Cracking of quasi-brittle structures under monotonic and cyclic loadings: A d+/d− damage model with stiffness recovery in shear

The formulation is integrated with a multidirectional damage procedure, addressed to extend the microcrack closure-reopening (MCR) capabilities of the model to shear cyclic conditions, characterized by orthogonal (or however intersecting) sets of cracks. Maintaining unaltered the dependence of the constitutive law from two scalar indeces, d+ and d−, this approach activates or deactivates a tensile (compressive) damage value on the base of the current maximum (minimum) principal strain direction. In correspondence with damage activation (crack opening) or deactivation (crack closure), a smooth transition is introduced, in order to avoid abrupt changes in stiffness and enhance the numerical performance and robustness of the multidirectional procedure. The adequacy of the proposed constitutive model in reproducing experimental results has been proven for both monotonic and cyclic loading conditions. The two examples of application involving cyclic loads, dominated by shear, constitute a validation of the multidirectional damage approach, showing how the suitable representation of unilateral effects and permanent deformations is essential to model the observed structural response in terms of maximum resistance, evolution of stiffness degradation and dissipation capacity.