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Fracture of viscoelastic materials is considered to be a complex phenomenondue to their highly rate sensitive behavior. In this context, we are interestedin the quasi-static response of a viscoelastic solid subjected to damage. Thispaper outlines a new incremental variational based approach and itscomputational implementation to model damage in viscoelastic solids. Thevariational formalism allows us to embed the local constitutive equations intoa global incremental potential, the minimization of which provides the solutionto the mechanical problem. Softening damage models in their local form areknown to result in spurious mesh-sensitive results, and hence non-locality (orregularization) has to be introduced to preserve the mathematical relevance ofthe problem. In the present paper, we consider two different regularizationtechniques for the viscoelastic damage model : a particular phase-field and alip-field approach. The model parameters are calibrated to obtain someequivalence between both these approaches. Numerical results are then presentedfor the bidimensional case and both these approaches compare well. Numericalresults also demonstrate the ability of the model to qualitatively representthe typical rate-dependent behaviour of the viscoelastic materials. Besides,the novelty of the present work lies in the use of lip-field approach for thefirst time in a viscoelastic context.

Variational Approach to Viscoelastic Fracture : Comparison of a phase-field and of a lip-field approach