Traction-based Completed Adjoint Double Layer Boundary Element Method in elasticity

Abstract

This paper is concerned with a traction-based Completed Adjoint Double Layer Boundary Element Method to solve for the surface traction of a system of rigid particles embedded in an elastic matrix. The main feature of the method is a single layer representation of the displacement field, which leads to a system of second-kind integral equations for the traction field, the extreme eigenvalue of which could be deflated, allowing iterative solution strategies to be effectively applied. The method is therefore most suitable for large-scale simulations of particulate solids. The method is benchmarked against some known analytic solutions, including the difficult stress singularity problems at sharp edges. The effectiveness of the method in dealing with a large number of inclusions is also demonstrated with an elongational deformation problem involving up to 25 inclusions.