On the strong closure of strains and stresses in linear elasticity

We consider the following special problem related to the optimal layout pro blems of materials: given two linear elastic materials, the elasticity tens ors of which are C-1 and C-2, and a force (f) over tilde, find the strong c losure of strains and stresses as the distribution of the materials varies, or, alternatively, find the sets of elasticity tensors which generate thes e strong closures. In this paper, it is shown that the local incompatibilit y conditions depending on C-1, C-2 and the local properties of strains or s tresses completely characterize these sets. A connection to multiple-well p roblems is established.