Issue 29

R. Dimitri et alii, Frattura ed Integrità Strutturale, 29 (2014) 266-283; DOI: 10.3221/IGF-ESIS.29.23 282 interface and the slope of the curve corresponds to the stiffness of the whole domain (matrix+fiber). Soon thereafter debonding starts taking place, leading to a strongly nonlinear behaviour. This is associated to the progressive decohesion of the interface leading to two separate debonding regions, which are symmetric with respect to the x2-axis as shown in Fig. 17b. A gradual unloading is then applied by reversing the boundary displacements with a subsequent behaviour returning to linearity along the secant stiffness to the origin (for g N >0 ), and the virgin tangent stiffness to the origin (for g N <0 ). A further reloading is finally applied until complete failure between the fiber and the surrounding matrix. In the final steps a linear behaviour is observed but the stiffness corresponds to that of the matrix alone, now fully detached from the fiber. (a) (b) Figure 17: Computational scheme (a) and numerical stresses (b) . Figure 18: Homogenized stress-strain curves. C ONCLUSIONS his paper presents a consistency check for some widely used exponential and bilinear mixed-mode CZMs. A parametric analysis on the effect of the coupling parameters on stress distributions and energy dissipation is performed in order to evaluate physical inconsistencies in the coupled elastic or softening mechanical response of the interface. The path-dependence of the mixed-mode debonding work of separation is additionally evaluated. Analytical predictions are also compared with results from numerical finite element models, where the interface is described with zero-thickness contact elements based on the node-to-segment strategy. The analyses reveal that all models, except for the XN model as modified by van den Bosch et al., present energetic inconsistencies due to incomplete dissipations or nonmonotonic variations of the total work of separation. The XN model modified by van den Bosch, on the other hand, is not derived from a potential and therefore, in the current formulation, presents the drawbacks that loading and T