NUMERICAL ANALYSIS OF SINGULARITIES IN TWO DIMENSIONS. PART 2: COMPUTATION OF GENERALIZED FLUX/STRESS INTENSITY FACTORS

A numerical method for the computation of the generalized flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties. Such singularities are of great interest from the point of view of failure initiation: The eigenpairs, computed in a companion paper,ʹ characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs/GSIFs. This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.