New compressible hyper-elastic models for rubberlike materials

Multi-axial hyper-elastic models for large strain rubberlike elasticity are established in a broad sense free of the commonly assumed constraint of incompressibility. Results are derived directly from uniaxial stress-strain relations by means of certain explicit procedures. Novelties in four respects are incorporated in the new models: (i) constitutive parameters of direct physical meanings may be introduced to represent features of rubberlike elasticity; (ii) the usual incompressibility constraint is no longer assumed and relevant issues may be rendered irrelevant; (iii) the incompressibility case may be derived as a natural limit; and (iv) accurate agreement with benchmark data for several deformation modes may be achieved, including uniaxial extension, equi-biaxial extension as well as plane-strain extension and others.