Keywords: fracture, concrete, RBSM, discrete.

Materials like concrete, toughened ceramics, fibre composites, sea ice, wood, rocks, stiff soils, paper and carton belong to the group of quasi-brittle heterogeneous materials. They consist of brittle constituents and, due to their heterogeneity, develop a fracture process zone of considerable size, so that the overall response is quasibrittle and not completely brittle. The prediction of size effects, i.e. the changes of the nominal strength due to a change of the size of the structure, requires an accurate description of the size and form of the fracture process zone and the energy that is dissipated within it.

The aim of the present research is to improve the description of the evolution of the shape and size of the fracture process zone in concrete, in particular of its dependence on the stress state and on boundary conditions and material properties. Thus, it is important to understand how the size of the fracture process zone is influenced by these conditions. This understanding cannot be gained by applying directly a regularized continuum model, since this prescribes explicitly the size of the fracture process zone. Instead, fracture is modelled on a lower scale, which results in an implicit description of the macroscopic fracture process zone due the heterogeneity of the material. The modelling of the fracture on the meso-scale of concrete requires a fine discretisation and is, therefore, a time consuming task. Thus, a discrete approach based on the rigid-body-spring model (RBSM) is chosen. The domain is decomposed into rigid bodies which are connected by springs. Fracture is idealised by gradually damaging the spring connections between the rigid bodies.

The present work illustrates that the rigid body spring model is suitable for a meso-scale description of fracture of concrete. The cell with a periodic mesh results in fracture patterns which are independent of the boundaries of the cell. The evolution of the fracture process zone leads to a localised crack, and the tortuosity of the crack is influenced by the size of the aggregates. Future work will be focused on the dependence of the fracture process zone on stress states and boundary conditions, so that a macroscopic regularized model can be developed, which incorporates the information obtained by the lower scale simulations.

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