Design of multi-layer materials using inverse homogenization and a level set method

TL;DR

This paper presents a method combining inverse homogenization and level set techniques to design multi-layer micro-structures with tailored mechanical properties, such as negative Poisson ratios, by optimizing their micro-geometry.

Contribution

It introduces a novel approach integrating inverse homogenization with level set and shape derivatives for micro-architecture design of multi-layer materials.

Findings

Successfully designed auxetic micro-structures with desired properties

Enhanced stress capacity through multi-layer configurations

Validated the algorithm with multiple micro-structure examples

Abstract

This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the shape derivative in the sense of Hadamard to identify material regions and track boundary changes within the context of the smoothed interface. The level set method and the shape derivative obtained in the smoothed interface context allows to capture, within the unit cell, the optimal micro-geometry. We test the algorithm by computing several multi-layer auxetic micro-structures. The multi-layer approach has the added benefit that contact during movement of adjacent "branches" of the micro-structure can be avoided in order to increase its capacity to withstand larger stresses.