Abstract
AbstractIn 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 discretization-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.
Funder
Università degli Studi di Napoli Federico II
Compagnia di San Paolo
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Ministero dell’Università e della Ricerca
Austrian Science Fund
Publisher
Springer Science and Business Media LLC
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