Topology optimization for three‐dimensional elastoplastic architected materials using a path‐dependent adjoint method

Abstract

This article introduces a computational design framework for obtaining three-dimensional (3D) periodic elastoplastic architected materials with enhanced performance, subject to uniaxial or shear strain. A nonlinear finite element model accounting for plastic deformation is developed, where a Lagrange multiplier approach is utilized to impose periodicity constraints. The analysis assumes that the material obeys a von Mises plasticity model with linear isotropic hardening. The finite element model is combined with a corresponding path-dependent adjoint sensitivity formulation, which is derived analytically. The optimization problem is parametrized using the solid isotropic material penalization method. Designs are optimized for either end compliance or toughness for a given prescribed displacement. Such a framework results in producing materials with enhanced performance through much better utilization of an elastoplastic material. Several 3D examples are used to demonstrate the effectiveness of the mathematical framework. K E Y W O R D S adjoint sensitivity analysis, energy absorption, metamaterials, periodic boundary conditions, von Mises plasticity 1 INTRODUCTION Recent advances in manufacturing technologies have created many possibilities in materials development. 1 Architected materials are cellular or composite materials possessing combinations of properties unattainable using monolithic materials. Materials with excellent structural properties (stiff, strong, tough, and yet lightweight) are needed for aerospace and automotive industries. 2 Hence, architected materials are of high interest to scientists and engineers. The performance of such architected materials is dependent on the constituent materials, the volume fractions of the constituents, and the architecture (design geometry). 3-9 Nevertheless, most of the approaches used to develop these materials are based on experiments, intuition, and/or bioinspiration. 10,11

Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method

“…With enhanced computer performance and the development of finite element methods (FEM), TO has gained increasing interest from researchers and industries, especially with the recent improvements in the additive manufacturing realm [2,3]. TO algorithms have been implemented for various material and structural optimization applications, including thermoelasticity [4,5], plasticity [6,7], heat conduction and convection systems [8,9], wave propagation [10,11], and others.…”