Homogenization-based computational design and two-scale performance optimization of electroactive structures

Abstract

Macroscopic materials and structures with enhanced characteristics have been extensively studied in the context of solid mechanics. The advantages of mi- crostructured materials with active constituents have been reported in the lit- erature. In view of tunable microstructures, further intriguing traits of such materials can be achieved through imposing external stimuli. The ultimate goal of the present study is to establish a homogenization-based computational design framework to actively control the time-varying macroscopic stress response and behavior of structures with piezoelectric constituents. This is accomplished by temporally adapting the macroscopic electric field enforced on a microstructure and controlling the time-variation of the macroscopic electric potential imposed on a macroscopic solid. This periodic microstructure is optimized in a non- restrictive design space that embodies not only the topology, but also anisotropic material orientation and the unit cell geometry. In order to enrich the optimiza- tion space to capture the intriguing time-varying mechanical aspects, additional optimization variables, namely performance variables, are developed. Extensive numerical investigations are conducted to test the limits of this framework based on the discreteness of the microstructure and the accurateness of attaining the targeted mechanical behavior. The overall computational work is implemented through a parallel C++-based in-house FE program.