Systematic design of compliant morphing structures: a phase-field approach

TL;DR

This paper introduces a phase-field method for the systematic design of compliant morphing structures, ensuring solution existence and demonstrating effectiveness through numerical examples.

Contribution

It proposes a novel phase-field approximation for designing morphing structures with a perimeter penalty, proving convergence and providing an efficient numerical implementation.

Findings

Successful numerical examples demonstrate the method's effectiveness.

The phase-field approach ensures solution existence for the design problem.

Convergence of the approximation as regularization length approaches zero is proven.

Abstract

We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this sharp interface problem, prove its convergence as the regularization length approaches 0 and present an efficient numerical implementation. We illustrate the strengths of our approach through a series of numerical examples.