Tailoring Materials for Specific Needs

Abstract

This paper describes a method to design the periodic microstructure of a material to obtain specified constitutive parameters. The problem can be called an inverse homogenization problem and is formulated as an optimization problem of finding the microstructure with the lowest possible weight which fulfills the specified behavioural requirements. A full ground structure known from topology optimization of trusses is used as starting guess for the optimization algorithm, which implies that the optimal microstructure of a base cell is found from a truss structure with 120 possi ble members in the 2-dimensional case and 2016 possible members in the 3-dimensional case. The material parameters are found by a numerical homogenization method using finite elements to model the representative base cell, and the optimization problem is solved by an optimality criteria method.

Numerical examples in two and three dimensions show that it is possible to design materials with many different properties, including isotropic materials with Poisson's ratio close to — 1 and 0.5, us ing base cells modelled as truss structures. Some of the proposed base cells have been tested as macro models and methods to produce them in practice are discussed.