Investigation of failure in anisotropic composite structures via an efficient data-driven multiscale strategy

In this work, a computationally efficient multiscale strategy is proposed for accurately predicting failure in composite materials under general loading conditions. The main ingredient of this strategy is a data-driven surrogate model for damaging anisotropic microstructures, to be obtained through several nonlinear hierarchical homogenization processes performed on the same repeating unit cell subjected to different macrostrain paths. The adopted macroscale constitutive model considers the overall secant elastic moduli as internal variables, and introduces a general fourth-order damage surface tensor, representing the macroscale anisotropic damage evolution, which depends on both the overall secant moduli and applied macrostrains. A deep neural network (DNN) approach is used to derive an approximate functional form for this damage surface tensor, based on the best fitting of nonlinear micromechanical results. Then, the numerical accuracy of the proposed data-driven multiscale model is assessed by comparing the relevant results with those coming from a nonlinear periodic homogenization approach, with reference to a regularly perforated microstructure subjected to arbitrary macrostrain histories, involving both proportional and nonproportional paths.