Development of methods for modelling the failure of quasi-brittle materials

The fracture and failure of quasi-brittle materials such as concrete and rock is a complicated process and difficult to model numerically. Such materials are heterogeneous and contain small internal defects and often fail in a quasi-brittle manner, caused by the growth and coalescence of the internal cracks, which adjoin to cause a macroscopic fracture with a considerable fracture process zone. The aim of this work is to develop methods for modelling the different phases of the failure process of quasi-brittle materials, starting from the behaviour of microcracks, onto the coalescence of the microcracks into macrocracking and finally to the continuous propagation of the macrocracks. The methods are based on fracture mechanics, continuum mechanics and numerical techniques and they were developed to be compatible with commercial finite element software. A combined analytical-numerical method for capturing the effects of microcracks on a continuum scale is presented and applied for large arrays of microcracks. The results show that the interaction of the microcracks is essential as it increases the susceptibility to fracture and affects the material's continuum response. Crack interaction plays a key role in compressive failure, which is demonstrated by studying wing-crack growth under compression. The growth of wing-cracks can lead to compressive failure, but the growth is easily halted by lateral confinement. The numerical study of 3-D wing-crack systems suggests that the interaction of suitably oriented crack systems can overcome the arresting effects of lateral confinement, leading to compressive failure. A remeshing method was developed to discretize internal fracturing, based on a fictitious crack approach. Directional softening of the material creates a stress-free plane, which can be converted into a free surface without disturbing the equilibrium. The method was implemented on top of Abaqus FE software and demonstrated with simple test cases. The post-failure phase of the failure process was captured with a cohesive surface method implemented in Abaqus. Cohesive elements that are potential fracture locations were inserted at each element boundary and the fragmentation continuously progresses as the interface elements fail. The crushing of an ice sheet simulated with the method predicted failure modes, contact forces and high-pressure locations similar to that observed experimentally. The development of quasi-brittle failure modelling methods is gaining new momentum with the increase of computational power, which allows the application of more sophisticated tools. This work contributes to that field with new methods, case studies and novel results relevant for the engineering community.