{'fraction_non_alphanumeric': 0.033606325896639366, 'fraction_numerical': 0.01125590027030298, 'mean_word_length': 5.141724479682854, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Bioinspired rational design of multi-material 3D printed soft-hard interfaces

Durable interfacing of hard and soft materials is a major design challenge caused by the ensuing stress concentrations. In nature, soft-hard interfaces exhibit remarkable mechanical performance, with failures rarely happening at the interface but in the hard or soft material. This superior performance is mechanistically linked to such design features as hierarchical structures, multiple types of interlocking, and functional gradients. Here, we mimic these strategies to design efficient soft-hard interfaces using voxel-based multi-material 3D printing. We designed several types of soft-hard interfaces with interfacial functional gradients and various types of bio-inspired interlocking mechanisms. The geometrical designs were based on triply periodic minimal surfaces (i.e., octo, diamond, and gyroid), collagen-like triple helices, and randomly distributed particles. We utilized a combination of the finite element method and experimental techniques, including uniaxial tensile tests, quad-lap shear tests, and full-field strain measurement using digital image correlation, to characterize the mechanical performance of different groups. The analysis of the best performing designs (i.e., the gyroid, collagen, and particle designs) suggests that smooth interdigitated connections, compliant gradient transitions, and either decreasing or constraining the strain concentrations regions between the hard and soft phases led to simultaneously strong and tough interfaces. Increasing the gradient length was only beneficial when the resulting interface geometry reduced strain concentrations (e.g., in collagen and particles). Combining the gyroid-based architecture with a random distribution of particles yielded the best-performing soft-hard interface, with strengths approaching the upper limit of the possible strengths and up to 50% toughness enhancement as compared to the control group.


INTRODUCTION
Joining materials with dissimilar mechanical properties is inherently challenging due to the complexities present at the soft-hard interfaces [1][2][3]. These complexities include the different load-carrying capacities of both materials, interfacial damages caused by the failure of any adhesives present at the interface, and the stress concentrations caused by the sudden changes in the material properties [4][5][6][7]. Among those factors, the lattermost is particularly concerning because interfacial microarchitecture and geometry play key roles in the development of stress singularities [8]. In contrast, several millennia of evolution has endowed natural architected structures with remarkable mechanical properties that originate from their complex yet highly efficient arrangements of mechanically dissimilar phases [9][10][11]. Given the failure of engineered constructs in reproducing the high level of efficiency exhibited by natural materials, it is important to understand and mimic the naturally occurring design strategies.
A prime example of such high performing interface is the tendon enthesis, where the soft tendon connects to the much stiffer bony tissue along a relatively short transitional length [12], employing an efficient mixture of design features, such as morphological interdigitations and anisotropic orientations [13][14][15][16]. Moreover, functional gradients (FGs) enable a smooth transition of material properties from bone to tendon, reducing interfacial stresses [17][18][19][20][21]. The synergy of these mechanisms makes the bone-tendon connection highly efficient [12].
To date, a major impediment to the application of such design features has been the lack of suitable manufacturing techniques. The emergence of multi-material additive manufacturing (=3D printing) techniques has addressed this limitation and has enabled us to closely emulate the abovementioned natural design paradigms. In particular, controlling the type of the deposited material at the level of individual voxels makes polyjet multi-material 3D printing highly suitable for the emulation of natural soft-hard interfaces [22][23][24].
Many types of architectures could be used as a basis for the design of biomimetic interfaces.
Here, we selected a few types of architectures to study the effects of architecture types and design parameters on the mechanical performance of the resulting soft-hard interfaces. Triply periodic minimal surfaces (TPMS) [25][26][27] were one of the selected architectures because they offer a large surface area to volume ratios and high genus values, both of which are highly beneficial for an enhanced interlocking of the interfacing phases. A high genus value means that there are multiple surface-connected yet volume-separated compartments available in the architecture of the material. Each of those compartments could be occupied by one of the interfacing phases. In this way, the phases interlock volumetrically across the vast surface area of the unit cells. A higher contact area between the material phases can also reduce strain concentrations. Architectures based on collagen-like helices [28,29] were also considered because they facilitate the creation of functional gradients while offering open cells and high surface areas. The design matrix was complemented by including randomly distributed particles, which are known to generate smooth functional gradients and arrest propagating cracks [30]. Moreover, the random distribution of particles can be integrated into multihierarchical arrangements [31] to prevent failure within the interface region.
We used both experiments and computational models to compare the various design options mentioned above and to elucidate the mechanisms determining the relative performance of different architectures. In particular, we studied the relation between the internal geometry, the type of the transition function, and the contact surface on the one hand and the mechanical characteristics of the soft-hard interfaces, and the ensuing strain concentrations [32] on the other. This novel approach provides us with a pathway towards a better understanding of the mechanisms at play in the design of soft-hard interfaces and enables us to devise some design guidelines for improving the mechanical performance of bioinspired soft-hard interfaces with potential applications in tissue engineering, soft robotics, and architected materials.

