Strong Ellipticity Conditions for Orthotropic Bodies in Finite Plane Strain

Abstract

Necessary and sufficient conditions for strong ellipticity of the equilibrium equations governing finite plane deformations are established for the class of orthotropic and compressible hyperelastic materials. The conditions are then specialized to the case of an orthotropic material having the symmetry axes parallel to the principal directions of deformation. This case is relevant in experimental protocols employed in the characterization of constitutive relations of rubber-like materials and biological tissues. The classical conditions for infinitesimal linear elasticity and isotropic finite elasticity are recovered as particular cases.