Elastic moduli of hyperelastic models of biological tissues

S. Muslov; S. Pertsov; P. Sukhochev; A. Minasyan

bg | en

S. Muslov

, S. Pertsov

, P. Sukhochev

, A. Minasyan

Abstract: Objective: The study addresses the behavior of elastic moduli of hyperelastic models from the point of view of their dependence on the deformation (by the example of the human duodenum).
Materials and methods: The initial data were based on the results of the uniaxial mechanical tests of the duodenal tissues from patients aged 22–29 years, conducted in both longitudinal and transverse directions. The software package Mathcad 15.0 was used for the analysis. The study considers neohookean, Mooney-Rivlin, Ogden, polynomial, Yeoh, and Veronda-Westmann models, which are the most frequently cited in literature. The mechanical stability of these models was examined within the investigated strain range. Results and discussion: The elastic moduli of the duodenum, calculated within the framework of hyperelastic models neohookean, Mooney-Rivlin, and Ogden, are incremental (increasing with the strain ∂E/∂λ > 0). In the polynomial, Yeoh, and Veronda-Westmann models, the moduli decrease in magnitude at small strains, and their derivative with respect to strain is negative. Conclusion: The elastic moduli of hyperelastic models cannot be expressed as a single number and exhibit different behavior.

Series on Biomechanics, No.2 (2025), 24-33
DOI:10.7546/SB.02.02.2025

Keywords: biological tissues; Elastic moduli; hyperelastic models

References: (click to open/close)

[1] Shmurak M.I., Kuchumov A.G., Voronova N.O., 2017. Analysis of hyperelastic models for describing the behavior of soft tissues of the human body. Master`s Journal. 1, 230-243.
[2] Muslov S.A., Pertsov S.S., Arutyunov S.D., 2023. Physical and mechanical properties of biological tissues: monograph. Ed. by Academician of the Russian Academy of Sciences O.O. Yanushevich. Moscow: Practical Medicine, 456 p. https://doi.org/10.17513/np.594.
[3] S.A. Muslov, S.D. Arutyunov, I.V. Maev [et al.], 2024. Hyperelastic properties of biological tissues: monograph, edited by S.S. Pertsov, S.V. Panin. - M.: Practical Medicine, 232 p. ISBN 978-5-98811-658-5.
[4] He H., Zhang Q., Zhang Y., Chen J., Zhang L., Li F., 2022. A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material, Nano Materials Science, 4, 64-82. https://doi.org/10.1016/j.nanoms.2021.07.003
[5] Duane A. Morrow, Tammy Haut Donahue, Gregory M. Odegard, and Kenton R. Kaufman., 2010. A method for assessing the fit of a constitutive material model to experimental stress-strain data. Comput. Methods Biomech. Biomed. Engin.13, 2, 247-256. doi:10.1080/10255840903170686.
[6] Gerhard A. Holzapfel, Thomas C. Gasser, Ray W. Ogden., 2000. A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models, 61, 1-3, 1-48. doi:10.1023/a:1010835316564.
[7] Gerhard A. Holzapfel, Hans W. Weizsacker, 1998. Biomechanical behavior of the arterial wall and its numerical characterization. Computers in Biology and Medicine 28, 377-392.
[8] Hill, R., 1958. General theory of uniqueness and stability in elastic-plastic solids. Journal of the Mechanics and Physics of Solids, 6, 3, 236–249, doi:10.1016/0022-5096(58)90029-2.
[9] Drucker, D.C., 1959. A definition of a stable inelastic material. Journal of Applied Mechanics, 26, 1,101-195, doi:10.1115/1.4011929.
[10] N. Kumar, V.V. Rao, 2016. Hyperelastic Mooney-Rivlin model: Determination and physical interpretation of material constants, MIT International Journal of Mechanical Engineering, 6, 143-46.
[11] S. Muslov, S. Arutyunov, S. Pertsov, K. Karakov, 2023. Analysis of mechanical properties of human hair using hyperelastic Mooney-Rivlin models, Modern issues of biomedicine, 7. 2. DOI: 10.51871/2588-0500_2023_07_02.
[12] Yamada Hiroshi., 1970. Strength of biological materials. Williams & Wilkins, 297.
[13] Muslov S.A., Arutyunov S.D., 2021. Physical properties of dental tissues: monograph. Moscow: Practical Medicine,176 https://doi.org/10.17513/np.597.

DOI: 10.7546/SB.02.02.2025

Date published: 2025-07-09

(Price of one pdf file: 39.00 BGN/20.00 EUR)