Finite Element Procedures for the Numerical Simulation of CRack Propagation and Bilateral Contact

Doctoral thesis, 2006

This thesis concerns finite element methods for the numerical simulation of crack propagation including contact formulations for the contact between deformable bodies. The classical integral formulations for the energy release rate at crack growth are considered and adaptive algorithms are developed. In addition, we derive three different strategies for computing the material forces at a cracktip and the different strategies are compared. A new stabilized Lagrange multiplier method is presented where the multipliers are discretized with global polynomials. The method allows for non-matching meshes at the contact interface and the delicate problem of integrating products of basis functions between the master and slave body is alleviated. A discontinuous Galerkin method for cutting elements independent of the mesh structure is extended to the problem of a propagating crack whereby different strategies for computing the crack driving force are considered.