Multiple holes, cracks, and inclusions in anisotropic viscoelastic solids

Abstract

By using the elastic–viscoelastic correspondence principle, the problems with multiple holes, cracks, and inclusions in two-dimensional anisotropic viscoelastic solids are solved for the cases with time-invariant boundaries. Based upon this principle and the existing methods for the problems with anisotropic elastic materials, two different approaches are proposed in this paper. One is concerned with an analytical solution for certain specific cases such as two collinear cracks, collinear periodic cracks, and interaction between inclusion and crack, and the other is a boundary-based finite element method for the general cases with multiple holes, cracks, and inclusions. The former considers only specific cases in infinite domain and can be used as a reference for any other numerical methods, and the latter is applicable to any combination of holes, cracks and inclusions in finite domain, whose number, size and orientation are not restricted. Unlike the conventional finite element method or boundary element method which usually needs very fine meshes to get convergence solutions, in the proposed boundary-based finite element method no meshes are needed along the boundaries of holes, cracks and inclusions. To show the accuracy and efficiency of these two proposed approaches, several representative examples are implemented analytically and numerically, and they are compared with each other or with the solutions obtained by the finite element method.