10. The Boundary Element Method for Viscoelasticity Problems

The Boundary Element Method (BEM) is derived through the discretization of an integral equation (the classical Somigliana identity, first published in 1886). An interesting account of BEM early development may be found in (Cheng and Cheng 2005). This formulation can only be derived for certain classes of problems and hence, is not as widely applicable as the finite element method. However, when applicable, it often results in numerical methods that are easier to use and computationally more efficient. The advantages of the BEM arise from the fact that only the boundary of the domain requires sub-division. In cases where the domain is exterior to the boundary (e.g. the atmosphere surrounding an airplane, the soil surrounding a tunnel, the material surrounding a crack tip) the advantages of the BEM are even greater as the equation governing the infinite domain is reduced to an equation over the (finite) boundary. In this chapter we shortly review two alternative procedures for the solution of problems in linear viscoelasticity: the solution in the Laplace transformed domain and the use of a general inelastic formulation. For the latter, we make reference to the use of the Dual Reciprocity Method (DRM) that allows a pure boundary formulation.