Numerical simulation of fracture in plain and fibre-reinforced concrete

Abstract

Localised failure in quasibrittle materials is due mainly to the effects of combined shear and compression. Once the cohesion strength is reached, shear tractions generate slip and aggregate interlocking that cause dilatancy inducing crack opening. Further damage reduces the cohesion and dilatancy so that eventually only a residual friction state remains. The energy dissipated due to friction and interlocking needs to be considered in the constitutive law. Initially, a Mohr-Coulomb yield surface with a tension cut-off will be investigated. A compression cap will be included when the modelled interfaces are not appropriately aligned and compressive failure must be controlled. The evolution of the yield surface and the appropriate flow rules to be used in the interface/particle model, are questions which will be examined. The particle/interface model with plasticity concentrated at the interface nodes, which can produce the correct volumetric expansion, will also be studied. A composite model has been developed to represent the heterogeneity of concrete consisting of coarse aggregates, mortar matrix and the mortar-aggregate interface. The constituents of concrete are modelled using triangular elements with six interface nodes along their sides. Fracture is captured through a constitutive softening-fracture law at the interface nodes, which bound the elastic domain inside each element. The inelastic displacement at an interface node represents the crack opening, which is associated to the conjugate internodal force by a single branch softening law. The path-dependent softening behaviour is derived in irreversible rate formulation within a quasi-prescribed displacement control. At each event in the loading history, all equilibrium solutions for the prescribed mesh can be obtained and the critical equilibrium path with the minimum increment of external work adopted. The crack profile develops restrictively to the interface boundaries of the defined mesh. No re-meshing is carried out. Solutions to the irreversible rate formulation are obtained using a mathematical programming procedure in the form of a linear complementary problem. Other work is aimed at incorporating fibre reinforcement in the model. Fibre particles are modelled by introducing additional linear elements interconnecting distant interface nodes in the matrix media after the generation of matrix-aggregate structure.