COMPLAS 2025

Accelerating Multiscale Damage Prediction in Heterogeneous Brittle Materials Using Macro Clustering

  • Chaouch, Souhail (INSA Lyon, CNRS, LaMCoS, UMR 5259)
  • Yvonnet, Julien (University Gustave Eiffel, MSME, CNRS UMR 820)

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Predicting damage in heterogeneous brittle materials such as composites, bone tissue or 3D printed materials presents significant challenges. In such materials, microstructure can induce highly anisotropic damage, and constructing empirical macroscopic models is in this case a delicate task. Describing the cracking of a heterogeneous structure, while accounting for all details of the heterogeneities, implies high-performance calculations, requiring to be carried out on supercomputers. On the other hand, classical multi-scale methods for modelling nonlinear, heterogeneous materials, with time-dependent behaviour (e.g., FE2) suffer from the involvement of huge amount of computational time and memory storage. This is because a nonlinear Finite Element Method problem must be solved at each Gauss point of the macro mesh and for all macro Newton iterations. To address these computational challenges, the KMFE2 method was developed and applied to anelastic composites [1] . The KMFE2 method is an AI-based unsupervised machine learning technique based on k-means clustering to select the Gauss points in the macro structure mesh that have close mechanical states. An extension of this method to damage modeling was introduced in [2] in which several key developments are proposed, including:(i) A novel definition of vectors enabling macro-scale clustering of integration points by incorporating macroscopic internal variables that describe an anisotropic damage state related to micro cracking in each RVE via harmonic analysis of damage. (ii) An arc-length technique integrated into the macro-scale resolution to capture potential snap-back instabilities. (iii) A regularization at the macroscopic scale to avoid issues of non-convergence of dissipated energy related to micro damage and mesh-dependency. The method is applied to the cracking of heterogeneous porous and composite structures exhibiting strong anisotropies, leading to different macro-crack orientations depending on the microstructure. Acceleration factors of approximately 12 to 15 can be achieved without requiring a precomputed database or micro-level solution approximations.