A dynamic phase field model with no attenuation of wave speed for rapid fracture instability in hyperelastic materials

Abstract

Numerical experiments on phase field modeling of the fracture in pre-strained hyperelastic materials reveal that the classical mechanical-based dynamic phase field model is ineffective in the framework of non-linear deformation. The aspiration to gain insight into rapid fracture instability motivated us to develop a novel dynamic phase field model characterized by wave velocity invariance, enabling crack propagation at a velocity approach to the asymptotic limit. Given that the numerical treatment of rapid fractures involves extremely high spatiotemporal resolution, robust explicit dynamics and a tried-and-tested multi-level hybrid adaptive mesh algorithm are invoked. More crucially, an original adaptive distorted mesh removal scheme (ADMR) was developed to cope with the intractable finite element mesh distortion problem in large deformation fractures. The detailed numerical implementation for entire procedures is outlined, and its reliability is verified by two quasi-static fracture benchmarks. Utilizing the proposed model and innovative algorithms, the arresting ultrahigh-speed crack oscillation and tip-splitting instabilities captured in the fracture experiments of brittle gels were successfully reproduced. The critical crack velocity at the onset of the instability is also identified, close to the experimental measurements.