  In this paper we consider a dynamic model of fracture for viscoelastic
materials, in which the constitutive relation, involving the Cauchy stress and
the strain tensors, is given in an implicit nonlinear form. We prove the
existence of a solution to the associated viscoelastic dynamic system on a
prescribed time-dependent cracked domain via a discretisation-in-time argument.
Moreover, we show that such a solution satisfies an energy-dissipation balance
in which the energy used to increase the crack does not appear. As a
consequence, in analogy to the linear case this nonlinear model exhibits the
so-called viscoelastic paradox.
