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A framework for neural network based constitutive modelling of inelastic materials

Wulf Dettmer Orcid Logo, Eugenio J. Muttio Orcid Logo, Reem Alhayki, Djordje Perić, Eugenio Muttio Zavala, Djordje Peric Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 420, Start page: 116672

Swansea University Authors: Wulf Dettmer Orcid Logo, Reem Alhayki, Eugenio Muttio Zavala, Djordje Peric Orcid Logo

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Abstract

Given the significant recent advances in added layer manufacturing and materials engineering, new types of materials or new material micro-structures are becoming available at a fast rate. The finite element analysis of structures or structural components requires a constitutive model that describes...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825 1879-2138
Published: Elsevier BV 2024
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa65340
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Abstract: Given the significant recent advances in added layer manufacturing and materials engineering, new types of materials or new material micro-structures are becoming available at a fast rate. The finite element analysis of structures or structural components requires a constitutive model that describes the behaviour of the new materials. The formulation of accurate constitutive equations is generally complex and time consuming. Hence, suitable machine learning strategies may be used to render this process obsolete and bridge the gap between experimental data and finite element analysis. In this work, a generic stress update procedure is presented that is suitable for the modelling of rate-independent, elastic or inelastic, isotropic or anisotropic material behaviour. The proposed strategy is based on a recurrent neural network architecture and must be trained on stress and strain data sequences that represent physical or numerical experiments. A training strategy based on gradient-free optimisation is presented. It is shown that piecewise linear behaviour, such as uniaxial elasto-plasticity, can be represented exactly. Further numerical examples include uniaxial damage mechanics and elasto-plasticity under plane strain conditions. An efficient criterion for the verification of thermodynamic consistency is proposed and applied to the trained stress update models. The strategy is compared to GRU or LSTM based architectures and shown to offer advantages.
Keywords: Data driven computational mechanics, Neural network, Constitutive modelling, Elasto-plasticity, Damage mechanics
College: Faculty of Science and Engineering
Funders: Eugenio J. Muttio gratefully acknowledges research support provided by UKAEA and EPSRC through the Doctoral Training Partnership (DTP) scheme. This work has been part-funded by the EPSRC Energy Programme [grant number EP/W006839/1].
Start Page: 116672