On the Calculation of Displacement, Stress, and Strain Induced by Triangular Dislocations

Abstract Integral equation‐based methods in elasticity require the calculation of integrals that involve a singular (or weakly singular) matrix Green’s function and a traction or displacement vector field defined on a surface. A variety of numerical methods based on analytic quadratures have been developed for such calculations, using either rectangular or triangular surface patches. Unfortunately, without correction, these analytic rules are subject to numerical instabilities in certain parameter regimes. In this paper, we present a stable, semi‐analytic collection of quadrature rules that can be applied to both infinite medium and half‐space simulations. We describe our underlying approach and illustrate its performance with numerical examples. Online Material: Fortran routines.