Research Papers

A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties

[+] Author and Article Information
Enrui Zhang, Yuan Liu

Applied Mechanics Laboratory,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Yihui Zhang

Applied Mechanics Laboratory,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China;
Center for Flexible Electronics Technology,
Tsinghua University,
Beijing 100084, China
e-mail: yihuizhang@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 21, 2018; final manuscript received March 24, 2018; published online April 13, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(7), 071002 (Apr 13, 2018) (9 pages) Paper No: JAM-18-1162; doi: 10.1115/1.4039815 History: Received March 21, 2018; Revised March 24, 2018

Soft network materials constructed with horseshoe microstructures represent a class of bio-inspired synthetic materials that can be tailored precisely to match the nonlinear, J-shaped, stress–strain curves of human skins. Under a large level of stretching, the nonlinear deformations associated with the drastic changes of microstructure geometries can lead to an evident mechanical anisotropy, even for honeycomb and triangular lattices with a sixfold rotational symmetry. Such anisotropic mechanical responses are essential for certain targeted applications of these synthetic materials. By introducing appropriate periodic boundary conditions that apply to large deformations, this work presents an efficient computational model of soft network materials based on the analyses of representative unit cells. This model is validated through comparison of predicted deformed configurations with full-scale finite element analyses (FEA) for different loading angles and loading strains. Based on this model, the anisotropic mechanical responses, including the nonlinear stress–strain curves and Poisson's ratios, are systematically analyzed for three representative lattice topologies (square, triangular and honeycomb). An analytic solution of the geometry-based critical strain was found to show a good correspondence to the critical transition point of the calculated J-shaped stress–strain curve for different network geometries and loading angles. Furthermore, the nonlinear Poisson's ratio, which can be either negative or positive, was shown to depend highly on both the loading angle and the loading strain.

