Dynamic analysis of crack growth using sub-parametric eXtended finite element method

This thesis presents a comprehensive study on the dynamic analysis of crack growth, with a focus on improving the accuracy of predicting stress intensity factors, crack tip velocity, and related parameters. It introduces some strategies to appropriately model crack propagation under dynamic loading conditions and mitigate numerical oscillations that commonly affect computational results. In the pursuit of more precise time integration methods, the study employs the Discontinuous Galerkin method, which proves to be superior to traditional approaches like the Newmark method. This choice is justified by the Discontinuous Galerkin method's ability to handle discontinuities in variables over time, aligning with the dynamic nature of crack growth analysis. As cracks extend, they generate residual forces that can destabilize numerical solutions. To address this issue, a balance recovery algorithm is implemented, effectively eliminating such forces and enhancing solution stability. The research also showcases the efficacy of an interaction integral method for calculating stress intensity factors. A series of practical examples is solved to demonstrate the method's utility in predicting crucial parameters related to crack growth. In scenarios involving non-uniform meshes, the thesis proposes a sub-parametric element approach. This approach utilizes 3-node elements for geometry discretization and 4-node elements for other field variables, ensuring a constant Jacobian matrix within each element. The application of this method serves to minimize errors in solution outcomes, particularly in situations where the mesh is non-uniform. Overall, this thesis offers a comprehensive framework for dynamic crack growth analysis, combining advanced numerical techniques with innovative strategies to enhance the accuracy and reliability of predictions in the field of fracture mechanics.