METHOD OF NEARBY PROBLEMS FOR LARGE DEFORMATION ANALYSIS OF NEARLY INCOMPRESSIBLE HYPERELASTICITY

Abstract

The method of nearby problems (MNP) developed by Roy et al. is a sophisticated verification procedure, in which the problems with exact solutions near the target problem of interest can be generated by a curve fitting of a numerical solution to a continuous function. In this work, we apply this approach to large deformation problems of nearly incompressible hyperelasticity. Nearby solutions are constructed by the projection of a finite element solution of displacement onto an approximating function space using the inner product in the Sobolev space H₁. In this projection, a penalty term associated with volumetric deformation is introduced to impose the nearly incompressible property on nearby solutions.