Power-Law Solutions of Anisotropic Multi-material Elasticity Problems

Abstract

Singular solutions play a major role in many areas of linear elasticity theory. For example, the displacement field near corners of a structure composed of anisotropic linear elastic materials can be approximated asymptotically by a series of power-law functions. Especially for problems in fracture mechanics the knowledge of the singular exponents and also the functions themselves is fundamental. The focus of this work is to derive explicit formulas for such solutions. The main tool is a complex approach developed by Costabel and Dauge in there works. We show, how solutions can be derived for multi-material structures also covering multiple roots in the characteristic material equations and logarithmic solutions in the case of multiple singular exponents.