Multi-axial strain-stiffening elastic potentials with energy bounds: explicit approach based on uniaxial data

According to the well-known models for rubberlike elasticity with strainstiffening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxial potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.