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A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification

Given the importance of hyperelastic constitutive models in the design of engineering components, researchers have been developing the improved and new constitutive models in search of a more accurate and even universal performance. Here, a modified hyperelastic constitutive model based on the Yeoh...

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Autores principales: Wang, Wei, Liu, Yang, Xie, Zongwu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10421088/
https://www.ncbi.nlm.nih.gov/pubmed/37571066
http://dx.doi.org/10.3390/polym15153172
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author Wang, Wei
Liu, Yang
Xie, Zongwu
author_facet Wang, Wei
Liu, Yang
Xie, Zongwu
author_sort Wang, Wei
collection PubMed
description Given the importance of hyperelastic constitutive models in the design of engineering components, researchers have been developing the improved and new constitutive models in search of a more accurate and even universal performance. Here, a modified hyperelastic constitutive model based on the Yeoh model is proposed to improve its prediction performance for multiaxial deformation of hyperelastic polymeric materials while retaining the advantages of the original Yeoh model. The modified constitutive model has one more correction term than the original model. The specific form of the correction term is a composite function based on a power function represented by the principal stretches, which is derived from the corresponding residual strain energy when the Yeoh model predicts the equibiaxial mode of deformation. In addition, a parameter identification method based on the cyclic genetic-pattern search algorithm is introduced to accurately obtain the parameters of the constitutive model. By applying the modified model to the experimental datasets of various rubber or rubber-like materials (including natural unfilled or filled rubber, silicone rubber, extremely soft hydrogel and human brain cortex tissue), it is confirmed that the modified model not only possesses a significantly improved ability to predict multiaxial deformation, but also has a wider range of material applicability. Meanwhile, the advantages of the modified model over most existing models in the literatures are also demonstrated. For example, when characterizing human brain tissue, which is difficult for most existing models in the literature, the modified model has comparable predictive accuracy with the third-order Ogden model, while maintaining convexity in the corresponding deformation domain. Moreover, the effective prediction ability of the modified model for untested equi-biaxial deformation of different materials has also been confirmed using only the data of uniaxial tension and pure shear from various datasets. The effective prediction for the untested equibiaxial deformation makes it more suitable for the practice situation where the equibiaxial deformation of certain polymeric materials is unavailable. Finally, compared with other parameter identification methods, the introduced parameter identification method significantly improves the predicted accuracy of the constitutive models; meanwhile, the uniform convergence of introduced parameter identification method is also better.
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spelling pubmed-104210882023-08-12 A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification Wang, Wei Liu, Yang Xie, Zongwu Polymers (Basel) Article Given the importance of hyperelastic constitutive models in the design of engineering components, researchers have been developing the improved and new constitutive models in search of a more accurate and even universal performance. Here, a modified hyperelastic constitutive model based on the Yeoh model is proposed to improve its prediction performance for multiaxial deformation of hyperelastic polymeric materials while retaining the advantages of the original Yeoh model. The modified constitutive model has one more correction term than the original model. The specific form of the correction term is a composite function based on a power function represented by the principal stretches, which is derived from the corresponding residual strain energy when the Yeoh model predicts the equibiaxial mode of deformation. In addition, a parameter identification method based on the cyclic genetic-pattern search algorithm is introduced to accurately obtain the parameters of the constitutive model. By applying the modified model to the experimental datasets of various rubber or rubber-like materials (including natural unfilled or filled rubber, silicone rubber, extremely soft hydrogel and human brain cortex tissue), it is confirmed that the modified model not only possesses a significantly improved ability to predict multiaxial deformation, but also has a wider range of material applicability. Meanwhile, the advantages of the modified model over most existing models in the literatures are also demonstrated. For example, when characterizing human brain tissue, which is difficult for most existing models in the literature, the modified model has comparable predictive accuracy with the third-order Ogden model, while maintaining convexity in the corresponding deformation domain. Moreover, the effective prediction ability of the modified model for untested equi-biaxial deformation of different materials has also been confirmed using only the data of uniaxial tension and pure shear from various datasets. The effective prediction for the untested equibiaxial deformation makes it more suitable for the practice situation where the equibiaxial deformation of certain polymeric materials is unavailable. Finally, compared with other parameter identification methods, the introduced parameter identification method significantly improves the predicted accuracy of the constitutive models; meanwhile, the uniform convergence of introduced parameter identification method is also better. MDPI 2023-07-26 /pmc/articles/PMC10421088/ /pubmed/37571066 http://dx.doi.org/10.3390/polym15153172 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Wei
Liu, Yang
Xie, Zongwu
A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification
title A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification
title_full A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification
title_fullStr A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification
title_full_unstemmed A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification
title_short A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification
title_sort modified constitutive model for isotropic hyperelastic polymeric materials and its parameter identification
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10421088/
https://www.ncbi.nlm.nih.gov/pubmed/37571066
http://dx.doi.org/10.3390/polym15153172
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