Algorithms for the Calculation of Exact Displacements, Strains, and Stresses for Triangular Dislocation Elements in a Uniform Elastic Half Space

Abstract

We present algorithms for analytically calculating the displacements, strains, and stresses associated with slip on a triangular dislocation element (TDE) in a homogeneous elastic half space. Following previous efforts, the solution is constructed as a dislocation loop where the deformation fields for each of the three triangle legs are calculated by the superposition of two angular dislocations. In addition to the displacements at the surface we derive the displacements and strains at arbitrary depth. We give explicit formulas for the strains due to slip on an angular dislocation, the calculation of angular dislocation slip components, a method for identifying observation coordinates affected by a solid body translation, and rules for internally consistent vertex ordering allowing for the superposition of multiple TDEs. Examples of surface displacements and internal stresses are given and compared with rectangular representations of geometrically complex fault surfaces.