Topology optimization of dissipative metamaterials at finite strains based on nonlinear homogenization
Topology optimization of dissipative metamaterials at finite strains based on nonlinear homogenization
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DOI：
10.1007/s00158-020-02566-8
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发表时间：
2020-05
影响因子：
3.9
通讯作者：
Guodong Zhang;Kapil Khandelwal
中科院分区：
文献类型：
--
作者：
Guodong Zhang;Kapil Khandelwal
这项研究提出了一种新的计算框架，设计最佳的耗散（阻尼）的超材料在有限变形下的时间相关的负载条件。在这个框架中，有限应变计算均匀化集成了基于密度的多材料拓扑优化。此外，一个一致的有限应变粘弹性模型被合并在一起的分析路径相关的灵敏度分析。考虑了有和没有刚度和质量约束的优化公式，并得到了各种新的阻尼超材料设计，联合收割机软粘弹性和刚性超弹性材料相结合。多尺度稳定性分析，使用布洛赫波分析和秩-1凸性检查也进行了调查的优化设计的稳定性。稳定性分析表明，包含空隙或软材料相可以使超材料更容易失去微观和宏观稳定性。此外，可调超材料的概念进行了探讨，其中超材料的响应转向一个稳定的变形路径，通过定制的设计与预选的微屈曲模式。
This study presents a novel computational framework for designing optimal dissipative (damping) metamaterials under time-dependent loading conditions at finite deformations. In this framework, finite strain computational homogenization is integrated with a density-based multimaterial topology optimization. In addition, a thermodynamically consistent finite strain viscoelasticity model is incorporated together with an analytical path-dependent sensitivity analysis. Optimization formulations with and without stiffness and mass constraints are considered, and various new damping metamaterial designs are obtained that combine soft viscoelastic and stiff hyperelastic material phases. Multiscale stability analysis using the Bloch wave analysis and rank-1 convexity checks is also carried out to investigate stability of the optimized designs. Stability analyses demonstrate that the inclusion of voids or soft material phases can make a metamaterial more prone to lose micro and macro-stability. Furthermore, the concept of tunable metamaterials is explored wherein metamaterial’s response is steered towards a stable deformation path by tailoring the design with a preselected micro buckling mode.