A generalization of Hencky’s strain-energy density to model the large deformations of slightly compressible solid rubbers

A power-law relationship between the stretches has been shown to describe the inherent slight compressibility of isotropic solid rubbers in simple tension. It is well known that the Hencky strain-energy function predicts such a kinematic power-law relationship. Although the resulting constitutive relation adequately models the stress response for moderate deformations, it is not capable of predicting the stress response for large deformations. A strain-energy function for slightly compressible rubber is derived that both incorporates the kinematic power-law relation and reduces to the Hencky form on using a simple linearization process. Special forms of this new general strain-energy function are shown to be consistent with the stress–stretch experimental data in simple tension over a large range of axial stretches. This general form is also shown to be consistent with the observed behavior of rubbers in compression tests involving moderate volume changes.