ECCOMAS 2024

An Unsupervised Machine Learning Approach to Reduce Nonlinear FE2 Multiscale Calculations Using Macro Clustering

  • Chaouch, Souhail (University Gustave Eiffel, MSME, CNRS UMR 820)
  • Yvonnet, Julien (University Gustave Eiffel, MSME, CNRS UMR 820)

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FE2 method [1] is one of the most accurate widespread approaches for multi-scale modeling of nonlinear heterogeneous materials. However, it suffers from the inconvenient of high computational cost, which limits its feasibility for industrial applications. A method based on unsupervised learning is developed [2] to reduce non-linear calculations in the FE2 method. The proposed method is based on k-means clustering at the macroscale. The main idea is to create clusters of macroscopic Gauss points based on similarity of mechanical states. Thus, the number of representative volume elements (RVEs) to be solved at each Newton iteration is reduced. This approach is different from ROM methods and from supervised surrogate model approaches; it doesn’t require an off-line stage and it reduces restrictive assumptions on the type of nonlinearity inside the RVE. Several important improvements are made to this method labeled as KMFE2 in [3]. Twodimensional applications using different behaviours and loading conditions are presented. The method is first applied to heterogeneous material with Neo-Hookean hypereleastic properties. Then, it is extended to take into account internal variables, and is tested for a problem including viscoelastic properties with small strains afterwards. Treatments to accelerate convergence are proposed. To illustrate its efficiency for a cyclic loadingunloading path, the method is applied for a problem with elasto-plastic micro phases. Finally, extensions of the method to damage are discussed. REFERENCES [1] F. Feyel. Multiscale FE2 elastoviscoplastic analysis of composite structures, Computational Materials Science, 344-354, 1999. [2] M. A. Benaimeche, J. Yvonnet, B. Bary, Q-C. He. A k-means clustering machine learning-based multiscale method for anelastic heterogeneous structures with internal variables, International Journal for Numerical Methods in Engineering, 2012–2041, 2022. [3] S. Chaouch, J. Yvonnet. An unsupervised machine learning approach to reduce nonlinear FE2 multiscale calculations using macro clustering,Finite Elements in Analysis and Design, 224:104069, 2024.