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Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors

A. Pérez-Escolar, J. Martínez-Frutos, Rogelio Ortigosa Martinez, N. Ellmer, Antonio Gil Orcid Logo

Computational Mechanics

Swansea University Authors: Rogelio Ortigosa Martinez, Antonio Gil Orcid Logo

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DOI (Published version): 10.1007/s00466-024-02446-8

Abstract

This paper introduces a metamodelling technique that employs gradient-enhanced Gaussian Process Regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor F and electric displacement field D0. The approach integrates principal invariants as inputs for the...

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Published in: Computational Mechanics
ISSN: 0178-7675 1432-0924
Published: Springer Science and Business Media LLC 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa65822
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spelling v2 65822 2024-03-12 Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors 80e7ab60860604f60530676f5037d225 Rogelio Ortigosa Martinez Rogelio Ortigosa Martinez true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2024-03-12 FGSEN This paper introduces a metamodelling technique that employs gradient-enhanced Gaussian Process Regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor F and electric displacement field D0. The approach integrates principal invariants as inputs for the surrogate internal energy density, enforcing physical constraints like material frame indifference and symmetry. This technique enables accurate interpolation of energy and its derivatives, including the first Piola-Kirchhoff stress tensor and material electric field. The method ensures stress and electric field-free conditions at the origin, which is challenging with regression-based methods like neural networks. The paper highlights that using invariants of the dual potential of internal energy density, i.e., the free energy density dependent on the material electric field E0, is inappropriate. The saddle pointnature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of F and E0 (free energy-based GPR), compared to those involving Fand D0 (internal energy-based GPR). Numerical examples within a 3D Finite Element framework assess surrogate model accuracy across challenging scenarios, comparing displacement and stress fields with ground-truth analytical models. Cases include extreme twisting and electrically induced wrinkles, demonstrating practical applicability and robustness of the proposed approach. Journal Article Computational Mechanics 0 Springer Science and Business Media LLC 0178-7675 1432-0924 Kriging, Machine Learning, Constitutive Modelling, Electro Active Polymers, Electromechanics 20 2 2024 2024-02-20 10.1007/s00466-024-02446-8 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University Another institution paid the OA fee Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. 2024-04-23T12:48:23.4496759 2024-03-12T10:47:22.8126273 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering A. Pérez-Escolar 1 J. Martínez-Frutos 2 Rogelio Ortigosa Martinez 3 N. Ellmer 4 Antonio Gil 0000-0001-7753-1414 5 65822__29688__ae697f7459f34ab7b50a215c7552d595.pdf 65822.pdf 2024-03-12T10:52:15.0454251 Output 1843199 application/pdf Version of Record true © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License. true eng http://creativecommons.org/licenses/by/4.0/
title Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
spellingShingle Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
Rogelio Ortigosa Martinez
Antonio Gil
title_short Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
title_full Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
title_fullStr Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
title_full_unstemmed Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
title_sort Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
author_id_str_mv 80e7ab60860604f60530676f5037d225
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 80e7ab60860604f60530676f5037d225_***_Rogelio Ortigosa Martinez
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Rogelio Ortigosa Martinez
Antonio Gil
author2 A. Pérez-Escolar
J. Martínez-Frutos
Rogelio Ortigosa Martinez
N. Ellmer
Antonio Gil
format Journal article
container_title Computational Mechanics
container_volume 0
publishDate 2024
institution Swansea University
issn 0178-7675
1432-0924
doi_str_mv 10.1007/s00466-024-02446-8
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 1
active_str 0
description This paper introduces a metamodelling technique that employs gradient-enhanced Gaussian Process Regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor F and electric displacement field D0. The approach integrates principal invariants as inputs for the surrogate internal energy density, enforcing physical constraints like material frame indifference and symmetry. This technique enables accurate interpolation of energy and its derivatives, including the first Piola-Kirchhoff stress tensor and material electric field. The method ensures stress and electric field-free conditions at the origin, which is challenging with regression-based methods like neural networks. The paper highlights that using invariants of the dual potential of internal energy density, i.e., the free energy density dependent on the material electric field E0, is inappropriate. The saddle pointnature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of F and E0 (free energy-based GPR), compared to those involving Fand D0 (internal energy-based GPR). Numerical examples within a 3D Finite Element framework assess surrogate model accuracy across challenging scenarios, comparing displacement and stress fields with ground-truth analytical models. Cases include extreme twisting and electrically induced wrinkles, demonstrating practical applicability and robustness of the proposed approach.
published_date 2024-02-20T12:48:20Z
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score 11.013148

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