3D printing setup
We used a poly-jet multi-material 3D printer (ObjetJ735 Connex3, Stratasys ® Ltd., USA) with voxel-level control to manufacture our biomimetic soft-hard interfaces. The commercially available photopolymers VeroCyan TM (RGD841, Stratasys ® Ltd., USA) and Agilus30 TM Clear (FLX935, Stratasys ® Ltd., USA) were used for the hard and soft phases, respectively. Stacks of binary images detailing the type of the deposited material at each voxel were provided as input to the printer. In this approach, every image represents a layer of the 3D design. The maximum printing resolution was 300×600×900 dpi. We used the minimum edge size to print cube-shaped voxels with an edge length of 85 μm.

Design and manufacturing of tensile test interfaces
We considered the narrow section of a standard tensile test specimen shape (type IV) described in ASTM D638-14 [33] to constrain the dimensions of our designs ( Figure 1A). These dimensions allowed for a design region of 384×96×48 voxels (32.51×8.1×4.0 mm 3 ). Within these regions, we kept the length of the soft region constant ( = 8.128 mm) and varied two interface parameters, namely the width ( ) and geometrical design of the functional gradient ( Figure 1B). We selected three different values of (i.e., 4.064, 8.128, 12.192 mm, equivalent to 48, 96, and 144 voxels), wherein we linearly varied the volume fraction of the hard phase ( ) from 0 to 100%. We discretized these functions using cubic-shaped unit-cells with five different geometries, including three TPMS-based architectures (i.e., octo (OC), diamond (DI), and gyroid (GY)), biomimetic collagen-like triple helices (CO), and randomly distributed particles (PA) ( Figure 1B). Section S1 of the supplementary document provides the details of the equations used for the generation of each design. It is important to note that the selected discretization strategy results in a significant discontinuity in the hard phase for the long OC design (i.e., = 12mm). We, nevertheless, included this design in the experimental groups to investigate the effects of such discontinuities on the mechanical performance of soft-hard interfaces. We included a control group without gradient transitions ( = 0 mm) ( Figure S1A of the supplementary document). Furthermore, to measure the morphological features of each interface, we calculated the percentage of soft-hard normal contact area ( ) across the gradient lengths ( Figure S1B of the supplementary document). Finally, we projected each design into the narrow-gauge region of the tensile test specimens. Three specimens from each design were 3D printed, resulting in a total of 48 specimens.

