A model for materials characterised by cohesive fracture, as concrete and fibrereinforced mortar is presented. They typically present different performances under tensile and compressive stress states and their strength is strongly influenced by confinement pressure. The proposed model treats plasticity, hardening, damage and fracture in a unified way through the Continuum Damage Mechanics principles. Each different mechanism is associated with a specific internal variable. The model is defined by the specification of the internal energy and dissipation functionals, based on few material parameters of easy physical identification. The form chosen in the paper allows a reasonably accurate description of the material response under rather complex strain histories. The numerical implementation is a straightforward generalisation of standard algorithms for elasto-plasticity with internal variables and an efficient treatment of the irregularities due to the corner points of the generalised elastic domain is obtained by means of an Augmented Lagrangian Regularisation of the constraints. The paper describes a particularisation of the model to the uniaxial case that allows to enlighten either the predicted physical behaviour and the structure of the numerical procedure.
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