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

• Published in: Journal of the mechanics and physics of solids Vol. 200; p. 106160
• Main Authors: Yvonnet, Julien, He, Qi-Chang
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2025
• Subjects: Anisotropic damage; Crack; Data-driven; Homogenization; Machine learning; Phase field; Homogenization; Data-driven; Anisotropic damage; Machine learning; Phase field; Crack
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2025.106160

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. •A machine learning framework is proposed for constructing anisotropic damage models from micro cracking simulations.•The model is able to handle arbitrary initially anisotropic RVEs, and anisotropic evolutions during micro cracking.•The model is able to handle loading–unloading for anisotropic damage situations.•The model can capture complex micro damage mechanisms such as progressive or compressive damage.•Evolution of internal variables, defined by harmonic analysis, are obtained by machine learning.