Rubber materials are used normally in large deformations, that is, in nonlinear conditions. So, nonlinear viscoelasticity is important for the characterization of rubber materials. So-called Payne effect, strain amplitude dependence of dynamic modulus, is one of the examples for nonlinear behaviors in rubber materials.

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The tensile deformation of thermoplastic polyurethanes (TPUs) with varying sizes of hard domain was investigated to produce a new form of constitutive equation. The equation is expressed using the plastic component of the deformation of the hard domains and a network component based on van der Waals' equation. A TPU formulation with a large hard domain shows a higher stress level and higher stress-strain gradient. It was found that the stress level is dominated by the plastic component, resulting from the stiffness of the hard domains and the stress gradient is determined by the network component, resulting from the extension of the soft segment chains between the hard domains.

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