Data-Driven Multi-scale Numerical Homogenization

Homogenization for complex, nonlinear materials, including composites and textiles, is considered. The effect of the microstructure, including nonlinearity, for various loadings is transferred to the homogenized medium through the Representative Volume Element technique. The classical approach through nested finite element analysis, the so-called FEM2 method, is very expensive. Data-driven techniques have been proposed, where the homogenization is replaced by a surrogate model based on data generated through selected numerical or physical experiments. An artificial neural network surrogate constitutive model leads to a FEANN method. Furthermore data-driven solution methods have been recently proposed, as a development of the LATIN iterative method. A short review of recent contributions is presented, with examples from composites, including woven composites and auxetics. Research topics will be discussed, including the development of Physics Informed Neural Network surrogates.