Reformulation of the virtual fields method using the variation of elastic energy for parameter identification of $${\textbf {QR}}$$ decomposition-based hyperelastic models
Reformulation of the virtual fields method using the variation of elastic energy for parameter identification of $${\textbf {QR}}$$ decomposition-based hyperelastic models
复制标题
使用弹性能量的变化重新表述虚拟场方法，用于 $${ extbf {QR}}$$ 基于分解的超弹性模型的参数识别
DOI：
10.1007/s00707-023-03626-y
复制
发表时间：
2023
期刊：
影响因子：
2.7
通讯作者：
Wang, Zhujiang
中科院分区：
文献类型：
--
作者：
Jiang, Mingliang;Du, Xinwei;Srinivasa, Arun;Xu, Jimin;Wang, Zhujiang
超弹性材料基于分解的本构关系引起了固体力学界的高度关注，作为畸变张量的超弹性模型 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{\widetilde{F}}$$\end{document} 具有明显的物理意义。然而，系统讨论基于分解的超弹性模型的材料参数识别的研究还很少。在这项工作中，我们通过将内部虚功视为由虚位移引起的弹性能的变化来重新表述虚场方法。与传统方法相比，这种方法（连同分解）更简洁，更容易实现，传统方法需要特定的应力，例如柯西应力、第一或第二 Piola-Kirchhoff 应力以及共轭虚拟应变来计算内部虚拟功。为了验证重新表述的虚拟场方法，我们在该框架下推导了 Mooney-Rivlin 模型，然后确定了双轴拉伸试验下不可压缩硅胶样本的材料参数。结果表明，所提出的虚拟场方法非常适合基于分解的模型。
decomposition-based constitutive relations for hyperelastic materials have attracted great attention from the community of solid mechanics, as hyperelastic models in terms of the distortion tensor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{\widetilde{F}}$$\end{document} have obvious physical meanings. However, there are few works systematically discussing the material parameter identification fordecomposition-based hyperelastic models. In this work, we reformulate the virtual fields method by considering the internal virtual work as the variation of elastic energy caused by virtual displacements. This approach (together with thedecompositions) is more concise and easier to be implemented when compared with the conventional approach, which requires specific stresses, such as Cauchy stress, first or second Piola–Kirchhoff stress, and conjugate virtual strains to calculate the internal virtual work. To validate the reformulated virtual fields method, we derive the Mooney–Rivlin model under theframework, and then identify its material parameters for incompressible silicone specimens under biaxial tensile tests. The results indicate that the proposed virtual fields method works very well fordecomposition-based models.