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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In order to provide a more in-depth comparison between MNS and DNS, the required number of degrees of freedom (DOFs) as well as the peak strength and the initial stiffness of the pre-preg layer are reported for both analyses in Table 4. These results show that the proposed multiscale methodology is very efficient and accurate at the same time, with respect to a fully meshed analysis. In particular, the percentage errors of these quantities with respect to DNS are less than 2%, and therefore, fully acceptable from an engineering point of view. Finally, Fig. 8 also show the numerically predicted crack pattern for both MNS and DNS. From the analysis of the deformed cracked configurations, it can be noted that the present multiscale approach is able to predict with a sufficient accuracy also the cracking pattern, together with the average crack width and spacing.

Fig. 8. Result comparison between Multiscale Numerical simulation (MNS) and Direct Numerical simulation (DNS) in terms of homogenized secant longitudinal modulus of the pre-preg layer (A) and homogenized stress (B) as functions of the applied macroscopic strain.

Table 4. Comparison between MNS and DNS in terms of required DOFs number and of initial stiffness and peak strength. Analysis type Number of DOFs E x pre-preg (MPa) Error (%) σ x pre-peg (MPa) Error (%) DNS 1,361,190 14,814 - 34.20 - MNS 18,044 14,670 0.97 33.56 1.88 In addition, as a further assessment of the validity of the proposed modeling approach, in order to investigate the mesh-size dependence of the present numerical results, a rigorous mesh sensitivity analysis has been performed by varying the resolution inside the pre-preg layer. Hence, three different mesh configurations have been considered, named as Mesh 1 (the coarsest), Mesh 2 and Mesh 3 (the finest), with an average element size in the pre-preg layer of 6.00, 3.00 and 1.50 μm, respectively. It is worth noting that Mesh 2 has been already used to obtain the numerical results shown in Fig. 8. The related results, depicted in Fig. 9, have shown a substantial mesh-size independence of the present multiscale approach, especially in terms of the effective longitudinal modulus, thus fully validating the reliability of the present numerical outcomes.