Mechanical testing and post-processing
After manufacturing, we performed quasi-static uniaxial tensile tests with a mechanical testing bench (LLOYD instrument LR5K, load cell = 100 N) at a rate of 2 mm/min until failure. The device measured the displacements ( ), forces ( ), and time ( ) at a sampling rate of 100 Hz.
For all the tensile test specimens, we obtained full-field strain maps (the equivalent von Mises strains) at a frequency of 1 Hz using a 3D digital image correlation (DIC) system (Q-400, two cameras each with 12 MPixel, LIMESS GmbH, Krefeld, Germany) and its associated software (Instra 4D v4.6, Danted Dynamics A/S, Skovunde, Denmark). We, therefore, painted all the specimens white, followed by the application of a black dot speckle pattern.
To generate the stress-strain curves, we defined virtual extensometers at the center of the soft section of every specimen using the DIC software and extracted the vectors of true (logarithmic) strains ( ). We then post-processed these vectors and their respective forces ( ) in MATLAB R2018b (Mathworks, USA) to generate their true stress vectors ( = ( / ) exp( ), = 32.512 mm 2 ). From the resulting curves, we calculated the elastic modulus, , as the slope of the linear region of the stress-strain curves measured between 0 and 20% strain, the ultimate tensile strength, , as the maximum recorded stress, and the strain energy density, , as the area under the stress-strain curve, also known as toughness.

Finite element analysis of the interface designs
We created quasi-static finite element method (FEM) models of our designs using a commercially available software suite (nonlinear solver, Abaqus Standard v.6.13, Dassault Systèmes Simulia, France). Since the designs were symmetric across their length, we considered one longitudinal half of each design ( Figure

Determination of maximum equivalent strains and strain concentration parameters
We used the true von Mises strains obtained from the DIC measurements and FEM simulations to study how the strains concentrated at the interfaces. To this end, we extracted the curves of the maximum equivalent strains , ( ) from every cross-section layer across the length of the specimens. Additionally, we extracted the maximum strain value from these plots ( ) and divided it over the average equivalent strain at the center of the specimen ( ) to define the single-valued strain concentration parameter ( = / ) (Figure 2A), which we obtained from the DIC measurements and FEM estimations. We used the strain values corresponding to a stress magnitude of = 0.186 MPa. Overall, these strain concentration parameters and the FEM-predicted strain distributions were used to study how the local geometry affected the performance of the functional gradients within the elastic loading regime.

Determination of the elastic modulus functions
We used the results from our computational models to study the elastic behavior exhibited by various designs. Towards this goal, we idealized the interfaces as linear systems of springs, where the elastic modulus function ( ( ) = / ( )) is equivalent to the applied surface traction on the system, , over the average strain, ( ) , of every transversal layer over each interface point ( Figure S2B of the supplementary document). We used these estimated functions to study how different factors, including the elastic modulus and overall rigidity, affect the performance of the interfaces.

Quad-lap shear designs, testing, post-processing, and finite element analysis
We extended our analyses to study the shear response of the designed architectures using quadlap shear test specimens. We chose the designs that performed the best in the tensile tests (i.e., GY, CO, and PA, = 4.572 mm) and compared them to the control design (i.e., without a gradient). To obtain the appropriate dimensions of the specimens, we generated multiple geometries with the FEM software and simulated them. We used the dimensions of the specimen that yielded the elastic properties of the soft material ( using only the forces and displacements of the virtual crosshead. After assigning the designs to the gradient regions, we printed these specimens (three per experimental group) and tested them under the same conditions as described above for the tensile tests. We calculated the true shear

Design of a hybrid design based on our final findings
We further extended our analyses to exploit the full bioinspired potential of soft-hard interfaces.
To do so, we combined multi-scale hierarchical organization, crack deflection mechanisms, functional gradients, and smooth contact areas to generate a hybrid design. We selected and combined the best-performing designs from the initial analysis, defining a PA structure in which the particles were randomly scattered within a GY architecture, resulting in the GP group. To create a less stiff elastic modulus function, we decreased the densities of the hard phase, , by 50%. We then 3D printed, tested, and computationally analyzed these designs under the same conditions as described above for the quasi-static tensile tests.

