Microstructural Stress Shape Optimization Using the Level Set Method

Abstract

This paper applies stress-based shape optimization to microstructures, a scarcely explored topic in the literature. As the actual stresses arising at the macroscopic structure are scale separated, the microstrucural stress is considered herein as the state of a representative volume element (RVE) after applying test unit strain load cases, not related to the macroscale loads. The three stress states in 2D are aggregated via p-norm functions, which are used for stress minimization. A stress-based level set method is applied. The method linearizes the objective and constraint functions and solves an optimization problem at every iteration to obtain the boundary velocities. The Ersatz material approach is used to compute the stiffness of the elements sliced by the boundary. A single hole inclusion microstructure is optimized for minimum stress in order to verify the methodology.