A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking
By just replacing the infinitesimal strains by logarithmic strains, the Hencky strain energy has proven to extend successfully the infinitesimal framework to moderately large strains, as those found in brain. However, as polymers and soft tissues, brain presents an important strain-stiffening toward...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-01-01
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| Series: | Brain Multiphysics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666522021000162 |
| _version_ | 1798026715167981568 |
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| author | Luis Saucedo-Mora Olatz García-Bañales Francisco Javier Montáns José María Benítez |
| author_facet | Luis Saucedo-Mora Olatz García-Bañales Francisco Javier Montáns José María Benítez |
| author_sort | Luis Saucedo-Mora |
| collection | DOAJ |
| description | By just replacing the infinitesimal strains by logarithmic strains, the Hencky strain energy has proven to extend successfully the infinitesimal framework to moderately large strains, as those found in brain. However, as polymers and soft tissues, brain presents an important strain-stiffening towards locking. Based on both observations, in this paper we propose a simple two-parameter isotropic strain energy function for representing the inviscid (conservative) behavior of brain matter. The two parameters of the model are the Young modulus (or alternatively the shear modulus) and the locking stretch during a test. Through a comparison with experimental data, we show that with this simple model, employing the two material parameters directly measured from a tensile test, we capture the qualitative aspects and quantitative behavior of brain mater in tension, compression and simple shear tests with good accuracy. Statement of Significance: This paper shows a simple mathematical model capable of reproducing qualitative aspects and quantitative behavior of brain matter in tension, compression and simple shear tests with good accuracy. The model is governed by only two parameters, namely Young's modulus (or alternatively the shear modulus) and the locking stretch. |
| first_indexed | 2024-04-11T18:39:51Z |
| format | Article |
| id | doaj.art-7acfc43c8cd24df59fa47ee2085dda81 |
| institution | Directory Open Access Journal |
| issn | 2666-5220 |
| language | English |
| last_indexed | 2024-04-11T18:39:51Z |
| publishDate | 2021-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Brain Multiphysics |
| spelling | doaj.art-7acfc43c8cd24df59fa47ee2085dda812022-12-22T04:09:03ZengElsevierBrain Multiphysics2666-52202021-01-012100036A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate lockingLuis Saucedo-Mora0Olatz García-Bañales1Francisco Javier Montáns2José María Benítez3E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, Madrid, 28040, Spain; Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PJ, UKE.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, Madrid, 28040, SpainE.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, Madrid, 28040, Spain; Department of Mechanical and Aerospace Engineering, Herbert Wertheim College of Engineering, University of Florida, FL32611, USACorresponding author.; E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, Madrid, 28040, SpainBy just replacing the infinitesimal strains by logarithmic strains, the Hencky strain energy has proven to extend successfully the infinitesimal framework to moderately large strains, as those found in brain. However, as polymers and soft tissues, brain presents an important strain-stiffening towards locking. Based on both observations, in this paper we propose a simple two-parameter isotropic strain energy function for representing the inviscid (conservative) behavior of brain matter. The two parameters of the model are the Young modulus (or alternatively the shear modulus) and the locking stretch during a test. Through a comparison with experimental data, we show that with this simple model, employing the two material parameters directly measured from a tensile test, we capture the qualitative aspects and quantitative behavior of brain mater in tension, compression and simple shear tests with good accuracy. Statement of Significance: This paper shows a simple mathematical model capable of reproducing qualitative aspects and quantitative behavior of brain matter in tension, compression and simple shear tests with good accuracy. The model is governed by only two parameters, namely Young's modulus (or alternatively the shear modulus) and the locking stretch.http://www.sciencedirect.com/science/article/pii/S2666522021000162Hyperelasticitybrain matterinvariantssoft tissues |
| spellingShingle | Luis Saucedo-Mora Olatz García-Bañales Francisco Javier Montáns José María Benítez A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking Brain Multiphysics Hyperelasticity brain matter invariants soft tissues |
| title | A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking |
| title_full | A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking |
| title_fullStr | A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking |
| title_full_unstemmed | A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking |
| title_short | A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking |
| title_sort | two parameter strain energy function for brain matter an extension of the hencky model to incorporate locking |
| topic | Hyperelasticity brain matter invariants soft tissues |
| url | http://www.sciencedirect.com/science/article/pii/S2666522021000162 |
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