A k-means clustering machine learning-based multiscale method for anelastic heterogeneous structures with internal variables

Mohamed Amine Benaimeche (1, 2) , Julien Yvonnet (2) , Benoît Bary (1) , Qi-Chang He (2)

1 CEA - CEA- Saclay
2 MSME - Laboratoire Modélisation et Simulation Multi-Echelle

A new machine-learning based multiscale method, called k-means FE 2 , is introduced to solve general nonlinear multiscale problems with internal variables and loading history-dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k-means clustering-machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE 2 calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi-brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions.

Mots clés: Multiscale; FE2; k-means clustering; Nonlinear; Homogenization; Machine learning

Domaines: Sciences de l'ingénieur [physics]

Mohamed Amine Benaimeche, Julien Yvonnet, Benoît Bary, Qi-Chang He. A k-means clustering machine learning-based multiscale method for anelastic heterogeneous structures with internal variables. International Journal for Numerical Methods in Engineering, 2022, 123, pp.2012-2041. ⟨10.1002/nme.6925⟩. ⟨hal-03621332⟩