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Ni Annaidh, A. , Bruyere, K. , Destrade, M. , Gilchrist, M. D. , Maurini, C. , Ottenio, M. , and Saccomandi, G. , 2012, “ Automated Estimation of Collagen Fibre Dispersion in the Dermis and Its Contribution to the Anisotropic Behaviour of Skin,” Ann. Biomed. Eng., 40(8), pp. 1666–1678. [CrossRef] [PubMed]
Fratzl, P. , Misof, K. , Zizak, I. , Rapp, G. , Amenitsch, H. , and Bernstorff, S. , 1998, “ Fibrillar Structure and Mechanical Properties of Collagen,” J. Struct. Biol., 122(1–2), pp. 119–122. [CrossRef] [PubMed]
Provenzano, P. P. , Heisey, D. , Hayashi, K. , Lakes, R. , and Vanderby, R., Jr. , 2002, “ Subfailure Damage in Ligament: A Structural and Cellular Evaluation,” J. Appl. Physiol., 92(1), pp. 362–371. [CrossRef] [PubMed]
Gao, H. J. , Ji, B. H. , Jager, I. L. , Arzt, E. , and Fratzl, P. , 2003, “ Materials Become Insensitive to Flaws at Nanoscale: Lessons From Nature,” Proc. Natl. Acad. Sci. U. S. A., 100(10), pp. 5597–5600. [CrossRef] [PubMed]
Mayer, G. , 2005, “ Rigid Biological Systems as Models for Synthetic Composites,” Science, 310(5751), pp. 1144–1147. [CrossRef] [PubMed]
Keten, S. , Xu, Z. , Ihle, B. , and Buehler, M. J. , 2010, “ Nanoconfinement Controls Stiffness, Strength and Mechanical Toughness of Beta-Sheet Crystals in Silk,” Nat. Mater., 9(4), pp. 359–367. [CrossRef] [PubMed]
Komatsu, K. , 2010, “ Mechanical Strength and Viscoelastic Response of the Periodontal Ligament in Relation to Structure,” J. Dent. Biomech., 2010, p. 502318. [CrossRef] [PubMed]
Launey, M. E. , Buehler, M. J. , and Ritchie, R. O. , 2010, “ On the Mechanistic Origins of Toughness in Bone,” Annu. Rev. Mater. Res., 40(1), pp. 25–53. [CrossRef]
Gautieri, A. , Vesentini, S. , Redaelli, A. , and Buehler, M. J. , 2011, “ Hierarchical Structure and Nanomechanics of Collagen Microfibrils From the Atomistic Scale Up,” Nano Lett., 11(2), pp. 757–766. [CrossRef] [PubMed]
Cranford, S. W. , Tarakanova, A. , Pugno, N. M. , and Buehler, M. J. , 2012, “ Nonlinear Material Behaviour of Spider Silk Yields Robust Webs,” Nature, 482(7383), pp. 72–76. [CrossRef] [PubMed]
Ortiz, C. , and Boyce, M. C. , 2008, “ Materials Science. Bioinspired Structural Materials,” Science, 319(5866), pp. 1053–1054. [CrossRef] [PubMed]
Munch, E. , Launey, M. E. , Alsem, D. H. , Saiz, E. , Tomsia, A. P. , and Ritchie, R. O. , 2008, “ Tough, Bio-Inspired Hybrid Materials,” Science, 322(5907), pp. 1516–1520. [CrossRef] [PubMed]
Hong, Y. , Huber, A. , Takanari, K. , Amoroso, N. J. , Hashizume, R. , Badylak, S. F. , and Wagner, W. R. , 2011, “ Mechanical Properties and In Vivo Behavior of a Biodegradable Synthetic Polymer Microfiber-Extracellular Matrix Hydrogel Biohybrid Scaffold,” Biomaterials, 32(13), pp. 3387–3394. [CrossRef] [PubMed]
Bouville, F. , Maire, E. , Meille, S. , Van de Moortele, B. , Stevenson, A. J. , and Deville, S. , 2014, “ Strong, Tough and Stiff Bioinspired Ceramics From Brittle Constituents,” Nat. Mater., 13(5), pp. 508–514. [CrossRef] [PubMed]
Naik, N. , Caves, J. , Chaikof, E. L. , and Allen, M. G. , 2014, “ Generation of Spatially Aligned Collagen Fiber Networks Through Microtransfer Molding,” Adv. Healthcare Mater., 3(3), pp. 367–374. [CrossRef]
Wegst, U. G. , Bai, H. , Saiz, E. , Tomsia, A. P. , and Ritchie, R. O. , 2015, “ Bioinspired Structural Materials,” Nat. Mater., 14(1), pp. 23–36. [CrossRef] [PubMed]
Yang, W. , Sherman, V. R. , Gludovatz, B. , Schaible, E. , Stewart, P. , Ritchie, R. O. , and Meyers, M. A. , 2015, “ On the Tear Resistance of Skin,” Nat. Commun., 6(1), p. 6649. [CrossRef] [PubMed]
