A non-local model with tension and compression damage mechanisms

A non-local isotropic damage model is proposed which can be used to predict the behaviour of rock-like materials up to failure. Two isotropic damage variables account for the progressive degradation of mechanical properties under stress states of prevailing tension and compression and two internal lengths, one for tension and the other for compression, are introduced as localisation limiters. A linear bifurcation analysis highlights the regularisation properties of the non-local model. An iterative scheme for the numerical solution of the finite-step problem consisting of a linear global predictor, an averaging phase and a non-linear local corrector is presented. Some illustrative examples of tension and splitting tests show the effectiveness of the proposed model.