  Fracture of viscoelastic materials is considered to be a complex phenomenon
due to their highly rate sensitive behavior. In this context, we are interested
in the quasi-static response of a viscoelastic solid subjected to damage. This
paper outlines a new incremental variational based approach and its
computational implementation to model damage in viscoelastic solids. The
variational formalism allows us to embed the local constitutive equations into
a global incremental potential, the minimization of which provides the solution
to the mechanical problem. Softening damage models in their local form are
known to result in spurious mesh-sensitive results, and hence non-locality (or
regularization) has to be introduced to preserve the mathematical relevance of
the problem. In the present paper, we consider two different regularization
techniques for the viscoelastic damage model : a particular phase-field and a
lip-field approach. The model parameters are calibrated to obtain some
equivalence between both these approaches. Numerical results are then presented
for the bidimensional case and both these approaches compare well. Numerical
results also demonstrate the ability of the model to qualitatively represent
the typical rate-dependent behaviour of the viscoelastic materials. Besides,
the novelty of the present work lies in the use of lip-field approach for the
first time in a viscoelastic context.
