Boundary elements for non-linear elasticity

A boundary element technique is employed to analyze perturbations in terms of small elastic deformations superimposed upon a given homogeneous strain. Plane strain deformations are considered of an incompressible hyperelastic solid within the elliptic range. The numerical method is based on a recently developed Green's function and boundary integral equations for non-linear incremental elastic deformations. The proposed approach is shown to yield bifurcation loads. In particular, strain localizations are analyzed as a special case of instability, and they are found to occur in the elliptic range as induced by perturbations.