The phase-field approach to self-healable fracture of elastomers: A model accounting for fracture nucleation at large, with application to a class of conspicuous experiments

In a recent contribution, Kumar et al. (2018) have introduced a phase-field formulation and associated numerical implementation aimed at modeling the nucleation and propagation of fracture and healing in elastomers undergoing arbitrarily large quasistatic deformations, phenomena that have come into clear focus thanks to new experiments carried out at high spatiotemporal resolution (Poulain et al., 2017; 2018). With the object of explaining the nucleation of internal fracture observed in those experiments, Kumar et al. (2018) also provided a specific model within the general formulation that accounted for fracture nucleation at material points in the bulk that are subject to purely hydrostatic stress. The first of two objectives of this paper is to introduce a complete model within the general formulation that accounts for fracture nucleation at large, be it within the bulk (under arbitrary states of stress, not just hydrostatic), from large pre-existing cracks, small pre-existing cracks, or from smooth and non-smooth boundary points. The second objective is to showcase the capabilities of the proposed complete model by deploying it to simulate the nucleation and propagation of fracture in a class of conspicuous experiments, that of rubber bands subject to tensile loading. Specifically, 3D simulations are presented of very short, short, and long rubber bands under tension, which are representative of two famed experiments known to feature very different — and, for the cases of the very short and the short rubber bands, very complex — types of nucleation and propagation of fracture.