Use of “Simple Solutions” in Regularizing Hypersingular Boundary Integral Equations in Elastoplasticity

Abstract

The subject of this paper is the use of “simple solutions” or “modes” to regularize a hypersingular boundary integral equations (HBIE) for small strain elastoplasticity. A particularly simple form of the regularized HBIE is obtained by the use of three global “modes” of deformation: rigid-body displacement, linear displacement, and a fully constrained plastic solution. The resulting regularized HBIE is used in an implicit boundary element method (BEM) scheme for solving elastoplasticity problems. Numerical results are presented for an illustrative plane-strain example.