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

TL;DR

This paper introduces a variational method for modeling viscoelastic fracture, comparing phase-field and lip-field regularization techniques, demonstrating their effectiveness and the novel application of lip-field in viscoelastic damage modeling.

Contribution

It presents a new incremental variational approach for viscoelastic damage, comparing phase-field and lip-field regularizations, and introduces lip-field to viscoelastic fracture modeling.

Findings

Both approaches compare well in numerical simulations.

The model captures rate-dependent behavior of viscoelastic materials.

Lip-field approach is successfully applied in a viscoelastic context.

Abstract

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.