants from the temperature are taken into account. Such effects of phase transformations under the temperature influence as shape memory are presented. It becomes possible in the scope of mathematically simple equations to describe a lot of effects induced by temperature.