Modeling Ductile Fracture Using Discontinuous Galerkin Finite Element Method

This dissertation focuses on the development and application of discontinuous Galerkin (DG) methods for modeling ductile fracture problems. A complete simulation of the fracture failure in the ductile materials undergoing large plastic deformation within traditionally preferred implicit finite element framework is often unavailable due to numerical instability issues. Current popular methods for modeling ductile fracture requires the direct releasing of nodal force or setting free the traction of the crack surface within the current load step. To achieve numerical convergence, for such a system that goes through a sudden change from a phase without a crack to a phase with cracks, is extremely challenging and rarely reported for the implicit numerical framework. With the advantage of broken meshes, discontinuous Galerkin(DG) methods can naturally accommodate cracks along DG interfaces overcoming these challenges. A relaxation scheme is used to gradually recover the traction-free condition on cracked surfaces in finite plastic media. A newly developed index named "fracture potential"(FP) index, is used to predict the crack initiation point and crack propagation direction in the ductile media. This FP index is essentially calculated from the ratio of equivalent plastic strain and the required plastic strain to failure at a particular stress-triaxility. Application of FP index is validated within different stress-triaxiality regions ranging from tensile-dominant to shear-dominant failure mode. Multiple crack openings, their simultaneous propagation, and coalescence are also successfully modeled in this research for nuclear fuel rod and a benchmark problem (Sandia fracture challenge). The application of the DG method is extended to model the fracture in the fiber-reinforced composite structures. Fiber/matrix interfacial debonding, which is one of the main micromechanical failure mechanisms in composites, is modeled using the DG interface framework. Furthermore, crack initiation and propagation leading to the complete failure of the bulk matrix is also modeled, which has not yet been reported in the literature. Failure of fiber-reinforced composite problems is validated by the experimental results reported for two fibers embedded in an epoxy matrix governed by the standard J2 plasticity theory. Finally and importantly, a material integrator including the updating stress and constructing algebraic tangent modulus for a newly popular pressure-dependent plasticity model is consistently formulated for modeling the failure of FRC where bulk matrix materials are ductile and may undergo significant plastic deformation. We demonstrate the excellent capability of our DG methods with this pressure-dependent plasticity model in modeling of FRC with randomly distributed multiple fibers with ductile bulk matrices.