Kwansa, A. L. , Empson, Y. M. , Ekwueme, E. C. , Walters, V. I. , Freeman, J. W. , and Laurencin, C. T. , 2010, “ Novel Matrix Based Anterior Cruciate Ligament (ACL) Regeneration,” Soft Matter, 6(20), p. 5016. [CrossRef]
Meyers, M. A. , McKittrick, J. , and Chen, P. Y. , 2013, “ Structural Biological Materials: Critical Mechanics-Materials Connections,” Science, 339(6121), pp. 773–779. [CrossRef] [PubMed]
Safar, M. E. , Blacher, J. , Mourad, J. J. , and London, G. M. , 2000, “ Stiffness of Carotid Artery Wall Material and Blood Pressure in Humans: Application to Antihypertensive Therapy and Stroke Prevention,” Stroke, 31(3), pp. 782–790. [CrossRef] [PubMed]
Ma, Y. , Feng, X. , Rogers, J. A. , Huang, Y. , and Zhang, Y. , 2017, “ Design and Application of ‘J-Shaped’ Stress-Strain Behavior in Stretchable Electronics: A Review,” Lab Chip, 17(10), pp. 1689–1704. [CrossRef] [PubMed]
Rogers, J. A. , Someya, T. , and Huang, Y. , 2010, “ Materials and Mechanics for Stretchable Electronics,” Science, 327(5973), pp. 1603–1607. [CrossRef] [PubMed]
Kim, D. H. , Lu, N. , Ma, R. , Kim, Y. S. , Kim, R. H. , Wang, S. , Wu, J. , Won, S. M. , Tao, H. , Islam, A. , Yu, K. J. , Kim, T. I. , Chowdhury, R. , Ying, M. , Xu, L. , Li, M. , Chung, H. J. , Keum, H. , McCormick, M. , Liu, P. , Zhang, Y. W. , Omenetto, F. G. , Huang, Y. , Coleman, T. , and Rogers, J. A. , 2011, “ Epidermal Electronics,” Science, 333(6044), pp. 838–843. [CrossRef] [PubMed]
Xu, S. , Zhang, Y. , Jia, L. , Mathewson, K. E. , Jang, K. I. , Kim, J. , Fu, H. , Huang, X. , Chava, P. , Wang, R. , Bhole, S. , Wang, L. , Na, Y. J. , Guan, Y. , Flavin, M. , Han, Z. , Huang, Y. , and Rogers, J. A. , 2014, “ Soft Microfluidic Assemblies of Sensors, Circuits, and Radios for the Skin,” Science, 344(6179), pp. 70–74. [CrossRef] [PubMed]
Zhang, Y. , Fu, H. , Xu, S. , Fan, J. A. , Hwang, K.-C. , Jiang, J. , Rogers, J. A. , and Huang, Y. , 2014, “ A Hierarchical Computational Model for Stretchable Interconnects With Fractal-Inspired Designs,” J. Mech. Phys. Solids, 72, pp. 115–130. [CrossRef]
Zhu, Y. , and Xu, F. , 2012, “ Buckling of Aligned Carbon Nanotubes as Stretchable Conductors: A New Manufacturing Strategy,” Adv. Mater., 24(8), pp. 1073–1077. [CrossRef] [PubMed]
Yao, S. , and Zhu, Y. , 2014, “ Wearable Multifunctional Sensors Using Printed Stretchable Conductors Made of Silver Nanowires,” Nanoscale, 6(4), pp. 2345–2352. [CrossRef] [PubMed]
Jang, K. I. , Chung, H. U. , Xu, S. , Lee, C. H. , Luan, H. , Jeong, J. , Cheng, H. , Kim, G. T. , Han, S. Y. , Lee, J. W. , Kim, J. , Cho, M. , Miao, F. , Yang, Y. , Jung, H. N. , Flavin, M. , Liu, H. , Kong, G. W. , Yu, K. J. , Rhee, S. I. , Chung, J. , Kim, B. , Kwak, J. W. , Yun, M. H. , Kim, J. Y. , Song, Y. M. , Paik, U. , Zhang, Y. , Huang, Y. , and Rogers, J. A. , 2015, “ Soft Network Composite Materials With Deterministic and Bio-Inspired Designs,” Nat. Commun., 6, p. 6566. [CrossRef] [PubMed]
Chen, P. , Xu, Y. , He, S. , Sun, X. , Pan, S. , Deng, J. , Chen, D. , and Peng, H. , 2015, “ Hierarchically Arranged Helical Fibre Actuators Driven by Solvents and Vapours,” Nat. Nanotechnol., 10(12), pp. 1077–1083. [CrossRef] [PubMed]
Khang, D. Y. , Jiang, H. , Huang, Y. , and Rogers, J. A. , 2006, “ A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates,” Science, 311(5758), pp. 208–212. [CrossRef] [PubMed]
Sun, Y. , Choi, W. M. , Jiang, H. , Huang, Y. Y. , and Rogers, J. A. , 2006, “ Controlled Buckling of Semiconductor Nanoribbons for Stretchable Electronics,” Nat. Nanotechnol., 1(3), pp. 201–207. [CrossRef] [PubMed]
Yu, C. J. , Masarapu, C. , Rong, J. P. , Wei, B. Q. , and Jiang, H. Q. , 2009, “ Stretchable Supercapacitors Based on Buckled Single-Walled Carbon Nanotube Macrofilms,” Adv. Mater., 21(47), pp. 4793–4797. [CrossRef] [PubMed]
