Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids

Abstract

A method of approach to the correlation of theory and experiment for incompressible isotropic elastic solids under finite strain was developed in a previous paper (Ogden 1972). Here, the results of that work are extended to incorporate the effects of compressibility (under isothermal conditions). The strain-energy function constructed for incompressible materials is augmented by a function of the density ratio with the result that experimental data on the compressibility of rubberlike materials are adequately accounted for. At the same time the good fit of the strain-energy function arising in the incompressibility theory to the data in simple tension, pure shear and equibiaxial tension is maintained in the compressible theory without any change in the values of the material constants. A full discussion of inequalities which may reasonably be imposed upon the material parameters occurring in the compressible theory is included.