An explicit, direct approach to obtain multi-axial elastic potentials which accurately match data of four benchmark tests for rubbery materials—Part 2: general deformations

Abstract

In a previous study (Xiao in Acta Mechanica 223:2039–2063, 2012), an explicit, straightforward approach has been proposed to obtain multi-axial elastic potentials for incompressible rubberlike materials. With a new idea of treating compressibility behavior, we extend this explicit, straightforward approach for incompressible deformations to a general case of finite compressible deformations. From data of a uniaxial test and a simple shear test, we obtain unified forms of multi-axial compressible elastic potentials which accurately match data of four benchmark tests. Reduced results are presented for the slight compressibility case. In particular, we apply the new approach with a simple form of rational interpolating function with two poles and from the uniaxial case derive a simple form of multi-axial compressible potential with a strain limit. It is found that this strain limit is a counterpart of the well-known von Mises limit for stress in elastoplasticity. For highly elastic materials with strain stiffening effects, this simple compressible potential is shown to be in good accord with data of four tests from small to large deformations.