Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies

In this work, we propose a reliable and stable procedure to characterize anisotropic hyperelastic materials. For this purpose, a metaheuristic optimization method known as evolutionary strategies is used. The advantage of this technique with respect to traditional methods used for non-linear optimiz...

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Main Authors: Claudio Canales, Claudio García-Herrera, Eugenio Rivera, Demetrio Macías, Diego Celentano
Format: Article
Language:English
Published: MDPI AG 2023-02-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/11/4/922
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author Claudio Canales
Claudio García-Herrera
Eugenio Rivera
Demetrio Macías
Diego Celentano
author_facet Claudio Canales
Claudio García-Herrera
Eugenio Rivera
Demetrio Macías
Diego Celentano
author_sort Claudio Canales
collection DOAJ
description In this work, we propose a reliable and stable procedure to characterize anisotropic hyperelastic materials. For this purpose, a metaheuristic optimization method known as evolutionary strategies is used. The advantage of this technique with respect to traditional methods used for non-linear optimization, such as the Levenberg–Marquardt Method, is that this metaheuristic algorithm is oriented to the global optimization of a problem, is independent of gradients and allows to solve problems with constraints. These features are essential when characterizing hyperelastic materials that have non-linearities and are conditioned to regions of stability. To characterize the mechanical behavior of the arteries analyzed in this work, the anisotropic hyperelastic models of Holzapfel–Gasser–Ogden and Gasser–Holzapfel–Ogden are used. An important point of the analysis is that these models may present a non-physical behavior: this drawback is overcome by defining a new criterion of stabilization in conjunction with the evolutionary strategies. Finally, the finite element simulations are used in conjunction with the evolutionary strategies to characterize experimental data of the artery pressurization test, ensuring that the parameters obtained are stable and representative of the material response.
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spelling doaj.art-cde0bde5e3d643b0a4f59bb438dd874d2023-11-16T21:55:54ZengMDPI AGMathematics2227-73902023-02-0111492210.3390/math11040922Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary StrategiesClaudio Canales0Claudio García-Herrera1Eugenio Rivera2Demetrio Macías3Diego Celentano4Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago 9170020, ChileDepartamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago 9170020, ChileDepartamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago 9170020, ChileLaboratory Light, Nanomaterials & Nanotechnologies—L2n, University of Technology of Troyes & CNRS EMR 7004, 12 Rue Marie Curie, CS 42060, 10004 Troyes, FranceDepartamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago 7820436, ChileIn this work, we propose a reliable and stable procedure to characterize anisotropic hyperelastic materials. For this purpose, a metaheuristic optimization method known as evolutionary strategies is used. The advantage of this technique with respect to traditional methods used for non-linear optimization, such as the Levenberg–Marquardt Method, is that this metaheuristic algorithm is oriented to the global optimization of a problem, is independent of gradients and allows to solve problems with constraints. These features are essential when characterizing hyperelastic materials that have non-linearities and are conditioned to regions of stability. To characterize the mechanical behavior of the arteries analyzed in this work, the anisotropic hyperelastic models of Holzapfel–Gasser–Ogden and Gasser–Holzapfel–Ogden are used. An important point of the analysis is that these models may present a non-physical behavior: this drawback is overcome by defining a new criterion of stabilization in conjunction with the evolutionary strategies. Finally, the finite element simulations are used in conjunction with the evolutionary strategies to characterize experimental data of the artery pressurization test, ensuring that the parameters obtained are stable and representative of the material response.https://www.mdpi.com/2227-7390/11/4/922evolutionary strategiesanisotropic hyperelasticitycharacterizationmechanical testsparameter fitting
spellingShingle Claudio Canales
Claudio García-Herrera
Eugenio Rivera
Demetrio Macías
Diego Celentano
Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies
Mathematics
evolutionary strategies
anisotropic hyperelasticity
characterization
mechanical tests
parameter fitting
title Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies
title_full Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies
title_fullStr Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies
title_full_unstemmed Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies
title_short Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies
title_sort anisotropic hyperelastic material characterization stability criterion and inverse calibration with evolutionary strategies
topic evolutionary strategies
anisotropic hyperelasticity
characterization
mechanical tests
parameter fitting
url https://www.mdpi.com/2227-7390/11/4/922
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