Multiple-integral viscoelastic constitutive equations

A class of nonlinear viscoelastic constitutive equations including the K-BKZ constitutive equations, linear viscoelasticity and the Green–Rivlin models is developed. A stored-energy functional is associated with each model in such a way that the energy dissipation rate is non-negative. The theory is developed for 1D viscoelasticity and extended to 3D viscoelastic media.