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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Upper-convected Maxwell model ： ウィキペディア英語版 Upper-convected Maxwell model The upper-convected Maxwell (UCM) model is a generalisation of the Maxwell material for the case of large deformations using the upper-convected time derivative. The model was proposed by James G. Oldroyd. The concept is named after James Clerk Maxwell. The model can be written as: :$\backslash mathbf\; +\; \backslash lambda\; \backslash stackrel$ where: * $\backslash mathbf$ is the stress tensor; * $\backslash lambda$ is the relaxation time; * $\backslash stackrel\; \backslash mathbf\; +\; \backslash mathbf\; \backslash cdot\; \backslash nabla\; \backslash mathbf\; -(\; (\backslash nabla\; \backslash mathbf)^T\; \backslash cdot\; \backslash mathbf\; +\; \backslash mathbf\; \backslash cdot\; (\backslash nabla\; \backslash mathbf))$ *$\backslash mathbf$ is the fluid velocity *$\backslash eta\_0$ is material viscosity at steady simple shear; *$\backslash mathbf$ is the tensor of the deformation rate. ==Case of the steady shear== For this case only two components of the shear stress became non-zero: :$T\_=\backslash eta\_0\; \backslash dot\; \backslash gamma\; \backslash ,$ and :$T\_=2\; \backslash eta\_0\; \backslash lambda\; ^2\; \backslash ,$ where $\backslash dot\; \backslash gamma$ is the shear rate. Thus, the upper-convected Maxwell model predicts for the simple shear that shear stress to be proportional to the shear rate and the first difference of normal stresses ($T\_-T\_$) is proportional to the square of the shear rate, the second difference of normal stresses ($T\_-T\_$) is always zero. In other words, UCM predicts appearance of the first difference of normal stresses but does not predict non-Newtonian behavior of the shear viscosity nor the second difference of the normal stresses. Usually quadratic behavior of the first difference of normal stresses and no second difference of the normal stresses is a realistic behavior of polymer melts at moderated shear rates, but constant viscosity is unrealistic and limits usability of the model. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Upper-convected Maxwell model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.