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Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues

Ankush Aggarwal, Bjørn Sand Jensen Orcid Logo, Sanjay Pant Orcid Logo, Chung-Hao Lee Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 404, Start page: 115812

Swansea University Author: Sanjay Pant Orcid Logo

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DOI (Published version): 10.1016/j.cma.2022.115812

Abstract

Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy d...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62031
first_indexed 2022-11-24T11:49:02Z
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spelling 2022-12-16T08:15:21.2296383 v2 62031 2022-11-24 Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues 43b388e955511a9d1b86b863c2018a9f 0000-0002-2081-308X Sanjay Pant Sanjay Pant true false 2022-11-24 ACEM Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantageof a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed frameworkis verified against an artificial dataset based on the Gasser–Ogden–Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulationbased predictions. Journal Article Computer Methods in Applied Mechanics and Engineering 404 115812 Elsevier BV 0045-7825 Constitutive modeling, nonlinear elasticity, tissue biomechanics, Gaussian processes, stochastic finite element analysis, machine learning 1 2 2023 2023-02-01 10.1016/j.cma.2022.115812 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Support from the National Institutes of Health (NIH) Grant R01 HL159475 and the Presbyterian Health Foundation Team Science Grants is greatly acknowledged 2022-12-16T08:15:21.2296383 2022-11-24T11:43:28.0075537 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Ankush Aggarwal 1 Bjørn Sand Jensen 0000-0001-8074-228x 2 Sanjay Pant 0000-0002-2081-308X 3 Chung-Hao Lee 0000-0002-8019-3329 4 62031__26074__bddb17d10bb84c8dbc0531d5d52c53bc.pdf 62031.pdf 2022-12-13T11:57:47.6426225 Output 4255716 application/pdf Version of Record true © 2022 The Author(s). This is an open access article under the CC BY license true eng http://creativecommons.org/licenses/by/4.0/
title Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
spellingShingle Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
Sanjay Pant
title_short Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
title_full Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
title_fullStr Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
title_full_unstemmed Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
title_sort Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
author_id_str_mv 43b388e955511a9d1b86b863c2018a9f
author_id_fullname_str_mv 43b388e955511a9d1b86b863c2018a9f_***_Sanjay Pant
author Sanjay Pant
author2 Ankush Aggarwal
Bjørn Sand Jensen
Sanjay Pant
Chung-Hao Lee
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 404
container_start_page 115812
publishDate 2023
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2022.115812
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
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 Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantageof a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed frameworkis verified against an artificial dataset based on the Gasser–Ogden–Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulationbased predictions.
published_date 2023-02-01T14:20:49Z
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score 11.048042

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