Stiffening by fiber reinforcement in soft materials: a hyperelastic theory at large strains and its application.

This work defines an incompressible, hyperelastic theory of anisotropic soft materials at finite strains, which is tested by application to the experimental response of fiber-reinforced rubber materials. The experimental characterization is performed using a uniaxial testing device with optical measures of the deformation, using two different reinforcing materials on a ground rubber matrix. In order to avoid non-physical responses of the underlying structural components of the material, the kinematics of the deformation are described using a novel deformation tensor, which ensures physical consistency at large strains. A constitutive relation for incompressible fiber-reinforced materials is presented, while issues of stability and ellipticity for the hyperelastic solution are considered to impose necessary restrictions on the constitutive parameters. The theoretical predictions of the proposed model are compared with the anisotropic experimental responses, showing high fitting accuracy in determining the mechanical parameters of the model. The constitutive theory is suitable to account for the anisotropic response at large compressive strains, opening perspectives for many applications in tissue engineering and biomechanics.