Invariant-based interpretation of anisotropic damage induced by cyclic loading

Damage of quasi-brittle materials appears as micro-cracks and is represented by a tensorial internal variable. Established anisotropic damage models are dedicated to monotonic –possibly multiaxial– loading. Additionally, the effective visualization and the interpretation of anisotropic damage are challenging. In materials with heterogeneous meso-structure, e.g., concrete, the damage field, and the corresponding induced anisotropy are heterogeneous as the orientation depends on the local mechanical state. The post-processing can be performed in the principal damage basis, but this basis can be a field that varies spatially and temporally. The present work addresses both problems: (i) the enhancement of an anisotropic damage model to tackle cyclic and alternate loading on quasi-brittle materials and (ii) the interpretation of the damage-induced anisotropy due to complex loading, such as alternate and non proportional ones. In the proposed model, the strain-based damage criterion function, more precisely the consolidation function, is constructed to be dependent on the so-called active damage. We define different invariant-based indicators of the anisotropy of both the damage and the effective elasticity tensors. These indicators are assessed for homogeneous and heterogeneous fields representing an aggregate embedded in a mortar matrix.