Gerbode, S. J. , Puzey, J. R. , McCormick, A. G. , and Mahadevan, L. , 2012, “ How the Cucumber Tendril Coils and Overwinds,” Science, 337(6098), pp. 1087–1091. [CrossRef] [PubMed]
Song, Z. , Ma, T. , Tang, R. , Cheng, Q. , Wang, X. , Krishnaraju, D. , Panat, R. , Chan, C. K. , Yu, H. , and Jiang, H. , 2014, “ Origami Lithium-Ion Batteries,” Nat. Commun., 5, p. 3140. [PubMed]
Shyu, T. C. , Damasceno, P. F. , Dodd, P. M. , Lamoureux, A. , Xu, L. , Shlian, M. , Shtein, M. , Glotzer, S. C. , and Kotov, N. A. , 2015, “ A Kirigami Approach to Engineering Elasticity in Nanocomposites Through Patterned Defects,” Nat. Mater., 14(8), pp. 785–789. [CrossRef] [PubMed]
Song, Z. M. , Wang, X. , Lv, C. , An, Y. H. , Liang, M. B. , Ma, T. , He, D. , Zheng, Y. J. , Huang, S. Q. , Yu, H. Y. , and Jiang, H. Q. , 2015, “ Kirigami-Based Stretchable Lithium-Ion Batteries,” Sci. Rep., 5(1), p. 10988. [CrossRef] [PubMed]
Zhang, Y. H. , Yan, Z. , Nan, K. W. , Xiao, D. Q. , Liu, Y. H. , Luan, H. W. , Fu, H. R. , Wang, X. Z. , Yang, Q. L. , Wang, J. C. , Ren, W. , Si, H. Z. , Liu, F. , Yang, L. H. , Li, H. J. , Wang, J. T. , Guo, X. L. , Luo, H. Y. , Wang, L. , Huang, Y. G. , and Rogers, J. A. , 2015, “ A Mechanically Driven Form of Kirigami as a Route to 3D Mesostructures in Micro/Nanomembranes,” Proc. Natl. Acad. Sci. U. S. A., 112(38), pp. 11757–11764. [CrossRef] [PubMed]
Maziz, A. , Concas, A. , Khaldi, A. , Stalhand, J. , Persson, N. K. , and Jager, E. W. , 2017, “ Knitting and Weaving Artificial Muscles,” Sci. Adv., 3(1), p. e1600327. [CrossRef] [PubMed]
Chen, C. , Lu, T. J. , and Fleck, N. A. , 1999, “ Effect of Imperfections on the Yielding of Two-Dimensional Foams,” J. Mech. Phys. Solids, 47(11), pp. 2235–2272. [CrossRef]
Lu, T. J. , and Chen, C. , 1999, “ Thermal Transport and Fire Retardance Properties of Cellular Aluminium Alloys,” Acta Mater., 47(5), pp. 1469–1485. [CrossRef]
Deshpande, V. S. , Ashby, M. F. , and Fleck, N. A. , 2001, “ Foam Topology Bending Versus Stretching Dominated Architectures,” Acta Mater., 49(6), pp. 1035–1040. [CrossRef]
Evans, A. G. , Hutchinson, J. W. , Fleck, N. A. , Ashby, M. F. , and Wadley, H. N. G. , 2001, “ The Topological Design of Multifunctional Cellular Metals,” Prog. Mater. Sci., 46(3–4), pp. 309–327. [CrossRef]
Hutchinson, R. G. , and Fleck, N. A. , 2006, “ The Structural Performance of the Periodic Truss,” J. Mech. Phys. Solids, 54(4), pp. 756–782. [CrossRef]
Fleck, N. A. , and Qiu, X. , 2007, “ The Damage Tolerance of Elastic–Brittle, Two-Dimensional Isotropic Lattices,” J. Mech. Phys. Solids, 55(3), pp. 562–588. [CrossRef]
Zhang, Y. H. , Qiu, X. M. , and Fang, D. N. , 2008, “ Mechanical Properties of Two Novel Planar Lattice Structures,” Int. J. Solids Struct., 45(13), pp. 3751–3768. [CrossRef]
Kang, S. H. , Shan, S. , Noorduin, W. L. , Khan, M. , Aizenberg, J. , and Bertoldi, K. , 2013, “ Buckling-Induced Reversible Symmetry Breaking and Amplification of Chirality Using Supported Cellular Structures,” Adv. Mater., 25(24), pp. 3380–3385. [CrossRef] [PubMed]
Kang, S. H. , Shan, S. , Kosmrlj, A. , Noorduin, W. L. , Shian, S. , Weaver, J. C. , Clarke, D. R. , and Bertoldi, K. , 2014, “ Complex Ordered Patterns in Mechanical Instability Induced Geometrically Frustrated Triangular Cellular Structures,” Phys. Rev. Lett., 112(9), p. 098701. [CrossRef] [PubMed]
Bertoldi, K. , 2017, “ Harnessing Instabilities to Design Tunable Architected Cellular Materials,” Annu. Rev. Mater. Res., 47(1), pp. 51–61. [CrossRef]
Li, T. , Hu, X. , Chen, Y. , and Wang, L. , 2017, “ Harnessing out-of-Plane Deformation to Design 3D Architected Lattice Metamaterials With Tunable Poisson's Ratio,” Sci. Rep., 7(1), p. 8949. [CrossRef] [PubMed]
