Working Paper Article Version 2 This version is not peer-reviewed

Data-Oriented Constitutive Modeling of Plasticity in Metals

Version 1 : Received: 9 March 2020 / Approved: 10 March 2020 / Online: 10 March 2020 (10:42:35 CET)
Version 2 : Received: 25 March 2020 / Approved: 26 March 2020 / Online: 26 March 2020 (14:51:50 CET)

A peer-reviewed article of this Preprint also exists.

Hartmaier, A. Data-Oriented Constitutive Modeling of Plasticity in Metals. Materials 2020, 13, 1600. Hartmaier, A. Data-Oriented Constitutive Modeling of Plasticity in Metals. Materials 2020, 13, 1600.


Constitutive models for plastic deformation of metals are typically based on flow rules determining the transition from elastic to plastic response of a material as function of the applied mechanical load. These flow rules are commonly formulated as a yield function, based on the equivalent stress and the yield strength of the material, and its derivatives. In this work, a novel mathematical formulation is developed that allows the efficient use of machine learning algorithms describing the elastic-plastic deformation of a solid under arbitrary mechanical loads and that can replace the standard yield functions with more flexible algorithms. By exploiting basic physical principles of elastic-plastic deformation, the dimensionality of the problem is reduced without loss of generality. The data-oriented approach inherently offers a great flexibility to handle different kinds of material anisotropy without the need for explicitly calculating a large number of model parameters. The applicability of this formulation in finite element analysis is demonstrated, and the results are compared to formulations based on Hill-like anisotropic plasticity as reference model. In future applications, the machine learning algorithm can be trained by hybrid experimental and numerical data, as for example obtained from fundamental micromechanical simulations based on crystal plasticity models. In this way, data-oriented constitutive modeling will also provide a new way to homogenize numerical results in a scale-bridging approach.

Supplementary and Associated Material GitHub repository of code and further applications


plasticity; machine learning; constitutive modeling


Chemistry and Materials Science, Materials Science and Technology

Comments (1)

Comment 1
Received: 26 March 2020
Commenter: Alexander Hartmaier
Commenter's Conflict of Interests: Author
Comment: This is the revised version after the reviewer comments. Some parts of the text have been clarified and Section 3.3 has been added. It corresponds to the revised version submitted for peer review, axcept that the changes are not highlighted.
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