连接各向同性超弹性材料的弱非线性弹性理论

IF 1.7 4区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY
Yangkun Du, Nicholas A Hill, Xiaoyu Luo
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引用次数: 0

摘要

软材料在外力作用下会产生明显的非线性几何变形和应力应变关系。本文探讨了弱非线性弹性理论,包括 Landau 和 Murnaghan 的公式,推进了对线性弹性的理解。我们建立了这些方法之间的联系,并将应变能函数扩展到[公式:见正文]的三阶和四阶幂,其中[公式:见正文]和[公式:见正文],[公式:见正文]是对变形梯度张量[公式:见正文]的扰动。此外,我们还讨论了适用于不可压缩材料的简化应变能函数。通过这项工作,我们有助于全面理解非线性弹性及其与弱非线性弹性的关系,促进软材料行为中的适度变形研究及其实际应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials
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 [Formula: see text], where [Formula: see text] and [Formula: see text], and [Formula: see text] is the perturbation to the deformation gradient tensor [Formula: see text]. 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.
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来源期刊
Mathematics and Mechanics of Solids
Mathematics and Mechanics of Solids 工程技术-材料科学:综合
CiteScore
4.80
自引率
19.20%
发文量
159
审稿时长
1 months
期刊介绍: Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science. The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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