Anisotropic continuum damage constitutive model to describe the cyclic response of quasi-brittle materials: The regularized unilateral effect

Within the framework of damage mechanic, numerous anisotropic damage models have been proposed in the literature with the aim to represent the anisotropic degradation of quasi-brittle materials. The benefits from such models arise from the fact they are consistent with the principles of the continuum mechanics enabling easy numerical implementation in the majority of finite element codes. Despite the wealth of anisotropic models in the literature, further developments are needed to simulate correctly the responses involving phenomena related to crack closure. The present paper proposes a new class of anisotropic damage models characterized by its capabilities to describe non linear progressive stiffness recovery with the possibility to introduce permanent strains. The theoretical framework takes benefits from some results of the operator function theory. Further mathematical features are established for sets of functions, which are termed opening (closure) cracking functions. These features are useful to control the material behavior when the tensile or the compressive strains are activated (deactivated) with more or less smoothness. The thermodynamical admissibility condition is fulfilled, as long as the damage variable and the cracking functions satisfy further conditions. The robustness associated with the time integration of the proposed class of models is illustrated by a structural case study. (C) 2018 Elsevier Ltd. All rights reserved.