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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 Polynomial (hyperelastic model) ： ウィキペディア英語版 Polynomial (hyperelastic model) The polynomial hyperelastic material model 〔 is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants $I\_1,I\_2$ of the left Cauchy-Green deformation tensor. The strain energy density function for the polynomial model is 〔Rivlin, R. S. and Saunders, D. W., 1951, '' Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber.'' Phi. Trans. Royal Soc. London Series A, 243(865), pp. 251-288.〕 :$$ W = \sum_^n C_ (I_1 - 3)^i (I_2 - 3)^j where $C\_$ are material constants and $C\_=0$. For compressible materials, a dependence of volume is added :$$ W = \sum_^n C_ (\bar_1 - 3)^i (\bar_2 - 3)^j + \sum_^m D_(J-1)^ where :$$ \begin \bar_1 & = J^~I_1 ~;~~ I_1 = \lambda_1^2 + \lambda_2 ^2+ \lambda_3 ^2 ~;~~ J = \det(\boldsymbol) \\ \bar_2 & = J^~I_2 ~;~~ I_2 = \lambda_1^2 \lambda_2^2 + \lambda_2^2 \lambda_3^2 + \lambda_3^2 \lambda_1^2 \end In the limit where $C\_=C=0$, the polynomial model reduces to the Neo-Hookean solid model. For a compressible Mooney-Rivlin material $n\; =\; 1,\; C\_\; =\; C\_2,\; C\_\; =\; 0,\; C\_\; =\; C\_1,\; m=1$ and we have :$$ W = C_~(\bar_2 - 3) + C_~(\bar_1 - 3) + D_1~(J-1)^2 ==References== 〔 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「Polynomial (hyperelastic 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.