Level set-based inverse homogenisation of three-dimensional piezoelectric materials

TL;DR

This paper introduces a level set-based topology optimization method for designing 3D piezoelectric materials with improved properties, demonstrating scalable solvers and robust structures for sensor and actuator applications.

Contribution

It develops a memory-distributed level set approach combined with efficient solvers for inverse homogenization of piezoelectric materials, providing new high-performance metamaterial designs.

Findings

Identified scalable iterative solvers for homogenization equations.

Designed robust piezoelectric metamaterials with enhanced properties.

Provided open-source implementation for community use.

Abstract

In this paper we use memory-distributed level set-based topology optimisation to design three-dimensional periodic piezoelectric materials with enhanced properties. We compare and assess several existing iterative solvers with respect to their weak scalability and find that an approximate Schur complement preconditioned generalized minimal residual method method demonstrates the best performance and scalability for solving the piezoelectric homogenisation equations. We use the developed techniques to computationally design high-resolution piezoelectric metamaterials with enhanced stiffness and piezoelectric properties that yield new insights into material design for sensor, hydrophone, and actuator applications. We suggest two robust structures with no fine-scale features that exhibit enhanced piezoelectric properties several times larger than those of the base material. We find that level set-based topology optimisation is well suited to problems involving piezoelectricity and has the advantage of avoiding large regions of intermediate density material. Our memory-distributed level-set implementation is open source and provided for practitioners in the community.