A fast elasto-plastic formulation with hierarchical matrices and the boundary element method

Abstract

Boundary element methods offer some advantages for the simulation of tunnel excavation since the radiation condition is implicitly fulfilled and only the excavation and ground surfaces have to be discretized. Hence, large meshes and mesh truncation, as required in the finite element method, are avoided. Recently, capabilities for efficiently dealing with inelastic behavior and ground support have been developed, paving the way for the use of the method to simulate tunneling. However, for large scale three dimensional problems one drawback of the boundary element method becomes prominent: the computational effort increases quadratically with the problem size. To reduce the computational effort several fast methods have been proposed. Here a fast boundary element solution procedure for small strain elasto-plasticity based on a collocation scheme and hierarchical matrices is presented. The method allows the solution of problems with the computational effort and sparse storage increasing almost linearly with respect to the problem size.