Equivalent and separable strain-energy functions in compressible, finite elasticity

A material non-uniqueness is identified for isotropic, homogeneous, hyperelastic, compressible materials. This non-uniqueness is a special case of the hyperelastic null Lagrangian. Equivalence classes of strain-energy functions (SEFs) are then obtained. This equivalence can be used to extend in a natural way some of the common SEF used in incompressible elasticity to compressible elasticity. The familiar Valanis-Landel separable form of the SEF for incompressible materials is extended in this way. Some necessary restrictions are imposed on this new form and its behaviour in uniaxial tension is discussed. Previous problems in using the Valanis-Landel form of the SEF in compressible elasticity have been overcome.