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.

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The aim of this study is to evaluate experimentally the influence of quartz (dune sand) incorporation in the cement matrix by mass substitution at different percentages and diameters, on the mechanical properties of the mortars. Properties of the mortars were determined by flexural traction and compressive strength; the results obtained highlight the effect of the sand dune grain diameter on the mechanical properties of the mortars tested. The use of quartz (dune sand) with a diameter of less than 0.16mm improved the mechanical strength of mortars.