Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition
Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition
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严格一阶凸性条件下柯西应力张量沿一阶连通线的内射性
DOI：
10.1007/s10659-016-9609-y
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发表时间：
2016
影响因子：
2
通讯作者：
L. A. Mihai
中科院分区：
文献类型：
--
作者：
P. Neff;L. A. Mihai
In this note, we show that the Cauchy stress tensor σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma$\end{document} in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that σ(F+ξ⊗η)=σ(F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma(F+\xi\otimes\eta)=\sigma(F)$\end{document} implies ξ⊗η=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\xi \otimes\eta=0$\end{document} under strict rank-one convexity. As a consequence of this seemingly unnoticed observation, it follows that rank-one convexity and a homogeneous Cauchy stress imply that the left Cauchy-Green strain is homogeneous, as is shown in Mihai and Neff (Int. J. Non-Linear Mech., 2016, to appear).
In this note, we show that the Cauchy stress tensor σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma$\end{document} in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that σ(F+ξ⊗η)=σ(F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma(F+\xi\otimes\eta)=\sigma(F)$\end{document} implies ξ⊗η=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\xi \otimes\eta=0$\end{document} under strict rank-one convexity. As a consequence of this seemingly unnoticed observation, it follows that rank-one convexity and a homogeneous Cauchy stress imply that the left Cauchy-Green strain is homogeneous, as is shown in Mihai and Neff (Int. J. Non-Linear Mech., 2016, to appear).
非均匀有限变形引起的均匀柯西应力下的超弹体
影响因子：
3.2
作者：
Mihai L
通讯作者：
Mihai L