Computational design of thermo-mechanical metadevices using topology optimization

Abstract

The present work has been conducted in order to introduce a novel approach for the design of mechanical devices conceived to manipulate the displacements field in linear elastic materials subjected to thermal gradients. Such an approach involves the solution of a topology optimization problem where the objective function defines the error in achieving a prescribed displacement field, and the mechanical device consists of two macroscopically distinguishable isotropic candidate materials. The material distribution is defined as a continuous function by following the solid isotropic microstructure (or material) with penalization (SIMP) method. The so-designed devices are easy to manufacture, since the design variables dictate the candidate materials distribution. Based on such an approach it is not necessary to devise further ways to simultaneously mimicking several thermal and mechanical effective properties, as required by coordinates transformation-based metamaterial design methods. Although the candidate materials are isotropic, the mechanical device behaves as a metamaterial allowing the desired manipulation of the displacements field. As an example, this topology optimization-based approach is applied to the design of an elastostatic cloaking device subjected to thermal gradients, considering also thermo-dependent mechanical properties.