Prediction of anisotropic damage evolution in nacre-inspired composites by using a data-driven nonlinear homogenization approach

This paper presents a computationally efficient data-driven multiscale strategy for accurately predicting failure in arbitrary 2D periodically microstructured materials. This strategy relies on a surrogate model specifically designed to represent macroscale anisotropic damage evolution under general loading conditions. This surrogate model is developed in two phases. In the first phase, named as off-line phase, the discrete evolution of the overall secant moduli, here treated as damage variables, is derived from several nonlinear micromechanical analyses conducted on the same Repeating Unit Cell (RUC) along different monotonic proportional loading paths. To derive a continuous evolution law, a deep neural network (DNN) is employed to fit all the resulting micromechanical data. Instead, in the second phase, called on-line phase, a complete surrogate model is developed by combining the previous data-driven evolution law with an ad-hoc stress update strategy to correctly enforce damage irreversibility during elastic unloading. The present numerical strategy is applied to predict the complex microscale failure mechanisms in nacre-inspired staggered composites subjected to diverse macrostrain histories, including both proportional and nonproportional paths. The accuracy of the data-driven multiscale results obtained here is evaluated by comparing them to those arising from a direct nonlinear micromechanical approach.