Localizing gradient damage model based on a decomposition of elastic strain energy density

The simplest form of the localizing gradient damage model assumes the standard elastic strain energy, with an isotropic damage variable driven by a scalar equivalent strain. Such models are simple to implement, but become inadequate for quasi-brittle materials, when the loading conditions induce significant compressive stresses. In this contribution, the elastic strain energy density is decomposed into tension and compression parts by the spectral decomposition method for incorporated into the isotropic localizing gradient damage model. Firstly, the improved performance of the proposed decomposition model is illustrated by a cantilever beam problem. For the decomposition model, damage only evolves under tension conditions, while for the conventional model, the damage evolves in both tension and compression conditions. Next, a series of geometrically similar Double-Edge-Notched (DEN) specimens and the L-shaped panel are considered to show the predictive capability of the decomposition model, in terms of crack trajectories for concrete complex mixed-mode fractures. To further demonstrate the superiority of the decomposition model, a series of concrete Brazilian disc compression tests are considered, where the decomposition model captures the crack profile under strong compression loads most accurately.