Isotropic continuum damage mechanics for concrete under cyclic loading: Stiffness recovery, inelastic strains and frictional sliding

A three dimensional set of constitutive equations for modelling quasi-brittle materials such as concrete is presented. It is formulated within the framework of irreversible processes thermodynamics in order to fulfill physical consistency. A single scalar damage variable has been introduced in order to take into account nonlinearities due to micro-cracking. The sliding influence and the partial stiffness recovery have been considered for cyclic loadings. Related numerical aspects are presented. Both plain and reinforced concrete structures are computed up to failure in order to show the efficiency and the robustness of the proposed model. Numerical results are both quantitatively and qualitatively compared to experimental data and highlight good agreement. The proposed constitutive equations seem accurate and robust enough for computing large scale structure subject not only to monotonic loadings but also to cyclic ones.