Microstructure-based machine learning of damage models including anisotropy, irreversibility and evolution

Abstract

A homogenization framework for materials incorporating evolving cracks is proposed, with machine learning to discover the evolution laws of the internal variables describing the homogenized anisotropic damage. The damage model is constructed using data-driven harmonic analysis of damage (DDHAD). First, simulations on Representative Volume Elements (RVEs) with local crack initiation and propagation are performed along different loading trajectories. The elastic tensor is homogenized for each loading increment and step, and recorded as data. Macroscopic internal variables defining arbitrary anisotropic damage are extracted by calculating orientation-dependent damage functions and expanding them into spherical harmonics, the independent coefficients of which are used as macroscopic internal variables. A reduction step is performed to minimize the number of internal variables using Proper Orthogonal Decomposition. A simple Feed-Forward neural network is used to discover the evolution laws of these internal variables, and an algorithm is proposed to manage loading/unloading scenarios. The technique is applied to different RVEs so as to construct anisotropic damage models, including initial and induced anisotropy, progressive and compressive damage.