Abstract: We have obtained natural characterization of incompressibility constraint, leading to stressstrain relations for isotropic, incompressible hyperelastic collagen materials using the logarithmic strain tensor measure. We have also obtained two sets of suitablydefined invariants of the logarithmic strain tensor. Constitutive equations for logarithmic strain and Cauchy stress are derived directly from the elastic energy density. Comparisons between the model and experimental data in uniaxial tension indicate efficiency of the constitutive model and dependence of material parameters.

Key words: constitutive equation, hyperelastic collagen material, invariant, logarithmic strain