A data-driven harmonic approach to constructing anisotropic damage models with a minimum number of internal variables

• Published in: Journal of the mechanics and physics of solids Vol. 162; p. 104828
• Main Authors: Yvonnet, Julien, He, Qi-Chang, Li, Pengfei
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01-05-2022; Elsevier BV; Elsevier
• Subjects: Anisotropic damage; Brittle materials; Craks; Damage assessment; Data-driven; Distribution functions; Engineering Sciences; Fourier analysis; Fourier series; Harmonic analysis; Harmonic damage models; Image-based models; Induced anisotropy; Load history; Mathematical models; Microcracks; Modulus of elasticity; Nucleation; Phase field; Tensors; Three dimensional models; Two dimensional models; Harmonic damage models; Anisotropic damage; Induced anisotropy; Phase field; Image-based models; Data-driven; Craks; craks; image-based models; data-driven; harmonic damage models; induced anisotropy; phase field
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2022.104828

A data-driven approach is proposed to construct anisotropic damage models with a minimal number of internal variables from numerical simulations on Representative Volume Elements (RVEs) of quasi-brittle materials. The approach resorts in particular to a harmonic analysis of damage. The orientation distribution functions of two elastic moduli are numerically determined while accounting for the effects of the nucleation and propagation of microcracks by the phase-field method. Given these two functions, the effective elastic tensor of a material without or with microcracks is uniquely determined. The expansions into two Fourier series of the relative variations of these two functions related to an undamaged reference state and to a damage state make appear damage internal variables naturally. The number and natures of these variables can be optimized by truncating the Fourier series according to the degree of approximation desired. Thus, 2D and 3D anisotropic damage models can be constructed without resorting to usual assumptions made in damage mechanics. This construction holds for complex microstructures including image-based ones and for arbitrary loading history. Two- and three-dimensional applications are provided to evaluate the accuracy of the damage models constructed and to show the potential of the approach proposed.