On material representation and constitutive branching in finite compressible elasticity

Abstract The mechanical properties of two porous rubbers of different compressibility have been investigated experimentally and represented by aid of a particular isotropic strain-energy function constructed by means of separable distortional and dilatational terms. It is shown that a reduced form of the adopted strain-energy function offers definite advantages for evaluation of experimental data and reproduces well the behaviour of the investigated materials under three different loadings; uniaxial tension, plane strain tension and equibiaxial tension. The possibility of homogeneous branching from fundamental paths of the associated motions is examined and illustrated in detail for axisymmetric loading employing constitutive properties pertinent to the two materials tested.