A Finite Element Method for Separable HRR Solutions in Bi-Material Systems

Separablesingular eigensolutions at points of geometric and/or material discontinuity are determined by the finite element method. The method is applicable to n-material anisotropic elastic behavior as shown by Pageau et al. (1995), and to n-material isotropic power-law hardening behavior, including the case of complex eigenvalues for plane stress, as shown by Zhang and Joseph (1996a,b,c). Separable HRR solutions for the nonlinear problem are limited to cases whereall materials have the same hardening exponent. This paper demonstrates these capabilities with several examples that have relevance to ceramic coatings on metal substrates. The examples include the elastic case of a crack touching an isotropic-orthotropic interface, and several power-law hardening cases for bi-material systems. Both plane strain and plane stress solutions are considered.