New compressible hyper-elastic models for rubberlike materials

Abstract

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.