The simulation of crack opening-closing and aggregate interlock behaviour in finite element concrete models

The ability to model crack-closure behaviour and aggregate interlock in finite element concrete models is extremely important. Both of these phenomena arise from the same contact mechanisms, and the advantages of modelling them in a unified manner are highlighted. An example illustrating the numerical difficulties that arise when abrupt crack closure is modelled is presented, and the benefits of smoothing this behaviour are discussed. We present a new crack-plane model that uses an effective contact surface derived directly from experimental data and which is described by a signed-distance function in relative-displacement space. The introduction of a crack-closure transition function into the formulation improves its accuracy and enhances its robustness. The characteristic behaviour of the new smoothed crack-plane model is illustrated for a series of relative-displacement paths. We describe a method for incorporating the model into continuum elements using a crack-band approach and address a previously overlooked issue associated with scaling the inelastic shear response of a crack band. A consistent algorithmic tangent and associated stress recovery procedure are derived. Finally, a series of examples are presented, demonstrating that the new model is able to represent a range of cracked concrete behaviour with good accuracy and robustness.