Homogeneous Hyperelastic Potentials

Strain energy density potential for isotropic linear hyperelastic solids is known to be a second degree homogeneous quadratic polynomial function of the strain tensor components. More general homogeneous potentials have been proposed for nonlinear hyperelastic materials. In this Paper, general properties of such single and mixed order homogeneous hyperelastic complementary of small strains are investigated. The relation between the strain energy and potential energy homogeneous hyperelastic potentials is explored. Possible restrictions on constitutive equations for isotropic solids are discussed. Significance of the present investigation for constitutive modeling is evaluated.