Structure of micro-crack population and damage evolution in concrete

Tensile behaviour of concrete is controlled by the generation and growth of micro-cracks. A 3D lattice model is used in this work for generating micro-crack populations. In the model, lattice sites signify solid-phase grains and lattice bonds transmit forces and moments between adjacent sites. The meso-scale features generating micro-cracks are pores located at the interfaces between solid-phase grains. In the model these are allocated to the lattice bonds with sizes dictated by an experimentally determined pore size distribution. Micro-cracks are generated by removal of bonds when a criterion based on local forces and pore size is met. The growing population of micro-cracks results in a non-linear stress-strain response, which can be characterised by a standard damage parameter. This population is analysed using a graph-theoretical approach, where graph nodes represent failed bonds and graph edges connect neighbouring failed bonds, i.e. coalesced micro-cracks. The evolving structure of the graph components is presented and linked to the emergent non-linear behaviour and damage. The results provide new insights into the relation between the topological structure of the population of micro-cracks and the macroscopic response of concrete. They are applicable to a range of quasi-brittle materials with similar dominant damage mechanisms. Copyright © (2013) by International Conference on Fracture.