ECCOMAS 2024

Error-Driven Hierarchical Modelling of Composite Structures

  • Feld, Nicolas (Safran Group)
  • Fergoug, Mouad (Safran Group)
  • Parret-Fréaud, Augustin (Safran Group)
  • Marchand, Basile (Mines ParisTech)
  • Forest, Samuel (Mines ParisTech)

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Aerospace composite structures are subjected to localized loads which are responsible for complex structural phenomena leading up to failure. The reason lies in the strong interactions between localized stress gradients and the characteristic dimensions of the mesostructure. In such cases, homogeneous modelling of the composite loses meaning and multiscale methods must be employed. Global-local analysis is based on the intuitive idea of connecting a fine – meso – local model in specific regions of interest with a coarser – macro – global one everywhere else. It has been shown that using global-local analysis efficiently in a multiscale framework, i.e. with non-compatible models featuring distinct scales, requires adapted connecting conditions, e.g. periodic homogenization-based. On the other hand, there are few studies on the issue of zoning the local model, i.e. positioning the connecting interface in space and time, despite its significance when stress localizations are not known beforehand. In this work, we propose a new model error estimator based on the violation of the fundamental hypotheses of first-order periodic homogenization, i.e. asymptotic scale separation and loading periodicity [1]. The true error at the scale of a representative volume element is therefore seen as the difference between first-order-relocalized fields and the direct numerical solution of the full mesostructure. Considered out of reach, this solution is replaced with a high-order relocalization process – up to 3rd order – combined with an original boundary layer correction [2]. Applied to an industrial-sized structure, this estimator may be computed on the coarse mesh only, allowing inexpensive steering of global-local zoning, similarly to adaptive remeshing. Higher-order-relocalized and boundary-layer-corrected fields may also be used to improve global-local connecting conditions. Several examples demonstrate each of these aspects, prove the convergence of the proposed strategy from different standpoints, and highlight remarkable accuracy improvements, both on the structural response and on local quantities of interest [3]. REFERENCES [1] Fergoug et al. (2022). EJM A/Solids, 96, 104754. [2] Fergoug et al. (2022). Comp. Struct., 285, 115091. [3] Fergoug et al. (2024). CMAME, 418, 116529.