The modelling of cracks and shearbands, arising from brittle and ductile response of materials, poses significant computational challenges. In this talk I will present our recent developments in the field of computational fracture mechanics that address some of these challenges.
The first part of the talk, devoted to brittle fracture, will focus on a new formulation based on a high order extended finite element method and Irwin’s integral to extract Strain Energy Release Rates in linear elastic fracture mechanics. Extended finite element methods provide an attractive alternative to standard finite elements in that they do not require fine spatial resolution in the vicinity of discontinuities nor do they require repeated re-meshing to properly address propagation of cracks. The significance of the approach presented is that it provides an efficient alternative to the J-integral method and can circumvent some of the J-integral limitations when applied to 3D fracture modelling and crack coalescence.
The second part of the talk will focus on dynamic fracture of metals which may be brittle or ductile depending on factors such as material properties, loading rate and specimen geometry. At high strain rates, a thermo-plastic instability known as shear banding may occur, which typically precedes fracture while at lower rates brittle fracture is observed. To date there is no model that captures both phenomenon in single framework. To this end, I will present a novel mixed finite element formulations with diffusive regularization for shear band instabilities combined with a phase field method for fracture. The governing nonlinear PDE system is solved robustly by an implicit monolithic solver. The main formulations along with some numerical examples to illustrate the performance of the model will be presented. I will briefly discuss a range of challenges including discretization and element formulation, mesh sensitivity, large deformations and re-meshing, parallel computing and solver technology.
