AN ALTERNATIVE MODEL FOR ANISOTROPIC ELASTICITY BASED ON FABRIC TENSORS

Motivated by the mechanical analysis of multiphase or damaged material s, a general approach relating fabric tensors characterizing microstru cture to the fourth rank elasticity tensor is proposed. Using a Fourie r expansion in spherical harmonics, the orientation distribution funct ion of a positive, radially symmetric microstructural property is appr oximated by a scalar and a symmetric, traceless second rank tenser. Fo llowing this approximation, a general expression of the elastic free e nergy potential is derived from representation theorems for anisotropi c scalar functions. Based on a homogeneity assumption for the elastic constitutive law with respect to the microstructural property, a parti cular elasticity model is developed that involves three independent co nstants beside the fabric tensors. Strict positive definiteness of the corresponding elasticity tensor is ensured under explicit conditions on the independent constants for arbitrary fabric tensors.