DESIGN ISOTROPIC MATERIALS USING ANISOTROPIC COMPONENTS VIA HOMOGENIZATION

This paper:studies some special situations when the G-limit of a seque nce of Gamma'-equivariant. matrices is Gamma-equivariant, but Gamma' i s only a proper subgroup of Gamma. For the particular case of periodic media, when only two components are involved, this is the case when t he microstructure (i.e. the geometry of the inclusion) can ''compensat e'' for the lack of symmetry of one of the components. After recalling a general result that gives a sufficient condition when; the G-conver gence preserve symmetry, we present a first example for diffusion in t he plane. The main argument is an a priori estimate, provided by the c ase of stratified materials, combined with a continuity argument. We a lso present an example when a special choice of the microstructure lea ds to a homogenized material having higher symmetry than both componen ts of the;mixture and a generalization to arbitrary geometries. (C) 19 98 Elsevier Science Ltd. All rights reserved.