This study is dedicated to the formulation of finite strain nonlocal elastoplastic topology optimization. In the primal problem, we employ the standard hyperelastic constitutive law and the Voce hardening laws to describe the elastoplastic response, the latter of which is enhanced by the micromorphic regularization to address the mesh-dependent issue of the finite element method or mesh-based methods. For the optimization problem, the objective function accommodates multiple objectives by writing it as the summation of several sub-functions. The continuous adjoint method is adopted for formulating the adjoint problem; therefore, the corresponding governing equations are written in a continuous manner, like the primal problem. Thus, these equations are independent of employed discretization methods and can be implemented into various simulation methodologies. In addition, the derived sensitivity is substituted into the reaction–diffusion equation to realize the update of the design variable. Both single-material (ersatz and genuine materials) and two-material (matrix and inclusion materials) topology optimizations are presented to demonstrate the promise and performance of the formulation. In particular, we discuss what values of material parameters should be given to the ersatz material, how the material nonlinearity affects the optimization result, and how the optimization trend alters by giving different values of weights of the objective function.

中文翻译：

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有限应变下非局部弹塑性的拓扑优化


本研究致力于制定有限应变非局部弹塑性拓扑优化。在原始问题中，我们采用标准的超弹性本构定律和 Voce 硬化定律来描述弹塑性响应，后者通过微态正则化得到增强，以解决有限元方法或基于网格的方法的网格依赖问题。对于优化问题，目标函数通过将其编写为多个子函数的总和来容纳多个目标。采用连续伴随法对伴随问题进行公式化;因此，相应的控制方程是以连续的方式编写的，就像 Primal 问题一样。因此，这些方程独立于所采用的离散化方法，并且可以在各种仿真方法中实现。此外，将导出的灵敏度代入反应-扩散方程中，以实现设计变量的更新。介绍了单一材料（仿制和真实材料）和双材料（基体和夹杂物材料）拓扑优化，以证明配方的前景和性能。特别是，我们讨论了应该为仿制材料提供哪些材料参数值，材料非线性如何影响优化结果，以及通过给出目标函数的不同权重值来改变优化趋势。