Esh3D, an Analytical and Numerical Hybrid Code for Full Space and Half-Space Eshelby's Inclusion Problems

Abstract

I present an open source code Esh3D that evaluates the quasi-static elastic displacement and stress fields perturbed by ellipsoidal inclusions, known as the Eshelby solution. The improvement over my previous work includes obtaining solutions in half-space by numerically canceling the traction to stage a free surface. The discrete numerical domain allows nonplanar surface. I first briefly introduce the ellipsoidal inclusion problem and solution evaluation. Then, I describe the traction cancellation method in forming the half-space solutions. Next, I emulate a planar fault with a low aspect ratio ellipsoid and compare the half-space solution against the well-known Okada solution for flat and topographic surfaces. Finally, I provide comparisons between the full space and half-space solutions to illustrate the free surface effects on the displacement and stress fields.