COMPLAS 2023

Multi-scale Failure in Architectured Materials

  • Eid, Elie (LaMCoS - UMR 5259)
  • Seghir, Rian (GeM - UMR 6183)
  • Réthoré, Julien (GeM - UMR 6183)

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Architectured materials provide tremendous possibilities in terms of functional properties. However, the real-life use of such highly heterogeneous materials is bridged by some limitations. In fact, despite the powerful computational methods that have been recently developed, explicitly modelling the architectures for numerical simulations remains a heavy task. Aside from determining their effective properties, there is a relevant need for incorporating small-scale mechanisms of deformation and damage in the assessment. As scale separation is not always well established in architectured materials, classical homogenisation techniques fall short. Plus, weak scale separation directly translates to strong interactions between fracture processes and the architecture independently of the considered scale. Accordingly, we believe that a consistent micro-meso analysis of the failure of such materials requires proceeding through multiple intermediate scales to ensure proper modelling [Eid et al., 2021]. Therefore, we follow the bottom-up approach in which information at the microscale is considered to inform the larger scale(s). The proposed scheme evolves from phase-field at the microscale to simulate brittle failure of architecture materials, towards a consistent establishment of the effective mechanical fields (displacement, strain, stress, etc.) at the mesoscopic scale(s) via a model-free coarse-graining technique. We adapt the technique from Goldhirsch, I. and Goldenberg, C. (2002) to evaluate continuum mechanics at different intermediate mesoscales. It is solely based on a definition of a coarse-grained mass density and a manipulation of the inviolable conservation laws: the balance of mass and the balance of linear momentum without requiring specific boundary conditions (as opposed to classical homogenisation). By analysing the coarse-grained response of the fractured architectured materials, the effective material properties, fracture strength and fracture toughness are established across the scales. The ‘homogeneity’ of these properties is analysed and discussions regarding the inevitability of considering an effective non-homogeneous material in which the influence of substructures is preserved at the mesoscopic scales are advanced.