Higher Order Methods for Simulating Curvilinear Crack Propagation
Understanding and predicting fracture propagation has been for a long time a topic of interest for engineers and scientists alike. Its applicability lies in the prediction of failure loads and mechanisms for the safe design of structural and mechanical components. More recently, a new wave of interest in simulating fracture propagation has risen due to the insurgence of hydraulic fracturing for hydrocarbon recovery and its eﬀects on cap rock in CO2 storage.
The main challenges in simulating a propagating fracture can be identiﬁed in (1) the continuously evolving displacement discontinuity, (2) the singular nature of the elasticity ﬁelds, and (3) the com-putation of the stress intensity factors for the prediction of crack of growth. Current state-of-the-art methods are plagued by low order of accuracy or high computational cost accompanied by complex data structures.
The presentation will discuss a computational framework for the simulation of crack propagation which addresses the challenges of (1)-(3). The key ingredients are a robust meshing tool for evolving domains, a computationally eﬃcient and optimally convergent ﬁnite element methods for singular solutions, as well as a family of functionals for the rapidly convergent computation of the stress intensity factors. The framework will be shown to be consistent and predictive, both through numerical examples and mathematical analysis, and its robustness will be showcased in the context of thermoelasticity to investigate the formation of unstable crack patterns in quenched brittle materials.