PSI - Issue 33

Daniele Gaetano et al. / Procedia Structural Integrity 33 (2021) 1042–1054 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 9. Mesh-size sensitivity analysis for the validation of Multiscale Numerical Simulations (MNS) results.

5. Conclusions In the present work, a novel two-scale failure model has been presented, able to accurately predict multiple crack nucleation and propagation in fiber-reinforced composite materials. Such a model adopts an inter-element cohesive finite element methodology for the numerical simulation of multiple cracking at both micro-and macro-scales. As the main ingredient of the proposed two-scale model, a very efficient off-line homogenization approach is introduced for the bulk and cohesive interface constitutive behavior. This approach includes a linear perturbation technique for the derivation of undamaged overall moduli and a nonlinear homogenization for the derivation of both the bulk damage evolution function and the homogenized traction-separation law as a post-processing outcome. The present model has been applied to the numerical simulation of transverse cracking and induced ply delamination in a particular Fiber Metal Laminate, known as GLARE TM , which is made of alternating aluminum and glass/epoxy pre-preg layers. The numerical results provided in Section 4 have shown that the proposed two-scale model is able to capture the loss of overall strength and stiffness associated with the occurrence of these microscopic failure mechanisms, together with the global cracking pattern (especially in terms of crack width and spacing within the pre-preg layer). Moreover, suitable comparisons with Direct Numerical Simulations (DNSs) performed on a fully detailed model, have demonstrated the computational efficiency and the numerical accuracy of the present MNS approach. On the one hand, almost superposed responses have been obtained via these two analyses. In particular, very small percentage errors on the initial stiffness and the peak strength of the pre-preg layer with respect to DNS have been reported (always less than 2% and, therefore, fully acceptable for engineering purposes), thus assessing the predictive capability of MNS. On the other hand, the computational efficiency associated with the present multiscale approach is attested by the very high ratio, of about 75, between the number of DOFs for the (reference) DNS and that for the present MNS. As a further validation of the proposed approach, a rigorous mesh-size sensitivity analysis has been performed. The numerical outcomes have confirmed the substantial mesh independence of the present multiscale results, in terms of initial stiffness and peak strength of the pre-preg layer. In conclusion, the present work has confirmed the reliability and effectiveness of a two-scale cohesive finite element approach for the numerical simulation of cracking phenomena in fiber-reinforced laminates, focusing of the prediction of transverse cracking and induced delamination between different plies. The main advantage of the