With the aid of the elasticviscoelastic correspondence principle, the boundary element developed for the linear anisotropic elastic solids can be applied directly to the linear anisotropic viscoelastic solids in the Laplace domain. Greens functions for the problems of two-dimensional linear anisotropic elastic solids containing holes, cracks, inclusions, or interfaces have been obtained analytically using Strohs complex variable formalism. Through the use of these Greens functions and the correspondence principle, special boundary elements in the Laplace domain for viscoelastic solids containing holes, cracks, inclusions, or interfaces are developed in this paper. Subregion technique is employed when multiple holes, cracks, inclusions, and interfaces exist simultaneously. After obtaining the physical responses in Laplace domain, their associated values in time domain are calculated by the numerical inversion of Laplace transform. The main feature of this proposed boundary element is that no meshes are needed along the boundary of holes, cracks, inclusions and interfaces whose boundary conditions are satisfied exactly. To show this special feature by comparison with the other numerical methods, several examples are solved for the linear isotropic viscoelastic materials under plane strain condition. The results show that the present BEM is really more efficient and accurate for the problems of viscoelastic solids containing interfaces, holes, cracks, and/or inclusions.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics