The phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy functional which consists of free energy and dissipation due to fracture. The free energy includes a contribution which is related to viscous dissipation that plays an essential role in coupling the phase-field and the viscous internal variables. The governing equations for the phase-field and the viscous internal variables are deduced in a consistent thermodynamic manner from the pseudo-energy functional. The resulting model establishes a two-way coupling between crack phase-field and relaxation mechanisms, i.e. viscous internal variables explicitly enter the evolution of phase-field and vice versa. Depending on the specific choice of the model parameters, it has flexibility in capturing the possible coupled responses, and the approaches of recently published formulations are obtained as limiting cases. By means of a numerical study of monotonically increasing load, creep and relaxation phenomena, rate-dependency of failure in viscoelastic materials is analysed and modelling assumptions of the present formulation are discussed.

This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the crack evolution in a regularized manner.The interface modeling implements two combined approaches. Firstly, a method from the literature is extended where the interface is incorporated by a local reduction of the fracture toughness. Secondly, variations of the elastic properties across the interface are enabled by approximating the abrupt change between two adjacent subdomains using a hyperbolic tangent function, which alters the elastic material parameters accordingly.The approach is validated qualitatively by means of crack patterns and quantitatively with respect to critical energy release rates with fundamental analytical results from Linear Elastic Fracture Mechanics, where a crack impinges an arbitrarily oriented interface and either branches, gets deflected or experiences no interfacial influence. The model is particularly relevant for phase-field analyses in heterogeneous, possibly complex-shaped solids, where cohesive failure in the constituent materials as well as adhesive failure at interfaces and its quantification play a role.

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Herein, a unified phase-field formulation of fracture in viscoelastic materials is presented. The model is characterised by a pseudo-energy functional from which the governing equations for the phase-field and the viscous internal variables are derived. Depending on the specific choice of the parameters, the formulation has flexibility in capturing the coupling between viscous mechanisms and fracture. By means of a numerical study, different assumptions on the coupling are compared.