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Fracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the resistance against crack propagation can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described. [ABSTRACT FROM AUTHOR]

In this work, the geometry-constraint-based non-ordinary state-based peridynamic (GC-NOSBPD) model is further generalized to study the mechanical responses and rate-dependent fracture behaviors of viscoelastic materials. The viscoelasticity is generated by directly incorporating the classical viscoelastic constitutive relation in the form of the Generalized Maxwell Model, which is expressed as Prony-series type expansion, into the GC-NOSBPD framework. A strain-based scalar damage variable only driven by elastic energy, whose evolution follows a rate-independent law, is proposed to describe the progressive growth of the mode-I crack. Combining the rate-independent damage variable and viscoelasticity results in a rate-dependent damage model in the hypothesis that the fracture of viscoelastic material is driven by both elastic and viscous components of the energy. The fidelity of this model is established in the absence of damage by comparison with the benchmark solution for the viscoelastic response of a 3D bar subjected to various load histories. Further, the proposed model is employed to simulate two quasi-static fracture tests under various loading rates: a three-point bend fracture test for concrete and a double-cantilever-beam delamination test for rubber interface. These numerical results agree well with experimental tests, showing that the proposed model can effectively capture rate-dependent crack propagation. [ABSTRACT FROM AUTHOR]

In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of plane stress and steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to examine the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The computational framework builds upon a previous work by the present author (Kroon in Int J Fract 169:49-60, ). The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. The predicted distributions of stress and dissipation around the propagating crack tip are presented. The predicted crack tip profiles also agree qualitatively with experimental findings. [ABSTRACT FROM AUTHOR]