Abstract
This paper presents a topology optimization framework for designing periodic viscoplastic microstructures under finite deformation. To demonstrate the framework, microstructures with tailored macroscopic mechanical properties, e.g., maximum viscoplastic energy absorption and prescribed zero contraction, are designed. The simulated macroscopic properties are obtained via homogenization wherein the unit cell constitutive model is based on finite strain isotropic hardening viscoplasticity. To solve the coupled equilibrium and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. A well-posed topology optimization problem is formulated by restriction using filtration which is implemented via a periodic version of the Helmholtz partial differential equation filter. The optimization problem is iteratively solved with the method of moving asymptotes, where the path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by optimizing several two-dimensional continuum composites exposed to a wide range of macroscopic strains.
Highlights
Topology optimization is a powerful tool that enables engineers to enhance structural performance
To model this microstructural response, nonlinear finite strain theory should be incorporated into the composite topology optimization
Most topology optimization frameworks that incorporate nonlinearities focus on macroscopic design; research on composite material design via inverse homogenization that incorporates inelastic constituents is scarce
Summary
Topology optimization is a powerful tool that enables engineers to enhance structural performance. Most topology optimization frameworks that incorporate nonlinearities focus on macroscopic design; research on composite material design via inverse homogenization that incorporates inelastic constituents is scarce Examples of such studies include the recent works by Chen et al (2018) and Alberdi and Khandelwal (2019) which assume infinitesimal deformation. Several studies (Bogomolny and Amir 2012; Wallin et al 2016; Zhang et al 2017; Amir 2017; Ivarsson et al 2018; Zhang and Khandelwal 2019) of topology optimization for path-dependent problems have successfully adopted the adjoint sensitivity recipe presented in Michaleris et al (1994) This requires the evaluation and storage of the primal response trajectory, and the solution of a terminal-valued adjoint sensitivity problem. The paper is closed by presenting several numerical examples of optimized composite designs and drawing conclusions
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