Constitutive modelling of fibre reinforced cementitious composites based on micromechanics

The paper presents a 3D constitutive model for fibre reinforced cementitious composites based on micromechanical solutions. The addition of randomly distributed short fibres in a concrete matrix can enhance the tensile strength and significantly increase the fracture toughness of the composite. The underlying failure mechanism is governed by fibre pull-out. As a crack opens, the fibres crossing it undergo debonding and start to pull out from the concrete matrix and in this process they apply closure tractions on the crack faces thus stabilising the crack. The crack bridging effect of fibres is taken into account in a local constitutive relationship that describes the behaviour of a crack plane, assuming that the principle contribution of fibres arises after crack initiation. The local stress transferred across the crack plane is expressed as a summation of the stress carried by the intact or undamaged material and the stress carried by the fibres. The local constitutive relationship makes use of a parameter that characterises the pull-out state of the fibres. This parameter essentially operates in the same way as a conventional damage parameter. The evolution of the equivalent damage parameter for fibre pull-out is based on the micromechanics crack bridging model of Lin & Li, 1997. Furthermore, a rough crack contact component is added to the crack plane formulation in order to account for stress recovery when the crack regains contact. The crack plane constitutive relationship is then incorporated into a 3D model for concrete in which it is assumed that cracks can form in any direction. In this model the plain concrete is simulated as a two-phase composite comprising a matrix phase representing the mortar and spherical inclusions representing the coarse aggregate particles. Additionally, the material contains microcracks that can have various orientations and are assumed to initiate in the interfacial transition zone between the aggregate particles and the mortar, according to a local principal stress criterion. Numerical results obtained with the proposed micromechanical constitutive model are compared with experimental data. Good correlation between numerical and experimental responses demonstrates the potential of the model to capture key characteristics of the mechanical behaviour of fibre reinforced cementitious composites.