基于拓扑优化和非线性均匀化的有限应变压电材料计算设计
Computational Design of Finite Strain Auxetic Metamaterials via Topology Optimization and Nonlinear Homogenization
摘要：
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匀化方法相结合，提出了一种新的计算框架，用于设计在大应变范围内具有负泊松比的超材料。提出了一种基于宏观变形的泊松比度量方法，并通过直接数值模拟进行了验证。利用基于非线性均匀化的一致性优化公式，系统地研究了不同加载方向和不同单胞域的拉胀超材料设计。此外，扩展到多材料拉胀超材料的设计也被认为是，稳定的优化配方，以获得有限应变下的离散超材料拓扑结构。各种新的拉胀设计的基础上提出的框架。为了验证优化设计的性能，使用Bloch波方法和秩一凸性检查进行多尺度稳定性分析。如所展示的，短和/或长波长的不稳定性可以在加载过程中发生，导致微结构的周期性的变化，这可以影响优化设计的性能。
英文摘要：
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 wave method 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.
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