RESULTS AND DISCUSSION
The integration of the different architectures into the soft-hard interfaces led to distinct patterns of ( Figure 1B) and resulted in different total values of the contact surface area ( . ) ( Figure 2B). None of these differences had a considerable effect on the initial elastic moduli ( Figure 2C) calculated using the obtained stress-strain curves ( Figure S3 of the supplementary document). Nevertheless, the varying geometries and gradient lengths did affect the strength and toughness of the interfaces ( Figure 2D-E). The best-performing designs were GY ( = 4 mm), CO ( = 12 mm), and PA ( = 12 mm). They all exhibited similar strengths and failure modes (i.e., failure within the soft region), suggesting that the upper strength boundary of these interfaces was reached [34]. The control group under-performed all but the OC designs, confirming the importance of the implemented design strategies in improving the mechanical performance of soft-hard interfaces.
We found some evidence of the mechanism responsible for the failure of the control group specimens when assessing their DIC-measured EXP values ( Figure 2F) and strain distributions ( Figure 3A). According to this evidence, the shear strains at the edges of the interface were the primary culprits, which is consistent with the available literature [4,35,36].
These superficial strain concentrations were not present in the DIC results of any functionally graded design. Moreover, the EXP values of the other groups were all much lower than those measured in the control group. This lack of shear strains explains the improved performance of most of the presented designs, because a proper interfacing of soft and hard materials requires a smooth transition from one phase to another so that the stress concentration in the softer material can be decreased [37]. The FEM-predicted values ( Figure 2G), however, indicated that strain concentrations take place within the 3D structure of the functionally graded interfaces. Therefore, a closer inspection to the results of the FEM simulations was necessary to elucidate the effects of the gradient morphology on the mechanical performance.
Comparing the DIC-measured strain distributions with the FEM results allowed us to validate our computational models ( Figure 3B-F see the peaks at the edges of the DI designs or between individual voxels in the PA gradients).
The absence of these peaks was likely caused by the limited DIC resolution (i.e., between 22×10 3 and 27×10 3 facets per experiment), which was approximately six times lower than the resolution of the 3D-printed specimens (i.e., 147×10 3 voxels). The FEM predictions were, therefore, more discerning when trying to understand the effects of geometrical design on the mechanical performance of soft-hard interfaces. This corroboration of the computational results allowed us to analyze the different designs individually in a quest to unravel the mechanisms underlying their mechanical performance.
Although generally better than the control group, most OC and DI specimens failed at the edge of the interface (only one DI specimen ( = 8 mm) failed at the center of the soft region).
An analysis of the FEM-predicted strain distributions of these groups showed the prevalence of severe strain concentrations at their interface edges ( Figure 3B-C), whose intensity was correlated to . Upon closer inspection ( Figure S4A An important parameter affecting the performance of the soft-hard interface is the length over which the transition takes place (i.e., ). The performance of a soft-hard interface is generally expected to improve as the length of the gradient increases, given that longer transitions lead to smoother changes in the elastic modulus, decreasing stress concentrations [37]. Indeed, the plots of the elastic modulus of the TPMS designs ( Figure S4A-C of the supplementary document) were increasingly smoother as increased. The performance of the TPMS designs was, however, inversely related to , as the strength values were higher for the specimens with shorter gradients while the FEM values were higher for the longer specimens. The local geometrical features at the end of a functional gradient are, therefore, more important in determining the mechanical performance of the interface than the overall smoothness of the function describing the transition of the elastic modulus. Consequently, it is important to utilize geometries that reduce the strain concentrations as increases or include features that help in arresting cracks.
