A jigsaw puzzle framework for homogenization of high porosity foams

TL;DR

This paper presents a novel homogenization framework for high porosity metallic foams, combining first-order bounds with Wang tilings to generate large representative samples for effective property estimation.

Contribution

It introduces a jigsaw puzzle approach using Wang tilings for homogenizing metallic foams, specifically applied to extit{Alporas} foam, integrating bounds and finite element analysis.

Findings

Derived effective property bounds for extit{Alporas} foam.

Validated the approach against experimental and numerical data.

Discussed the limitations of 2D modeling for foam homogenization.

Abstract

An approach to homogenization of high porosity metallic foams is explored. The emphasis is on the \Alporas{} foam and its representation by means of two-dimensional wire-frame models. The guaranteed upper and lower bounds on the effective properties are derived by the first-order homogenization with the uniform and minimal kinematic boundary conditions at heart. This is combined with the method of Wang tilings to generate sufficiently large material samples along with their finite element discretization. The obtained results are compared to experimental and numerical data available in literature and the suitability of the two-dimensional setting itself is discussed.