Unsupervised machine learning classification for accelerating FE2 multiscale fracture simulations

An approach is proposed to accelerate multiscale simulations of heterogeneous quasi-brittle materials exhibiting an anisotropic damage response. The present technique uses unsupervised machine learning classification based on k-means clustering to select integration points in the macro mesh within an FE${}^2$ strategy to track redundant micro nonlinear problems and to avoid unnecessary Representative Volume Element (RVE) calculations. More specifically, a classification vector including strains and internal damage variables is defined for each macro integration point. The macro internal damage variables are constructed using harmonic analysis of damage. At each step of the macro iterations, the integrations points are grouped into clusters and only one nonlinear problem is solved for each cluster. As a result, the computations are accelerated within an FE${}^2$ scheme by reducing the total number of RVE problems to be solved. The developed algorithm includes a macro regularization and an arc-length technique to capture macro snap-back due to the softening. Applications are proposed to simulate the response of different heterogeneous quasi-brittle materials with strong anisotropic responses. speed-up factors of the order of 12 to 15 can be achieved without the need to build a database, and without reduced-order modeling approximations at the micro level. Estimates of structural strength can be obtained with Speed-up factors between 45 and 85.