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

TLDR

The ability to predict properties of new materials without stress‑strain data may be particularly useful for future in‑silico design of new materials. The paper introduces constitutive artificial neural networks (CANNs), a novel machine learning architecture for data‑driven modeling of materials’ mechanical constitutive behavior. CANNs incorporate stress‑strain data, theoretical materials knowledge, and additional information such as microstructure or processing, and the architecture’s source code and example datasets are publicly available on GitHub. CANNs are easily implemented in standard software, require only modest training data and time, and can predict the behavior of new materials using microstructural inputs even when no stress‑strain data exist.

Abstract

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.