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In the one-dimensional isothermal case, we introduce a simple model ofnonlinear viscoelasticity within the Rational Extended Thermodynamics (RET)framework. The differential system is entirely determined by the universalprinciples of RET, exhibiting symmetric hyperbolic form and ensuring theexistence of smooth solutions for appropriately small initial data. In thelinear case, the system reduces to the well-known Maxwell model, therebyrepresenting a plausible nonlinear extension of the Maxwell-type model.

A Nonlinear approach to Viscoelasticity via Rational Extended Thermodynamics