Extending Esh3D Code to Solve Interacting Eshelby's Inhomogeneity Problems

Abstract

I present a new development of an open source code Esh3D in solving interacting Eshelby's inhomogeneity problems in whole, half, and finite spaces. The code resolves the interaction between multiple inhomogeneity bodies by assembling and solving a global linear system. For half or finite space problems, the code imposes Neumann and Dirichlet boundary conditions and resolves the surface-body interaction by hybridizing Eshelby's analytical solutions with a numerical part. I demonstrate the impact of multibody interaction and surface-body interaction by comparing the results of different problems in whole and finite spaces. This analytical-numerical hybrid approach, compared to conventional finite element method, is inexpensive and flexible in modeling multiple and evolving inhomogeneity bodies.