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Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors

Nathan Ellmer, Rogelio Ortigosa, Jesús Martínez-Frutos, Roman Poya, Johann Sienz Orcid Logo, Antonio Gil Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 432, Issue: B

Swansea University Authors: Nathan Ellmer, Johann Sienz Orcid Logo, Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.cma.2024.117408

Abstract

This paper introduces a new Gradient Enhanced Gaussian Predictor (Kriging) constitutive metamodel based on the use of principal stretches for hyperelasticity. The model further accounts for anisotropy by incorporating suitable invariants of the relevant symmetry integrity basis. The use of stretches...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825 1879-2138
Published: Elsevier 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67732
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The model further accounts for anisotropy by incorporating suitable invariants of the relevant symmetry integrity basis. The use of stretches is beneficial since it aligns to experimental practices for data gathering, removes the challenge associated with stress projections in isotropy, and increases the range of available constitutive models. This paper presents three significant novelties. The first arises from the proposed approach highlighting the need to enforce physical symmetries and resulted in the authors altering the standard Radial Basis style correlation function to incorporate invariants which naturally uphold these symmetries. The invariants used are both the commonly employed invariants of the right Cauchy–Green strain tensor and the lesser used invariants of the stretch tensor. Note that one may consider using invariants in the correlation function to be the same as using invariants for inputs to the metamodel and this would be true if Ordinary Kriging was used. But the derivatives used in the chain rule clearly result in a new formulation. Secondly, the authors compare two approaches to the infill strategies, one consisting of the error in stress and the other utilising uncertainty provided by Kriging directly. This enables Kriging to guide the user as to most efficient data to insert into the dataset. The final novelty involves the integration of calibrated constitutive metamodels into Finite Element simulations thereby showcasing the accuracy yielded even when handling highly complex deformations such as bending, wrinkling and pinching. Furthermore, the constitutive models are calibrated with data from both isotropic and anisotropic materials such as rank-one laminates, making the accuracy achieved with the small calibration sets even more impressive. 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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 Tecnologia de la Region de Murcia.</funders><projectreference/><lastEdited>2024-10-23T13:54:43.1422644</lastEdited><Created>2024-09-19T11:44:31.6562149</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering</level></path><authors><author><firstname>Nathan</firstname><surname>Ellmer</surname><order>1</order></author><author><firstname>Rogelio</firstname><surname>Ortigosa</surname><order>2</order></author><author><firstname>Jesús</firstname><surname>Martínez-Frutos</surname><order>3</order></author><author><firstname>Roman</firstname><surname>Poya</surname><order>4</order></author><author><firstname>Johann</firstname><surname>Sienz</surname><orcid>0000-0003-3136-5718</orcid><order>5</order></author><author><firstname>Antonio</firstname><surname>Gil</surname><orcid>0000-0001-7753-1414</orcid><order>6</order></author></authors><documents><document><filename>67732__31507__3242236f300a4e9598a4f05e851a5134.pdf</filename><originalFilename>67732.VOR.pdf</originalFilename><uploaded>2024-10-02T09:54:41.0426777</uploaded><type>Output</type><contentLength>4674176</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>© 2024 The Authors. 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spelling v2 67732 2024-09-19 Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors da413556083b41e614a5d2264a0124dd Nathan Ellmer Nathan Ellmer true false 17bf1dd287bff2cb01b53d98ceb28a31 0000-0003-3136-5718 Johann Sienz Johann Sienz true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2024-09-19 This paper introduces a new Gradient Enhanced Gaussian Predictor (Kriging) constitutive metamodel based on the use of principal stretches for hyperelasticity. The model further accounts for anisotropy by incorporating suitable invariants of the relevant symmetry integrity basis. The use of stretches is beneficial since it aligns to experimental practices for data gathering, removes the challenge associated with stress projections in isotropy, and increases the range of available constitutive models. This paper presents three significant novelties. The first arises from the proposed approach highlighting the need to enforce physical symmetries and resulted in the authors altering the standard Radial Basis style correlation function to incorporate invariants which naturally uphold these symmetries. The invariants used are both the commonly employed invariants of the right Cauchy–Green strain tensor and the lesser used invariants of the stretch tensor. Note that one may consider using invariants in the correlation function to be the same as using invariants for inputs to the metamodel and this would be true