Date of Award


Document Type

Open Access Dissertation


Civil and Environmental Engineering


College of Engineering and Computing

First Advisor

Robert Mullen,


Finite element methods for the simulation of dynamic fracture in plane structures are presented. The method is a modified extended finite element method (XFEM) for dynamic fracture simulations with a new methodology to construct the XFEM basis functions for discontinuities. In contrast to conventional XFEM in which the extended interpolation is defined to only capture the discontinuities, the proposed method describes the enrichment functions so that they reproduce both the discontinuities and the polynomial bases of sufficiently high order which are critical for finite element convergence. Such enrichment functions, by adopting the Duffy’s transformation, can be simply defined in terms of standard shape functions. The approach is applied to a linear three-node triangular element for element-by-element crack propagation modeling.

In the proposed method, the enrichment parameters effectively represent the physics of the discontinuity and are assigned to non-nodal points, which helps to simply impose Dirichlet boundary conditions in strong form. This feature successfully dissociates the finite element nodes from the extended approximation; it facilitates the treatment of arbitrary crack propagation in explicit methods.

The proposed method significantly simplifies the XFEM programming implementation; the enrichment functions are vanished outside the element domain without shifting techniques, so that no blending of the local partition unity is required. In addition, the enriching procedure depends on neither the crack direction nor the elements contiguous to the enriched element. Moreover, the proposed method facilitates the treatment of crack modeling in object-oriented programs (OOP) as the enrichment object is completely dissociated from the element nodes.

The proposed method combined with explicit time integration and a cohesive law quite well simulates the dynamic fracture of ductile and brittle materials. The methodology is applied to the simulation of several benchmark problems whose experimental results are available involving dynamic fracture and nonlinearities. The numerical results in terms of crack paths and speeds were effectively computed and matched the experimental results. The results are also compared to those obtained by standard XFEM to demonstrate the efficacy of the method. Through these numerical examples, the robustness and performance of the method in reproducing the observed failure modes are demonstrated.