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Abstract

In classical constitutive modeling, the response of a material to mechanical loads is described by explicit mathematical expressions for the relations between stress and strain or strain-rates. Such mathematical formulations can become rather intricate, e.g., when describing history-dependent plasticity for anisotropic materials. Yet, typically, such closed-form constitutive models do not take into account microstructural features, as grain size and shape or the crystallographic texture. This situation is rather unsatisfactory from a materials science point-of-view, as it is known that such microstructural features do not only control the mechanical behavior of a material but, moreover, they can be subject to change during plastic deformation. In this paper, it is demonstrated how microstructure-sensitive data on the mechanical behavior of polycrystals are used to train numerically efficient machine learning (ML) models as constitutive relations that can directly be applied in finite-element models of engineering structures. It is elucidated how work-hardening and information about crystallographic textures can be included in such ML flow rules for plasticity. The data sets that are necessary for the training of ML flow rules are generated by micromechanical simulations of polycrystalline samples. Such micromechanical models based on crystal plasticity have been shown to represent the real material behavior very well. In consequence, the trained ML model represents the deformation behavior of the micromechanical model and, thus, of the real material with high accuracy, including plastic anisotropy observed for different crystallographic textures. In a second step, it is discussed how micromechanical models can be used to describe damage that occurs on the microstructural scale during the deformation of polycrystals. Based on the data generated by such numerical simulations, machine learning models can be trained to describe the global damage evolution in the polycrystal, which effectively homogenizes the microstructural damage. In this way, an ML damage model is generated in form of a macro-scale constitutive model. In conclusion, the paper demonstrates how ML methods can be trained with data generated by micromechanical simulations. The trained ML models operate as data-oriented constitutive relations for plasticity and damage that can be applied in finite-element simulations. Thus, this data-oriented approach represents an efficient homogenization method bridging the microscopic to the macroscopic scale.