Holes, cracks, or inclusions in two-dimensional linear anisotropic viscoelastic solids

By combining the elastic-viscoelastic correspondence principle with the analytical solutions of anisotropic elasticity, the problems of two-dimensional linear anisotropic viscoelastic solids can be solved directly in the Laplace domain. After getting the solutions in the Laplace domain, their associated solutions in real time domain can be determined by numerical inversion of Laplace transform. Following this general adopted process, the problems of holes, cracks, or inclusions in two-dimensional linear anisotropic viscoelastic solids, which appear frequently in polymer matrix composites and cannot be solved directly by the commonly used commercial finite elements, are solved in this paper. Here, the hole can be elliptical or polygon-like; the crack can be a single crack, or two collinear cracks, or an interface crack; and the inclusion can be rigid, elastic or viscoelastic. The loads considered include the uniform load at infinity, and the point force applied at the arbitrary location. The solution of the point force is then employed as the fundamental solution of boundary element method which is used for further comparison of the analytical solutions. The accuracy and efficiency of the presented solutions are illustrated through four representative numerical examples which involve four isotropic viscoelastic and two anisotropic viscoelastic materials.