The unified nonlocal peridynamics-based phase-field damage theory

The peridynamic correspondence model is a promising and attractive candidate for the modeling of localized failure in solids, in that it can incorporate many local classical damage constitutive models through introducing a nonlocal averaged deformation gradient. However, the zero-energy mode and the limited bond breaking criterion greatly restrict the potential applications of this correspondence model. To address these two problems, a unified nonlocal peridynamics-based phase-field damage theory is proposed within the framework of thermodynamics. Firstly, the unified correspondence principle for the displacement field is developed on the basis of the energy compensation method in such a way that a new peridynamic deformation gradient, shape matrix and force state are derived and redefined. And then, the proposed principle is applied to derive the nonlocal phase-field damage constitutive model that the general nonlocal phase-field flux, phase-field flow state and phase-field internal force are defined. Moreover, we propose a mixed variational derivative method to obtain the coupled equilibrium governing equation and present the general linearization approach of the proposed peridynamics-based phase-field model (PD-PFM), where the double states for the coupled displacement and phase fields are derived in detail. It will be found that PD-PFM can not only resolve the zero-energy mode existed in the conventional peridynamic correspondence model, but also provide a rational criterion for the breakage of the peridynamic bond. Some representative numerical examples including mixed mode fracture of single-material media and interface fracture of ceramic coating systems are presented for the validation of PD-PFM. The satisfactory results show both quantitative and qualitative agreement with the available experiment.