Inelasticity–damage-based model for numerical modeling of concrete cracking

This paper deals with the development of a continuum inelasticity–damage-based model. The aim is to describe the behavior of plain and reinforced concrete under monotonic and cyclic loading. We consider that inelasticity is due to micro-crack openings, and that the material recovers its original elastic modulus when all micro-cracks are closed. We make the hypothesis that the displacement field, due to micro-crack openings, remains consistent with a strain called Unitary Crack Opening. The damage is described by a simple scalar which is taken as a multiplier of the Unitary Crack Opening tensor. Hence, the crack closure effects are directly described, the material recovers its original elasticity when micro-cracks are closed. Damage variable multiplied by the Unitary Crack Opening tensor gives a good description of anisotropy. Nonlinearity occurs when both damage and Unitary Crack Opening strains exist. Firstly, the thermodynamic and mathematical basis of the model are explored. Elementary tests are firstly considered for validation. Furthermore, the single edge notched beam and a beam subjected to cyclic loading are tested.