A boundary element technique for incremental, non-linear elasticity. Part I: Formulation.

Incremental elastic deformations superimposed upon a given homogeneous strain are analyzed with a boundary element technique. This is based on a recently-developed Green's function for non-linear incremental elastic deformations. Plane strain perturbations are considered of a broad class of incompressible material behaviours (including hyper-, hypoelastic and Navier–Stokes constitutive equations) within the elliptic range. Numerical treatment of the problem is detailed. A possibility of employingthe method in the fully non-linear range is outlined, which yields a boundary element approach where the use of domain integrals is avoided, at least in a conventional sense. The methods for bifurcation and shear band analyses will be reported in Part II.