if Ordinary Kriging was used. But the derivatives used in the chain rule clearly result in a new formulation. Secondly, the authors compare two approaches to the infill strategies, one consisting of the error in stress and the other utilising uncertainty provided by Kriging directly. This enables Kriging to guide the user as to most efficient data to insert into the dataset. The final novelty involves the integration of calibrated constitutive metamodels into Finite Element simulations thereby showcasing the accuracy yielded even when handling highly complex deformations such as bending, wrinkling and pinching. Furthermore, the constitutive models are calibrated with data from both isotropic and anisotropic materials such as rank-one laminates, making the accuracy achieved with the small calibration sets even more impressive. The formulation is shown to perform equally well for both synthetic and experimental type of collected data. Journal Article Computer Methods in Applied Mechanics and Engineering 432 B Elsevier 0045-7825 1879-2138 Gradient Kriging, constitutive modelling, principal stretches, hyperelasticity, anisotropy 1 12 2024 2024-12-01 10.1016/j.cma.2024.117408 COLLEGE NANME COLLEGE CODE Swansea University SU Library paid the OA fee (TA Institutional Deal) N. Ellmer and A. J. Gil wish to acknowledge the financial support provided by the defence, science and technology laboratory (Dstl). Additionally, R. Ortigosa and J. Mart´ınez-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 Tecnologia de la Region de Murcia. 2024-10-23T13:54:43.1422644 2024-09-19T11:44:31.6562149 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Nathan Ellmer 1 Rogelio Ortigosa 2 Jesús Martínez-Frutos 3 Roman Poya 4 Johann Sienz 0000-0003-3136-5718 5 Antonio Gil 0000-0001-7753-1414 6 67732__31507__3242236f300a4e9598a4f05e851a5134.pdf 67732.VOR.pdf 2024-10-02T09:54:41.0426777 Output 4674176 application/pdf Version of Record true © 2024 The Authors. This is an open access article distributed under the terms of the Creative Commons CC-BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
spellingShingle Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
Nathan Ellmer
Johann Sienz
Antonio Gil
title_short Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
title_full Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
title_fullStr Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
title_full_unstemmed Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
title_sort Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors
author_id_str_mv da413556083b41e614a5d2264a0124dd
17bf1dd287bff2cb01b53d98ceb28a31
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author_id_fullname_str_mv da413556083b41e614a5d2264a0124dd_***_Nathan Ellmer
17bf1dd287bff2cb01b53d98ceb28a31_***_Johann Sienz
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Nathan Ellmer
Johann Sienz
Antonio Gil
author2 Nathan Ellmer
Rogelio Ortigosa
Jesús Martínez-Frutos
Roman Poya
Johann Sienz
Antonio Gil
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 432
container_issue B
publishDate 2024
institution Swansea University
issn 0045-7825
1879-2138
doi_str_mv 10.1016/j.cma.2024.117408
publisher Elsevier
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 new Gradient Enhanced Gaussian Predictor (Kriging) constitutive metamodel based on the use of principal stretches for hyperelasticity. The model further accounts for anisotropy by incorporating suitable invariants of the relevant symmetry integrity basis. The use of stretches is beneficial since it aligns to experimental practices for data gathering, removes the challenge associated with stress projections in isotropy, and increases the range of available constitutive models. This paper presents three significant novelties. The first arises from the proposed approach highlighting the need to enforce physical symmetries and resulted in the authors altering the standard Radial Basis style correlation function to incorporate invariants which naturally uphold these symmetries. The invariants used are both the commonly employed invariants of the right Cauchy–Green strain tensor and the lesser used invariants of the stretch tensor. Note that one may consider using invariants in the correlation function to be the same as using invariants for inputs to the metamodel and this would be true if Ordinary Kriging was used. But the derivatives used in the chain rule clearly result in a new formulation. Secondly, the authors compare two approaches to the infill strategies, one consisting of the error in stress and the other utilising uncertainty provided by Kriging directly. This enables Kriging to guide the user as to most efficient data to insert into the dataset. The final novelty involves the integration of calibrated constitutive metamodels into Finite Element simulations thereby showcasing the accuracy yielded even when handling highly complex deformations such as bending, wrinkling and pinching. Furthermore, the constitutive models are calibrated with data from both isotropic and anisotropic materials such as rank-one laminates, making the accuracy achieved with the small calibration sets even more impressive. The formulation is shown to perform equally well for both synthetic and experimental type of collected data.
published_date 2024-12-01T13:54:41Z
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score 11.03559

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