Compression tests and constitutive models for the slight compressibility of elastic rubber-like materials

Constitutive models are proposed for the deformations of slightly compressible (or nearly incompressible) rubbers based solely on their experimentally observed response in compression tests. For small volume change, it has been observed in a variety of such tests that there is a linear relation between the applied pressure and volume change. We show how this relation leads to several different forms of the strain-energy density depending on the particular strain invariants used. The well known Levinson–Burgess strain-energy for slightly compressible rubber is recovered as a special case.