Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids

Viscoelastic fluids are non-Newtonian that exhibit both "viscous" and "elastic" characteristics in virtue of mechanisms to store energy produce entropy. Usually the storage properties such modelled using same concepts as classical theory nonlinear solids. Recently new models for elastic solids have been successfully developed by appealing implicit constitutive relations, these offer a different perspective old topic response materials. In particular, sub-class namely relations wherein left Cauchy-Green tensor is expressed function stress interest. We show how use this it development mathematical viscoelastic fluids, we provide discussion thermodynamic underpinnings models. focus on Gibbs free instead Helmholtz energy, standard Giesekus/Oldroyd-B models, alternative approach works case well-known The proposed straightforward generalise more complex setting might be impractical even inapplicable.