Directional model for isotropic and anisotropic hyperelastic rubber-like materials

A material direction-dependent constitutive model has been formulated for large deformations for isotropic and anisotropic rubber-like materials. Although such materials are usually isotropic, anisotropic behavior has been observed in calendered plates of filled rubbers. Strain energy density function characterizing rubber-like materials is usually dependent on principal stretch ratios and thus is unable to account for anisotropy, whereas the proposed strain energy density depends on material directions and accounts for anisotropy. The material directions have simply been chosen using regular solid geometry. The strain energy density is given as the sum, over all material directions, of elementary directional strain energy densities. Then the elementary strain energy form is phenomenologically determined to account for the state of strain dependence of the material response. The model response is compared to uniaxial tension experimental data for anisotropic hyperelastic rubber-like materials and to uniaxial and biaxial tension for isotropic rubber-like materials.