On the states of stress and strain adjacent to a crack in a strain-limiting viscoelastic body

The viscoelastic Kelvin–Voigt model is considered within the context of quasi-static deformations and generalized with respect to a nonlinear constitutive response within the framework of limiting small strain. We consider a solid possessing a crack subject to stress-free faces. The corresponding class of problems for strain-limiting nonlinear viscoelastic bodies with cracks is considered within a generalized formulation stated as variational equations and inequalities. Its generalized solution, relying on the space of bounded measures, is proved rigorously with the help of an elliptic regularization and a fixed-point argument.