Twenty years in since their introduction, it is now plain that the regularized formulations dubbed as phase-field of the variational theory of brittle fracture of Francfort and Marigo (1998) provide a powerful macroscopic theory to describe and predict the propagation of cracks in elastic brittle materials under arbitrary quasistatic loading conditions. Over the past ten years, the ability of the phase-field approach to also possibly describe and predict crack nucleation has been under intense investigation.  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). This formulation views the nucleation and propagation of fracture as well as the possibility of healing as three intertwined parts of the same phenomenon. It further establishes that the existing phase-field approach to fracture at large — irrespectively of its particular version — cannot possibly model crack nucleation. 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.

 

In this talk, I will 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 central idea is to implicitly account for the presence of the inherent microscopic defects in the material — whose defining macroscopic manifestation is precisely the strength of the material — through the addition of an external driving force in the equation governing the evolution of the phase field. Furthermore, I will 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.


The Phase-Field Approach to Self-Healable Fracture of Elastomers: A Model Accounting for Fracture Nucleation at Large

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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