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Abstract

Constitutive modeling of anisotropic plastic material behavior for continuum-scale simulations traditionally follows a deductive scheme, relying on empirical observations that are cast into analytic equations, the so-called phenomenological yield functions. Recently, data-driven constitutive modeling has emerged as an alternative to phenomenological models as it offers a more general way to describe the material behavior with no or fewer assumptions. In data-driven constitutive modeling, methods of statistical learning, often neural networks, are applied to infer the material model directly from a data set generated by experiments or numerical simulations. Currently, these data sets solely consist of stresses and strains, considering the microstructure only implicitly. Similar to the phenomenological approach, this limits the generality of the inferred material model, as it is only valid for the specific material employed in the virtual or physical experiments. In this work, we present an approach to overcome this limited generality by incorporating explicitly microstructural information into the yield function. The approach builds upon the support vector machine (SVM) for ideal plasticity introduced by Hartmaier 2020 and extends its feature space from stress only to stress + texture. The texture is described by the coefficients of the general spherical harmonics (GSH) series expansion of the orientation distribution function (ODF). We create a data set that contains the yield points in 140 different loading directions for over 7000 cubic-orthorhombic textures by using full-field crystal plasticity simulations. A single SVM classifier is trained on this data set to find the class boundary between elastic and plastic data points. This class boundary represents the yield surface, dependent on stress and texture. Studying the generalization property of the trained SVM on a hold-out test set shows that the model is capable of predicting the yield surface for unknown textures with sufficient accuracy. Our approach shows a way to incorporate microstructural information into data-driven constitutive modeling to derive more general material models that explicitly depend on the microstructure. By this extension, the derived material model stays valid even if the underlying microstructure of the material changes.