Chen, Y. , Jia, Z. , and Wang, L. , 2016, “ Hierarchical Honeycomb Lattice Metamaterials With Improved Thermal Resistance and Mechanical Properties,” Compos. Struct., 152, pp. 395–402. [CrossRef]
Kim, D. H. , Song, J. , Choi, W. M. , Kim, H. S. , Kim, R. H. , Liu, Z. , Huang, Y. Y. , Hwang, K. C. , Zhang, Y. W. , and Rogers, J. A. , 2008, “ Materials and Noncoplanar Mesh Designs for Integrated Circuits With Linear Elastic Responses to Extreme Mechanical Deformations,” Proc. Natl. Acad. Sci. U S A, 105(48), pp. 18675–18680. [CrossRef] [PubMed]
Widlund, T. , Yang, S. , Hsu, Y.-Y. , and Lu, N. , 2014, “ Stretchability and Compliance of Freestanding Serpentine-Shaped Ribbons,” Int. J. Solids Struct., 51(23–24), pp. 4026–4037. [CrossRef]
Zhang, Y. , Xu, S. , Fu, H. , Lee, J. , Su, J. , Hwang, K. C. , Rogers, J. A. , and Huang, Y. , 2013, “ Buckling in Serpentine Microstructures and Applications in Elastomer-Supported Ultra-Stretchable Electronics With High Areal Coverage,” Soft Matter, 9(33), pp. 8062–8070. [CrossRef] [PubMed]
Yang, S. X. , Chen, Y. C. , Nicolini, L. , Pasupathy, P. , Sacks, J. , Su, B. , Yang, R. , Sanchez, D. , Chang, Y. F. , Wang, P. L. , Schnyer, D. , Neikirk, D. , and Lu, N. S. , 2015, “‘ Cut-and-Paste’ Manufacture of Multiparametric Epidermal Sensor Systems,” Adv. Mater., 27(41), pp. 6423–6430. [CrossRef] [PubMed]
Yang, S. X. , Su, B. , Bitar, G. , and Lu, N. S. , 2014, “ Stretchability of Indium Tin Oxide (ITO) Serpentine Thin Films Supported by Kapton Substrates,” Int. J. Fract., 190(1–2), pp. 99–110. [CrossRef]
Huang, Y. A. , Dong, W. T. , Huang, T. , Wang, Y. Z. , Xiao, L. , Su, Y. W. , and Yin, Z. P. , 2015, “ Self-Similar Design for Stretchable Wireless LC Strain Sensors,” Sens. Actuators A, 224, pp. 36–42. [CrossRef]
Huang, Y. A. , Wang, Y. Z. , Xiao, L. , Liu, H. M. , Dong, W. T. , and Yin, Z. P. , 2014, “ Microfluidic Serpentine Antennas With Designed Mechanical Tunability,” Lab Chip, 14(21), pp. 4205–4212. [CrossRef] [PubMed]
Arslan, M. , and Boyce, M. C. , 2006, “ Constitutive Modeling of the Finite Deformation Behavior of Membranes Possessing a Triangulated Network Microstructure,” ASME J. Appl. Mech., 73(4), pp. 536–543. [CrossRef]
Ma, Q. , and Zhang, Y. , 2016, “ Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics,” ASME J. Appl. Mech., 83(11), p. 111008. [CrossRef]
Ma, Q. , Cheng, H. , Jang, K. I. , Luan, H. , Hwang, K. C. , Rogers, J. A. , Huang, Y. , and Zhang, Y. , 2016, “ A Nonlinear Mechanics Model of Bio-Inspired Hierarchical Lattice Materials Consisting of Horseshoe Microstructures,” J. Mech. Phys. Solids, 90, pp. 179–202. [CrossRef] [PubMed]
Li, H. , Ma, Y. , Wen, W. , Wu, W. , Lei, H. , and Fang, D. , 2017, “ In Plane Mechanical Properties of Tetrachiral and Antitetrachiral Hybrid Metastructures,” ASME J. Appl. Mech., 84(8), p. 081006. [CrossRef]
Kothari, K. , Hu, Y. , Gupta, S. , and Elbanna, A. , 2018, “ Mechanical Response of Two-Dimensional Polymer Networks: Role of Topology, Rate Dependence, and Damage Accumulation,” ASME J. Appl. Mech., 85(3), p. 031008. [CrossRef]
Onck, P. R. , Andrews, E. W. , and Gibson, L. J. , 2001, “ Size Effects in Ductile Cellular Solids. Part I: Modeling,” Int. J. Mech. Sci., 43(3), pp. 681–699. [CrossRef]
Liu, J. , and Zhang, Y. , 2018, “ A Mechanics Model of Soft Network Materials With Periodic Lattices of Arbitrarily Shaped Filamentary Microstructures for Tunable Poisson's Ratios,” ASME J. Appl. Mech., 85(5), p. 051003. [CrossRef]
Liu, J. , and Zhang, Y. , 2018, “ Soft Network Materials With Isotropic Negative Poisson's Ratios Over Large Strains,” Soft Matter, 14(5), pp. 693–703. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 5

