Boundary element method for finite elasticity

This paper describes some integral formulations and implementations of a Boundary Element Method to solve two- and three-dimensional finite deformation problems of rubber-like materials. The integral equations are formulated in terms of unknown incremental displacement and total boundary traction fields, or alternatively in terms of the incremental displacement and incremental boundary traction fields. The elastic material is either compressible or incompressible with given constitutive equations. Both formulations are implemented and tested. The uniaxial elongation and simple shear deformations of a model material are successfully simulated by both formulations. Some non-trivial examples are performed using the first formulation.