Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials

A three-dimensional damage model with induced damage anisotropy is proposed for quasi-brittle materials such as concrete. The thermodynamics framework is used, considering then a single second-order tensorial damage variable whatever the intensity and the sign of the loading. The quasi-unilateral conditions of micro-cracks closure are written on the hydrostatic stress only. Altogether with the consideration of damage laws ensuring a damage rate proportional to the positive part of the strain tensor this is sufficient to model a strongly different behavior due to damage in tension and in compression. A proof of the positivity of the intrinsic dissipation due to such an induced anisotropic damage is given.An efficient scheme for the implementation of the damage model in commercial Finite Element codes is then detailed and numerical examples of structural failures are given. Plain concrete, reinforced and pre-stressed concrete structures are computed up to high damage level inducing yielding of the reinforcement steels. Local and nonlocal computations are performed.A procedure for the control of rupture is proposed. It is a key point making the computations with anisotropic damage truly efficient.