Results of the unit-cell FEA and full-scale FEA on the normalized distance and the direction of different cross sections with respect to the center point of the unit cell for three representative examples in Fig. 4: (a) square networks with θ = 0 deg, (b) honeycomb networks with θ = −15 deg, and (c) triangular networks with θ = 19 deg. Here, LOA and LOB are the distance between O and A, and that between O and B, as shown in Fig. 1.

Grahic Jump Location
Fig. 4

Deformed configurations based on the unit-cell FEA and full-scale FEA for the three lattice topologies: (a) square, (b) honeycomb, and (c) triangular, with various loading strains and loading angles

Grahic Jump Location
Fig. 3

Full-scale FEA results of the three respective examples under a uniaxial stretching (εxx = 60%): (a) square networks with θ = 27 deg, (b) honeycomb networks with θ = 19 deg, and (c) triangular networks with θ = 19 deg. The insets denote a magnified view of the central area of the large networks.

Grahic Jump Location
Fig. 2

Schematic illustration of the periodic boundary conditions for a unit cell of the square network materials

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Fig. 1

Geometric construction of the soft network materials. Three different topologies are studied, including (a) square, (b) honeycomb, and (c) triangular lattices. The network materials are subject to a uniaxial loading along the horizontal direction (x-axis). Each horseshoe microstructure in the unit cells has the radius R, the arc angle γ, the width w, and the intersection angle β between OA and OB. The axis of symmetry of the unit cells has a tilted angle of θ relative to the x-axis (a, b) or y-axis (c).

Grahic Jump Location
Fig. 6

Unit-cell FEA results of (a)–(c) normalized stress–strain curves and (d)–(f) transverse–longitudinal strain curves for three lattice topologies: (a and d) square, (b and e) honeycomb, and (c and f) triangular network materials with a wide range of loading angles

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Fig. 7

(a) Schematic illustration of the main bearing components (bold) based on the unit-cell FEA. As the applied strain reaches the mechanical critical strain, the main bearing components are almost fully unraveled. (b) Stress–strain curve and its derivative curve based on the unit-cell FEA. The points (i)–(iv) in (b) correspond to deformed states (i)–(iv) in (a). (ce) Geometry-based critical strains predicted by the analytic solutions, as compared to the mechanical critical strains based on the unit-cell FEA, for the square, honeycomb, and triangular topologies, respectively. The geometric parameters are γ = 180 deg, w/R = 0.2; and γ = 120 deg, w/R = 0.173. (fh) Unit-cell FEA results of the normalized stress of the three lattice topologies, wherein each curve shows the stress response of the same loading strain from different loading directions normalized by the stress value of a special direction.



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