Mechanical Behavior of Hybrid Lattices Composed of Elastic and Elastoplastic Struts
Publication: Journal of Engineering Mechanics
Volume 146, Issue 2
Abstract
The mechanical behavior of cellular solids has been extensively studied in the literature. Nevertheless, possible structural effects of inhomogeneities in the form of elastoplastic struts have not yet been investigated. We present a numerical analysis of the tensile behavior of triangular, diamond, and hexagonal hybrid lattices composed of both elastic and elastoplastic struts. In particular, some struts are assumed to behave as strain-hardening elastoplastic beams while others are assumed to behave as a linear elastic material. It is found that both the stiffness and the strength of the lattices decrease with increasing percentage of elastoplastic struts. Furthermore, the presence of elastoplastic struts markedly alters fracture toughness. The effect of relative density on the tensile behavior of hybrid lattices is also investigated. It is concluded that in addition to the microstructure of cellular solids, the constitutive behavior of individual struts significantly affects their macroscopic mechanical response. Thus, the spatial distribution of struts with different material properties can be considered a novel approach in the design of cellular solids with desired properties.
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Acknowledgments
The authors would like to acknowledge the partial support of the National Science Foundation (Grant No. 1351461).
References
Ajdari, A., H. Nayeb-Hashemi, P. Canavan, and G. Warner. 2008. “Effect of defects on elastic–plastic behavior of cellular materials.” Mater. Sci. Eng. 487 (1): 558–567. https://doi.org/10.1016/j.msea.2007.10.050.
Chen, C., T. J. Lu, and N. A. Fleck. 2001. “Effect of inclusions and holes on the stiffness and strength of honeycombs.” Int. J. Mech. Sci. 43 (2): 487–504. https://doi.org/10.1016/S0020-7403(99)00122-8.
Deshpande, V. S., M. F. Ashby, and N. A. Fleck. 2001. “Foam topology: Bending versus stretching dominated architectures.” Acta Mater. 49 (6): 1035–1040. https://doi.org/10.1016/S1359-6454(00)00379-7.
Fleck, N. A., V. S. Deshpande, and M. F. Ashby. 2010. “Micro-architectured materials: Past, present and future.” Proc. R. Soc. Math. Phys. Eng. Sci. 466 (2121): 2495–2516. https://doi.org/10.1098/rspa.2010.0215.
Fleck, N. A., and X. Qiu. 2007. “The damage tolerance of elastic–brittle, two-dimensional isotropic lattices.” J. Mech. Phys. Solids 55 (3): 562–588. https://doi.org/10.1016/j.jmps.2006.08.004.
Gibson, L. J., and M. F. Ashby. 1997. Cellular solids: Structure and properties. New York: Cambridge University Press.
Grenestedt, J. L. 1998. “Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids.” J. Mech. Phys. Solids 46 (1): 29–50. https://doi.org/10.1016/S0022-5096(97)00035-5.
Gu, H., M. Pavier, and A. Shterenlikht. 2018. “Experimental study of modulus, strength and toughness of 2D triangular lattices.” Int. J. Solids Struct. 152 (Nov): 207–216. https://doi.org/10.1016/j.ijsolstr.2018.06.028.
Guo, X. E., and L. J. Gibson. 1999. “Behavior of intact and damaged honeycombs: A finite element study.” Int. J. Mech. Sci. 41 (1): 85–105. https://doi.org/10.1016/S0020-7403(98)00037-X.
Hatami-Marbini, H. 2016a. “Nonaffine behavior of three-dimensional semiflexible polymer networks.” Physical Rev. E 93 (4): 042503. https://doi.org/10.1103/PhysRevE.93.042503.
Hatami-Marbini, H. 2016b. “Scaling properties of three-dimensional random fibre networks.” Philos. Mag. Lett. 96 (5): 165–174. https://doi.org/10.1080/14786435.2016.1177223.
Hatami-Marbini, H. 2018. “Effect of crosslink torsional stiffness on elastic behavior of semiflexible polymer networks.” Physical Rev. E 97 (2): 022504. https://doi.org/10.1103/PhysRevE.97.022504.
Hatami-Marbini, H., and C. R. Picu. 2012. “Modeling the mechanics of semiflexible biopolymer networks: Non-affine deformation and presence of long-range correlations.” In Advances in soft matter mechanics, 119–145. Berlin: Springer.
Hatami-Marbini, H., and R. Picu. 2009. “An eigenstrain formulation for the prediction of elastic moduli of defective fiber networks.” Eur. J. Mech. A. Solids 28 (2): 305–316. https://doi.org/10.1016/j.euromechsol.2008.07.010.
Hatami-Marbini, H., and R. C. Picu. 2008. “Scaling of nonaffine deformation in random semiflexible fiber networks.” Physical Rev. E 77 (6): 062103. https://doi.org/10.1103/PhysRevE.77.062103.
Hatami-Marbini, H., and M. Rohanifar. 2019. “Stiffness of bi-modulus hexagonal and diamond honeycombs.” J. Mech. Sci. Technol. 33 (4): 1703–1709. https://doi.org/10.1007/s12206-019-0322-1.
Hatami-Marbini, H., and V. Shriyan. 2017. “Topology effects on nonaffine behavior of semiflexible fiber networks.” Physical Rev. E 96 (6): 062502. https://doi.org/10.1103/PhysRevE.96.062502.
Ma, Q., H. Cheng, K.-I. Jang, H. Luan, K.-C. Hwang, J. A. Rogers, Y. Huang, and Y. Zhang. 2016. “A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures.” J. Mech. Phys. Solids 90 (May): 179–202. https://doi.org/10.1016/j.jmps.2016.02.012.
Maxwell, J. C. 1864. “L. On the calculation of the equilibrium and stiffness of frames.” Philos. Mag. 27 (182): 294–299. https://doi.org/10.1080/14786446408643668.
Silva, M. J., and L. J. Gibson. 1997. “The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids.” Int. J. Mech. Sci. 39 (5): 549–563. https://doi.org/10.1016/S0020-7403(96)00065-3.
Tankasala, H. C., V. S. Deshpande, and N. A. Fleck. 2017. “Tensile response of elastoplastic lattices at finite strain.” J. Mech. Phys. Solids 109 (Dec): 307–330. https://doi.org/10.1016/j.jmps.2017.02.002.
Zhu, H. X., J. R. Hobdell, and A. H. Windle. 2001. “Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs.” J. Mech. Phys. Solids 49 (4): 857–870. https://doi.org/10.1016/S0022-5096(00)00046-6.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Sep 26, 2018
Accepted: Apr 29, 2019
Published online: Dec 3, 2019
Published in print: Feb 1, 2020
Discussion open until: May 3, 2020
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