MATERIALS WITH PRESCRIBED CONSTITUTIVE PARAMETERS - AN INVERSE HOMOGENIZATION PROBLEM

This paper deals with the construction of materials with arbitrary pre scribed positive semi-definite constitutive tensors. The construction problem can be called an inverse problem of finding a material with gi ven homogenized coefficients. The inverse problem is formulated as a t opology optimization problem, i.e. finding the interior topology of a base cell such that cost is minimized and the constraints are defined by the prescribed constitutive parameters. Numerical values of the con stitutive parameters of a given material are found using a numerical h omogenization method expressed in terms of element mutual energies. Nu merical results show that arbitrary materials, including materials wit h Poisson's ratio - 1.0 and other extreme materials, can be obtained b y modelling the base cell as a truss structure. Furthermore, a wide sp ectrum of materials can be constructed from base cells modelled as con tinuous discs of varying thickness. Only the two-dimensional case is c onsidered in this paper but formulation and numerical procedures can e asily be extended to the three-dimensional case.