A Dynamic Fracture Simulation Based on Embedded Finite Element Methods

In this thesis, a hybrid numerical approach is proposed for modeling dynamic fracture in brittle materials. This method is based on a combination of embedded finite element methods and extrinsic cohesive zone models. The effect of different methods to enforce the kinematics at the embedded interface for crack initiation and propagation are investigated and numerically compared. Finally, Nitsche's method is suggested within the hybrid numerical schemes to simulate dynamic fracture. In the pre-failure stage, terms for consistency and stabilization are introduced into the finite element framework with Nitsche's method. When the fracture criterion is met, the extrinsic cohesive law governs the behavior of the opening surfaces by a simple change of framework without modifications of the mesh. This traction and separation law is directly implemented at the interface through an interface approach. Upon closure of the crack surfaces in compression, Nitsche's method is suggested to weakly enforce contact conditions at crack surfaces.

The applicability of the proposed hybrid method is investigated in numerical examples. By using Nitsche's method, the main advantage of the hybrid method for modeling dynamic crack propagation is to avoid unphysical initial slopes in the numerical implementation of extrinsic cohesive laws, which affords us more accurate crack initiation than with the penalty method. Another advantage is that the consistency and stability at unfractured interfaces during crack propagation are maintained and hence the issues caused by the penalty method in explicit dynamic schemes are avoided. Importantly, Nitsche's method performs better than the penalty method conventionally used to prevent interpenetration under compressive loadings.