Computational Design of Finite Strain Auxetic Metamaterials via Topology Optimization and Nonlinear Homogenization
Computational Design of Finite Strain Auxetic Metamaterials via Topology Optimization and Nonlinear Homogenization
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DOI：
10.1016/j.cma.2019.07.027
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
Guodong Zhang;Kapil Khandelwal
中科院分区：
文献类型：
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作者：
Guodong Zhang;Kapil Khandelwal
这项工作提出了一种新颖的计算框架，用于设计在大应变范围内具有负泊松比的超材料，通过将基于密度的拓扑优化与混合应力/变形驱动的非线性均质化方法相结合。提出了一种基于宏观变形的泊松比测量方法，并通过直接数值模拟进一步验证了该方法。通过基于非线性均质化的一致优化公式，系统地探索了不同加载方向和不同晶胞域的拉胀超材料设计。此外，还考虑了对多材料拉胀超材料设计的扩展，并提出了稳定的优化公式以获得有限应变下的离散超材料拓扑。基于所提出的框架获得了各种新的拉胀设计。为了验证优化设计的性能，使用布洛赫分析和一阶凸性检查进行多尺度稳定性分析。正如所证明的，在加载过程中可能会出现短波长和/或长波长的不稳定性，导致微结构的周期性发生变化，从而影响优化设计的性能。
A novel computational framework for designing metamaterials with negative Poisson’s ratio over a large strain range is presented in this work by combining the density-based topology optimization together with a mixed stress/deformation driven nonlinear homogenization method. A measure of Poisson’s ratio based on the macro deformations is proposed, which is further validated through direct numerical simulations. With the consistent optimization formulations based on nonlinear homogenization, auxetic metamaterial designs with respect to different loading orientations and with different unit cell domains are systematically explored. In addition, the extension to multimaterial auxetic metamaterial designs is also considered, and stable optimization formulations are presented to obtain discrete metamaterial topologies under finite strains. Various new auxetic designs are obtained based on the proposed framework. To validate the performance of optimized designs, a multiscale stability analysis is carried out using the Bloch analysis and rank-one convexity check. As demonstrated, short and/or long wavelength instabilities can occur during the loading process, leading to a change of periodicity of the microstructure, which can affect the performance of an optimized design.