Du, Y. , Luo, X. and Hill, N. A. (2024) Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865241238985) (Early Online Publication)
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Abstract
Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of ε, where ε = √H·H, and 0 < ε ≤ 1, and H is the perturbation to the deformation gradient tensor F = I + H. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.
Item Type: | Articles |
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Additional Information: | The authors thank the EPSRC for funding this research through grants EP/S030875/1 and EP/S020950/1. Y.D. also acknowledgessupport from the European Union GA n◦101105740 “Multi-scale and Multi-physics Modelling of Soft Tissues - MULTI-SOFT.” |
Status: | Early Online Publication |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Luo, Professor Xiaoyu and Hill, Professor Nicholas and Du, Dr Yangkun |
Authors: | Du, Y., Luo, X., and Hill, N. A. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Mathematics and Mechanics of Solids |
Publisher: | SAGE Publications |
ISSN: | 1081-2865 |
ISSN (Online): | 1741-3028 |
Published Online: | 27 April 2024 |
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