The standard cohesive volumetric finite element (CVFE) method has successfully been applied to a variety of dynamic fracture problems involving the formation and propagation of cracks. However, the method is computationally inefficient for problems containing many degrees of freedom as well many failure paths. In its current form, the method requires that dynamic fracture problems be evenly discretized with small volumetric elements all interconnected with the interfacial (cohesive) elements. The presence of the cohesive elements requires not only the duplication of nodes and therefore an increase in the number of degrees of freedom, but also a reduction in the critical time step of the domain. This time step reduction is necessary to ensure the cohesive element stability and the accuracy of the solution.

The purpose of this thesis was to develop an adaptive version of the CVFE scheme which addresses its critical issues. We first investigated the use of different time steps in different regions through the multi-time step nodal subcycling algorithm. Next we developed a dynamic insertion algorithm to insert cohesive elements anywhere in the domain and at any time. This allows us to begin the simulation cohesive element free and only insert these elements as necessary. Finally, we implemented a parallelization technique in order to decrease our simulation time or increase the problem size. We initially applied all of the methods and algorithms to 1-D problems in order to gain a better understanding of the results while using very simple problems. We then moved on to 2-D problems where both the problem complexity and solution times increased. We present the conclusions from our analysis in the next section