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Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity

Nathan Ellmer Orcid Logo, Rogelio Ortigosa Orcid Logo, Jesus Martinez Frutos, Antonio Gil Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 418, Start page: 116547

Swansea University Authors: Jesus Martinez Frutos, Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.cma.2023.116547

Abstract

This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825 1879-2138
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa64772
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The approach adopted incorporates principal invariants as inputs for the surrogate of the strain energy density. This integration enables the surrogate to inherently enforce fundamental physical constraints, such as material frame indifference and material symmetry, right from the outset. The proposed approach provides accurate interpolation for energy and the first Piola–Kirchhoff stress tensor (e.g. first order derivatives with respect to inputs). The paper presents three notable innovations. Firstly, it introduces the utilisation of Gradient-Enhanced Kriging to approximate a diverse range of phenomenological models, encompassing numerous isotropic hyperelastic strain energies and a transversely isotropic potential. Secondly, this study marks the inaugural application of this technique for approximating the effective response of composite materials. This includes rank-one laminates, for which analytical solutions are feasible. However, it also encompasses more complex composite materials characterised by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centred spherical inclusion. This extension opens the door for future application of this technique to various RVE types, facilitating efficient three-dimensional computational analyses at the macro-scale of such composite materials, significantly reducing computational time compared to FEM. The third innovation, facilitated by the integration of these surrogate models into a 3D Finite Element computational framework, lies in the assessment of these models scenarios encompassing intricate cases of extreme twisting and more importantly, buckling instabilities in thin-walled structures, thereby highlighting both the practical applicability and robustness of the proposed approach.</abstract><type>Journal Article</type><journal>Computer Methods in Applied Mechanics and Engineering</journal><volume>418</volume><journalNumber/><paginationStart>116547</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0045-7825</issnPrint><issnElectronic>1879-2138</issnElectronic><keywords>Kriging, Machine learning, Constitutive modelling, Hyperelasticity, Anisotropy</keywords><publishedDay>5</publishedDay><publishedMonth>1</publishedMonth><publishedYear>2024</publishedYear><publishedDate>2024-01-05</publishedDate><doi>10.1016/j.cma.2023.116547</doi><url>http://dx.doi.org/10.1016/j.cma.2023.116547</url><notes/><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><funders>R. Ortigosa and J. Martínez-Frutos acknowledge the support of grant PID2022-141957OA-C22 funded by MCIN/AEI/10.13039/501100011033 and by “RDF A way of making Europe”. The authors also acknowledge the support provided by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundacion Seneca - Agencia de Ciencia y Tecnologia de la Region de Murcia. 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spelling v2 64772 2023-10-18 Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity 30997d7d1b7fc2aa27407e744f0ec770 Jesus Martinez Frutos Jesus Martinez Frutos true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2023-10-18 FGSEN This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs for the surrogate of the strain energy density. This integration enables the surrogate to inherently enforce fundamental physical constraints, such as material frame indifference and material symmetry, right from the outset. The proposed approach provides accurate interpolation for energy and the first Piola–Kirchhoff stress tensor (e.g. first order derivatives with respect to inputs). The paper presents three notable innovations. Firstly, it introduces the utilisation of Gradient-Enhanced Kriging to approximate a diverse range of phenomenological models, encompassing numerous isotropic hyperelastic strain energies and a transversely isotropic potential. Secondly, this study marks the inaugural application of this technique for approximating the effective response of composite materials. This includes rank-one laminates, for which analytical solutions are feasible. However, it also encompasses more complex composite materials characterised by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centred spherical inclusion. This extension opens the door for future application of this technique to various RVE types, facilitating efficient three-dimensional computational analyses at the macro-scale of such composite materials, significantly reducing computational time compared to FEM. The third innovation, facilitated by the integration of these surrogate models into a 3D Finite Element computational framework, lies in the assessment of these models scenarios encompassing intricate cases of extreme twisting and more importantly, buckling instabilities in thin-walled structures, thereby highlighting both the practical applicability and robustness of the proposed approach. Journal Article Computer Methods in Applied Mechanics and Engineering 418 116547 Elsevier BV 0045-7825 1879-2138 Kriging, Machine learning, Constitutive modelling, Hyperelasticity, Anisotropy 5 1 2024 2024-01-05 10.1016/j.cma.2023.116547 http://dx.doi.org/10.1016/j.cma.2023.116547 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University R. Ortigosa and J. Martínez-Frutos acknowledge the support of grant PID2022-141957OA-C22 funded by MCIN/AEI/10.13039/501100011033 and by “RDF A way of making Europe”. The authors also acknowledge the support provided by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundacion Seneca - Agencia de Ciencia y Tecnologia de la Region de Murcia. The fourth author also acknowledges the financial support received through the European Training Network Protechtion (Project ID: 764636) and of the UK Defense, Science and Technology Laboratory 2023-11-20T12:08:05.9808365 2023-10-18T12:52:48.6909775 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Electronic and Electrical Engineering Nathan Ellmer 0000-0003-0926-0485 1 Rogelio Ortigosa 0000-0002-4542-2237 2 Jesus Martinez Frutos 3 Antonio Gil 0000-0001-7753-1414 4 64772__28819__a8fcffab96bb472b80ecd4863a6da271.pdf Kriging_polymer_Nathan_paper_AAM.pdf 2023-10-18T13:10:02.3876120 Output 12898925 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/
title Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
spellingShingle Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
Jesus Martinez Frutos
Antonio Gil
title_short Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
title_full Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
title_fullStr Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
title_full_unstemmed Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
title_sort Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
author_id_str_mv 30997d7d1b7fc2aa27407e744f0ec770
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 30997d7d1b7fc2aa27407e744f0ec770_***_Jesus Martinez Frutos
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Jesus Martinez Frutos
Antonio Gil
author2 Nathan Ellmer
Rogelio Ortigosa
Jesus Martinez Frutos
Antonio Gil
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 418
container_start_page 116547
publishDate 2024
institution Swansea University
issn 0045-7825
1879-2138
doi_str_mv 10.1016/j.cma.2023.116547
publisher Elsevier BV
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 - Electronic and Electrical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Electronic and Electrical Engineering
url http://dx.doi.org/10.1016/j.cma.2023.116547
document_store_str 1
active_str 0
description This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs for the surrogate of the strain energy density. This integration enables the surrogate to inherently enforce fundamental physical constraints, such as material frame indifference and material symmetry, right from the outset. The proposed approach provides accurate interpolation for energy and the first Piola–Kirchhoff stress tensor (e.g. first order derivatives with respect to inputs). The paper presents three notable innovations. Firstly, it introduces the utilisation of Gradient-Enhanced Kriging to approximate a diverse range of phenomenological models, encompassing numerous isotropic hyperelastic strain energies and a transversely isotropic potential. Secondly, this study marks the inaugural application of this technique for approximating the effective response of composite materials. This includes rank-one laminates, for which analytical solutions are feasible. However, it also encompasses more complex composite materials characterised by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centred spherical inclusion. This extension opens the door for future application of this technique to various RVE types, facilitating efficient three-dimensional computational analyses at the macro-scale of such composite materials, significantly reducing computational time compared to FEM. The third innovation, facilitated by the integration of these surrogate models into a 3D Finite Element computational framework, lies in the assessment of these models scenarios encompassing intricate cases of extreme twisting and more importantly, buckling instabilities in thin-walled structures, thereby highlighting both the practical applicability and robustness of the proposed approach.
published_date 2024-01-05T12:08:07Z
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