A field boundary element formulation for material nonlinear problems at finite strains

Abstract

A boundary element formulation for geometrical nonlinear problems is presented, which is applicable for arbitrary constitutive equations based on the concept of hyperelastic response relative to an intermediate configuration. This includes purely hyperelastic problems at large elastic strains. In contrast to other formulations, the Total-Lagrange framework employed in this work significantly increases the numerical efficiency as the system matrices remain constant during the incremental solution and have to be computed only once. A nonlinear set of equations with an identical structure for both boundary and internal unknowns is derived. The basic unknowns are displacement gradients, which are calculated via integral equations and not by differentiation of the shape functions. The formulation can be consistently linearised to allow for the implementation of efficient iteration schemes using gradients, e.g. the Newton-Raphson scheme.