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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 Wagner model ： ウィキペディア英語版 Wagner model Wagner model is a rheological model developed for the prediction of the viscoelastic properties of polymers. It might be considered as a simplified practical form of the Bernstein-Kearsley-Zapas model. The model was developed by German rheologist Manfred Wagner. For the isothermal conditions the model can be written as: :$\backslash mathbf(t)\; =\; -p\; \backslash mathbf\; +\; \backslash int\_^\; M(t-t\text{'})h(I\_1,I\_2)\backslash mathbf(t\text{'})\backslash ,\; dt\text{'}$ where: *$\backslash mathbf(t)$ is the Cauchy stress tensor as function of time ''t'', *''p'' is the pressure *$\backslash mathbf$ is the unity tensor *''M'' is the memory function showing, usually expressed as a sum of exponential terms for each mode of relaxation: :$M(x)=\backslash sum\_^m\; \backslash frac\backslash exp(\backslash frac)$, where for each mode of the relaxation, $g\_i$ is the relaxation modulus and $\backslash theta\_i$ is the relaxation time; *$h(I\_1,I\_2)$ is the ''strain damping'' function that depends upon the first and second invariants of Finger tensor $\backslash mathbf$. The ''strain damping function'' is usually written as: :$h(I\_1,I\_2)=m^$ *\exp(-n_1 \sqrt)+(1-m^ *)\exp(-n_2 \sqrt), The strain hardening function equal to one, then the deformation is small and approaching zero, then the deformations are large. The Wagner equation can be used in the non-isothermal cases by applying time-temperature shift factor. ==References== *M.H. Wagner ''Rheologica Acta'', v.15, 136 (1976) *M.H. Wagner ''Rheologica Acta'', v.16, 43, (1977) *B. Fan, D. Kazmer, W. Bushko, ''Polymer Engineering and Science'', v44, N4 (2004) 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「Wagner 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.