A model for rubber elasticity

A constitutive equation for rubber-like materials is developed using the left stretch tensor. This process starts with a model for hyperelastic solids based on a separable energy function. This model accurately fits extensional data for vulcanized natural rubber until the onset of hysteresis at intermediate strains. Better predictions outside the hyperelastic range are obtained by directly modifying this constitutive equation to describe limited extensibility. The resulting model accurately fits biaxial, planar, and uniaxial extension data for a variety of rubber-like materials using three constants. This model also predicts simple shear results derived from planar extension data and characterizes inflation of spherical membranes for elastomers and soft tissue. A final modification accurately describes hardening associated with crystallization at large tensile strains.