Modelling of large deformation crack propagation based on the extended finite element method

Abstract: This thesis is concerned with the finite element modelling of large deformation crack propagation, based on the extended finite element methodology. The benefit from this approach is the possibility of locally enriching the finite element space, i.e. to add a priori knowledge about the local behaviour of the solution in order to improve accuracy. As to crack modelling, this means that additional functions are added to the finite element approximation in the vicinity of the crack in order to facilitate the modelling of crack propagation independent of the spatial discretisation. The focus of the present work has been on the evaluation of existent models and the development of new modelling techniques for large deformation crack propagation in this context, concerning as well the theoretical development as aspects of implementation and application. Considered areas of applications include quasi-static and dynamic crack propagation modelling in quasi-brittle as well as ductile materials. In addition, the fully coupled thermo-mechanical problem is addressed, including the explicit heat generation due to the fracture process. For these purposes, two approaches to describe and to analyse the process of fracture have been investigated and compared; the material crack driving force approach and the cohesive zone approach. In the former approach, a (fictitious) material force is defined as a vectorial measure of the energy release rate upon a small shift of placement of the crack tip. This leads to a natural formulation of a fracture criterion based on the evaluation of this force, which has been developed and evaluated. In contrast, and also for the purpose of comparison, the cohesive zone approach has also been incorporated in this work. In this case, the basic idea is to project the existing process zone, of localised micro-cracking and plastic flow in the vicinity of the crack tip, to an equivalent traction-separation law.

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