Abstract
Macro-architectured cellular (MAC) material is defined as a class of engineered materials having configurable cells of relatively large (i.e., visible) size that can be architecturally designed to achieve various desired material properties. Two types of novel MAC materials, negative Poisson’s ratio material and biomimetic tendon reinforced material, were introduced in this study. To estimate the effective material properties for structural analyses and to optimally design such materials, a set of suitable homogenization methods was developed that provided an effective means for the multiscale modeling of MAC materials. First, a strain-based homogenization method was developed using an approach that separated the strain field into a homogenized strain field and a strain variation field in the local cellular domain superposed on the homogenized strain field. The principle of virtual displacements for the relationship between the strain variation field and the homogenized strain field was then used to condense the strain variation field onto the homogenized strain field. The new method was then extended to a stress-based homogenization process based on the principle of virtual forces and further applied to address the discrete systems represented by the beam or frame structures of the aforementioned MAC materials. The characteristic modes and the stress recovery process used to predict the stress distribution inside the cellular domain and thus determine the material strengths and failures at the local level are also discussed.
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References
Ma Z D. Homogenization method for designing novel architectured cellular materials. In: Proceedings of VII ECCOMAS Congress. Crete Island, 2016
Fleck N A, Deshpande V S, Ashby M F. Micro-architectured materials: Past, present and future. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010, 466 (2121): 2495–2516
Wang Y Q, Chen F F, Wang M Y. Concurrent design with connectable graded microstructures. Computer Methods in Applied Mechanics and Engineering, 2017, 317: 84–101
Alexandersen J, Lazarov B S. Topology optimization of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner. Computer Methods in Applied Mechanics and Engineering, 2015, 290: 156–182
Ma Z D. US Patent, 7910193, 2011–03-22
Ma Z D. US Patent, 7563497, 2009–07-21
Ma Z D, Cui Y. US Patent, 20110117309, 2011–05-19
Weinan E, Engquist B, Li X, et al. The heterogeneous multiscale methods: A review. Communications in Computational Physics, 2004, 2(3): 367–450
Kanouté P, Boso D P, Chaboche J L, et al. Multiscale methods for composites: A review. Archives of Computational Methods in Engineering, 2009, 16(1): 31–75
Nguyen V P, Stroeven M, Sluys L J. Multiscale continuous and discontinuous modeling of heterogeneous materials: A review on recent developments. Journal of Multiscale Modelling, 2011, 3(4): 229–270
Sanchez-Palencia E. Non-Homogenous Media and Vibration Theory. Berlin: Springer, 1980
Benssousan A, Lions J L, Papanicoulau G. Asymptotic analysis for periodic structures. Amsterdam: Elsevier, 1978
Cioranescu D, Paulin J S J. Homogenization in open sets with holes. Journal of Mathematical Analysis and Applications, 1979, 71(2): 590–607
Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197–224
Ma Z D, Kikuchi N, Cheng H C. Topological design for vibrating structures. Computer Methods in Applied Mechanics and Engineering, 1995, 121(1–4): 259–280
Arabnejad S, Pasini D. Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods. International Journal of Mechanical Sciences, 2013, 77: 249–262
Terada K, Kikuchi N. A class of general algorithms for multi-scale analyses of heterogeneous media. Computer Methods in Applied Mechanics and Engineering, 2001, 190(40–41): 5427–5464
Abdulle A, Bai Y. Reduced-order modelling numerical homogenization. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 2014, 372(2021): 20130388
Cong Y, Nezamabadi S, Zahrouni H, et al. Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling. International Journal for Numerical Methods in Engineering, 2015, 104(4): 235–259
Dos Reis F, Ganghoffer J F. Discrete homogenization of architectured materials: Implementation of the method in a simulation tool for the systematic prediction of their effective elastic properties. Technische Mechanik, 2010, 30: 85–109
Guyan R J. Reduction of stiffness and mass matrices. AIAA Journal, 1965, 3(2): 380
Lakes R S. Negative Poisson’s ratio materials. Science, 1987, 238 (4826): 551
Zhou G, Ma Z D, Li G, et al. Design optimization of a novel NPR crash box based on multi-objective genetic algorithm. Structural and Multidisciplinary Optimization, 2016, 54(3): 673–684
Ma Z D, Liu Y Y, Liu X M, et al. US Patent/Chinese patent, 8544515/201110401962.4, 2013–10-01
Ma Z D. US Patent, 9376796, 2016–06-18
Ma Z D, Liu Y Y. US Patent, 20110029063, 2011–02-03
Ma Z D, Wang H, Cui Y, et al. Designing an innovative composite armor system for affordable ballistic protection. In: Proceedings of 25th Army Science Conference. Orlando, 2006
Jiang D, Liu Y, Qi C, et al. Innovative Composite Structure Design for Blast Protection. SAE Technical Paper 2007–01-0483. 2007
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This work was supported by MKP Structural Design Associates, Inc., a corporation in Ann Arbor, Michigan, USA.
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Ma, ZD. Macro-architectured cellular materials: Properties, characteristic modes, and prediction methods. Front. Mech. Eng. 13, 442–459 (2018). https://doi.org/10.1007/s11465-018-0488-8
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DOI: https://doi.org/10.1007/s11465-018-0488-8