Constitutive artificial neural networks : a fast and general approach to predictive data-driven constitutive modeling by deep learning

In this paper we introduce constitutive artificial neural networks (CANNs), a novel machine learning architecture for data-driven modeling of the mechanical constitutive behavior of materials. CANNs are able to incorporate by their very design information from three different sources, namely stress-strain data, theoretical knowledge from materials theory, and diverse additional information (e.g., about microstructure or materials processing). CANNs can easily and efficiently be implemented in standard computational software. They require only a low-to-moderate amount of training data and training time to learn without human guidance the constitutive behavior also of complex nonlinear and anisotropic materials. Moreover, in a simple academic example we demonstrate how the input of microstructural data can endow CANNs with the ability to describe not only the behavior of known materials but to predict also the properties of new materials where no stress-strain data are available yet. This ability may be particularly useful for the future in-silico design of new materials. The developed source code of the CANN architecture and accompanying example data sets are available at https://github.com/ConstitutiveANN/CANN.

Subjects

Constitutive modeling

Data-driven

Deep learning

Hyperelasticity

MLE@TUHH

DDC Class

600: Technik

Funding(s)

SFB 986: Teilprojekt B09 - Mikrostrukturbasierte Klassifizierung und mechanische Analyse nanoporöser Metalle durch maschinelles Lernen

Vaskuläre Wachstums- und Umbildungsprozesse in Aneurysmen

I³-Lab - Modell-gestütztes maschinelles Lernen für die Weichgewebsmodellierung in der Medizin

More Funding Information

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 257981274; Projektnummer 192346071 -SFB 986. Moreover, K. P. Abdolazizi and C. J. Cyron greatfully acknowledge financial support from TUHH within the I3-Lab ‘Modellgestütztes maschinelles Lernen fuer die Weichgewebsmodellierung in der Medizin’.

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https://creativecommons.org/licenses/by-nc-nd/4.0/

Name

1-s2.0-S0021999120307841-main.pdf

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1.58 MB

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Constitutive artificial neural networks : a fast and general approach to predictive data-driven constitutive modeling by deep learning