PSI - Issue 41

8

Daniele Gaetano et al. / Procedia Structural Integrity 41 (2022) 439–451 Author name / Structural Integrity Procedia 00 (2019) 000–000

446

The numerical outcomes of these three different steps have been obtained exclusively through off-line computations, and their validity is independent of the particular geometry and boundary conditions of the considered macroscopic problem. Therefore, both the macroscopic damage evolution function and the macroscopic traction separation law may be regarded as material properties (for bulk and interface elements, respectively) to be used for performing general structural analyses of different specimens made of the same composite material. After performing all these off-line computations involving the considered RUC, a macro-scale analysis of the composite beam, here referred to as Multiscale Numerical Simulation, is performed by using the previously derived databases (i.e., the aforementioned damage evolution and traction-separation laws) as material inputs. The macro scale response is here reported in terms of relations between the applied force, F , and the Crack Mouth Opening Displacement, CMOD. In order to investigate the influence of the mesh topology on the predicted overall structural behavior, two triangular mesh configurations have been considered for the Diffuse Interface Model (DIM), i.e., a cross-triangle quadrilateral (mapped) mesh and a Delaunay-type (random) mesh, shown in Figs. 6a and 6b, respectively. For comparison purposes, an additional Single Interface Model is considered, in which the macro-crack path is assumed to be known in advance, as depicted in Fig. 6c. All these models have been equipped with the previous micromechanically derived bulk and interface properties.

Fig. 6. Different finite element models for the Multiscale Numerical Simulation (MNS): (a) Diffuse Interface Model with a mapped mesh; (b) Diffuse Interface Model with a random mesh; (c) Single Interface Model.

As a validation step, the results of these multiscale analyses, here called Multiscale Numerical Simulations (MNSs), have been compared with the outcomes of a fully microscopic analysis, here denoted as Direct Numerical Simulation (DNS). In this analysis, taken as the reference, all the microstructural details are explicitly modelled. As shown in Fig. 7a, the MNS results obtained with a cross-triangle quadrilateral mesh are in perfect agreement with the (reference) DNS results, as confirmed by the little error for the peak load predicted by the two models (less than 1%). Conversely, the comparison between the MNS results with an unstructured mesh and the DNS results, shown in Fig. 7b, highlights a little overestimation of the peak load (with an error of about 3%). Finally, Fig. 7c shows the MNS results obtained via a Single Interface Model, here considered for validating the adopted homogenization scheme in the frequent case of a priori known single crack path. The comparison with the DNS results highlights again a perfect agreement. Therefore, it is important to note that the strength overestimation occurring in the case of unstructured meshes is not due to the adopted homogenization scheme, whose accuracy is fully validated by the outcomes reported in Figs. 7a and 7c, but rather to the artificial crack path tortuosity induced by the DIM approach used at the macro-scale (please note the jagged crack path reported in Fig. 7b).