Although ceramics are generally considered as to be elastic brittle solids, some of them are quasi brittle. These ceramics show a non linear mechanical behaviour resulting most of the time in a difference between their tensile and compressive stress-strain laws. The characterization of their fracture strengths might be biased if elastic linear formulae are used to analyze classical tests like bending tests. Based on Digital Image Correlation (DIC), an efficient technique to measure full field displacements, a methodology is proposed to characterize and model materials with dissymmetric behaviours between tension and compression. Applying specific basis functions for DIC displacement decompositions for bending, compressive and tensile tests, a stress-strain model and its damage law are identified and then validated for aluminium titanate, a damageable micro cracked ceramic at room temperature. This identification method using DIC can obviously be applied to other quasi brittle materials.