A study on boundary integral equations for dynamic elastoplastic analysis for the plane problem by TD-BEM

The equivalent stress fundamental solution for the elastoplastic dynamic plane strain problem is proposed to transform the virtual work in the third direction to the plane. Subsequently, based on Betti reciprocal theorem, by adopting the time dependent fundamental solutions in terms of displacement, traction and equivalent stress, the boundary integral equations for dynamic elastoplastic analysis for the plane strain problem are established. The establishment procedures for the displacement and the stress boundary integral equations, together with the stress equation at boundary points, are presented in details, while the standard discretization both in time and space under the frame of time domain boundary element method (TD-BEM) and the solution of the algebraic equations are also briefly stated. Two verification examples are presented from different viewpoints, for elastic and elastoplastic analysis, for 1-D and 2-D geometries, and for finite and infinite domains. The TD-BEM formulation for dynamic elastoplastic analysis is presented for the plane strain problem as an example, where the formulation is also applicable for the plane stress problem by properly transforming the elastic constants and adopting the corresponding fundamental solutions. The equivalent stress fundamental solution for the elastoplastic dynamic plane strain problem is proposed to transform the virtual work in the third direction to the plane. Subsequently, the equivalent stress and the boundary integral equations for dynamic elastoplastic analysis for the plane strain problem, where a cavity under an uniformly distributed impact in an infinite medium, are established in the frame of the time domain boundary element method (TD-BEM).