In contrast with the TPMS structures, the mechanical performance of the CO and PA designs was enhanced as increased. In fact, the CO and PA designs with long gradients ( = 12 mm) were some of the toughest designs within this study. Moreover, most specimens of these two groups failed at the center of the soft region and not at the interface. When analyzing the computationally predicted strain distribution of the CO designs ( Figure 3D, Figure S4D  For the PA designs, the predicted FEM increased with but were not substantially higher than those of the control group. The locations of these strain concentrations were not necessarily at the end of the interface, but in single voxel locations across the entire gradient ( Figure 3F, Figure S4E of the supplementary document). If a crack initiates around those stress concentration points, the nearby voxels could deflect it or arrest its progress, similar to what other studies have observed [38]. Furthermore, the comparatively higher magnitudes of strains across the gradient length produced more compliant elastic modulus functions in these designs, similar to the CO specimens ( Figure S5E of the supplementary document). These high strains mean more strain energy is stored in such specimens, resulting in higher toughness values, particularly for the long PA gradients. Overall, both CO and PA achieved their high toughness because they could store more energy in their gradient region and because of the crack arresting features of their internal morphology.
We have so far only considered tension because this loading mode is typical in soft-hard interfaces (e.g., cables, tendons, muscles). Soft-hard interfaces may, however, also fail under shear deformations, motivating the study of the presented designs under this loading regime.
Since no standards are available for the geometrical design of functionally graded quad-lap specimens, a custom-made design was used ( Figure 4A), enabling us to manufacture the specimens and perform mechanical testing ( Figure 4B). After post-processing, all the hyperelastic − curves had similar initial values of the shear modulus ( = 0.308 MPa, Figure 4C), confirming the proper design of the specimens and the satisfactory distribution of materials in the presented designs. In terms of the shear strength and toughness, however, the PA designs outperformed all other groups ( Figure 4D). Moreover, the performance of the specimens was inversely related to their predicted FEM , suggesting that the internal morphology of these interfaces was responsible for this outcome. Based on these observations, we concluded that using PA reinforcement in the design of soft-hard interfaces can enhance their performance under shear deformations.
In summary, the data and analysis presented above indicate that there are several morphological and mechanical principles that can lead to a tough soft-hard interface. First, the must be smooth to prevent any sudden changes in with PA ( Figure 5A-B). We hypothesized that adding particles to a gyroid design (GY + PA = GP) will hinder the propagation of critical cracks while producing a smooth pattern.
Additionally, we decreased the ratio of the hard material, , to 50% of its original value so that higher magnitudes of strain energy can be accommodated by the interface.
Our experiments confirmed that the GP specimens, indeed, exhibit many of the characteristics of high-performing soft-hard interfaces. The DIC-measured strain distributions of the GP specimens ( Figure 5C) shared certain features with both the GY and PA designs while lacking any significant superficial strain concentrations. Overall, the 3D FEM models showed higher strain magnitudes and relatively higher levels of strain concentrations across the length of the functional gradient ( Figure S4F of the supplementary document). All in all, the GP designs yielded the smoothest modulus functions in this study, enabling more strain energy to be stored within the FG. Furthermore, their , plots showed that the strain concentrations vanish before the end of the gradient region ( Figure S5F of the supplementary document). Similar to the short GY and long PA designs, the presence of hard material around the locations of peak strains indicates that the interface can arrest initial cracks ( Figure 5E). The performance of the GP specimens increased with ( Figure 5D). In fact, the long ( = 12 mm) GP specimens presented the highest toughness values in this study (i.e., 1.48 times tougher than the control specimens), confirming that the implementation of multi-scale features into a highly interdigitated and compliant functionally graded design further enhances the performance of soft-hard interfaces.

CONCLUSIONS
We studied how the design of soft-hard interfaces influences their mechanical performance.
Our results clearly show the role of increased contact area, elastic modulus functions, and design features that attenuate or constrain strain concentrations in the rational design of highperforming soft-hard interfaces. The application of the abovementioned design features yielded soft-hard interfaces whose strength approached the upper boundary of the possible strengths and whose toughness increased by ≈ 50% as compared to that of the control specimens. Future work should employ these guidelines with computational methods to design optimized softhard interfaces. The presented results ultimately contribute to the development of the next generation of designer materials with applications in, among other areas, medical devices, tissue engineering, soft robotics, and the design of architected flexural mechanisms.     Representative strain distributions measured using DIC and predicted using computational models as well as , plots for these designs. D) A scatterplot comparing the vs.
results for the GY, PA, and GP designs. The GP specimens were among the best-performing ones. E) A detailed comparison of the mechanistic features of the best-performing GY, PA, and GP designs.