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Abstract

In classical constitutive modeling, the response of a material to mechanical loads is described by explicitmathematical 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 on the level of single-crystalline regions, as it is done in crystal plasticity. 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 work, two approaches are highlighted how microstructure-sensitive data on plastic deformation of polycrystals are used to train numerically efficient machine learning models as constitutive relations that can directly be applied in finite-element models of engineering structures. In the first approach, the anisotropic yield function Barlat Yld2004-18p is parametrized from micromechanical simulations for different textures. The structure-property relationship between the crystallographic texture and the material parameters is then identified by applying supervised Machine Learning (ML) methods on that data set. As part of this identification process, different descriptors for the crystallographic texture are tested in their capability to relate unimodal and also fibre textures to a unique set of anisotropic parameters. In the second approach, it is investigated how an optimal data-generation strategy for the training of a ML model can be established that produces reliable and accurate ML yield functions with the least possible effort. It is shown that even for materials with a significant plastic anisotropy, as polycrystals with a pronounced Goss texture, 300 data points representing the yield locus of the material in stress space, are sufficient to train the ML yield function successfully. Furthermore, the formulation of a full ML flow rule is discussed, including strain hardening captured from micromechanical data.