Asymptotic expansion homogenisation and topology optimisation of cellular materials

Abstract

Topology optimisation defines a set of tools associated to the modelling of an effective material domain within structural optimisation. Based on this type of optimisation, it is possible to obtain an optimal material distribution for several applications and requirements. Cellular materials are part of the most prominent materials today, both in terms of applications, and in terms of research and development. However, their potentially complex and heterogeneous structures carry some complexities, associated to the prediction of effective constitutive properties and to its design. Homogenisation procedures can provide answers for both cases. On the one hand, the asymptotic expansion homogenisation can be used to determine thermomechanical effective properties for these materials through the detailed modelling of representative unit-cells, in a flexible and accurate fashion, regardless of the type of constituent distribution. On the other hand, this homogenisation technique integrates a localisation procedure, able to obtain detailed information on the behaviour of the material within the unit-cell, giving way to local sensitivities that can be used to control optimisation procedures. This leads to a material topology optimisation approach, perfectly suited for the design of this type of material. Within this scope, this work focuses on the analysis of effective thermomechanical material properties of cellular materials designed with topology optimisation procedures.