翻訳と辞書 Words near each other ・ Mooney Memorial Fountain ・ Mooney Mooney Bridge ・ Mooney Mooney Creek ・ Mooney Mooney Creek, New South Wales ・ Mooney Mooney, New South Wales ・ Mooney Site ・ Mooney TX-1 ・ Mooney units ・ Mooney viscometer ・ Mooney viscosity ・ Mooney's Bay Park ・ Mooney, Visalia, California ・ Mooneye ・ Mooneyham ・ Mooneys Building ・ Mooney–Rivlin solid ・ Moonface ・ Moonfire ・ Moonfire (1973 film) ・ Moonfire (album) ・ Moonfish ・ Moonfleet ・ Moonfleet & Other Stories ・ Moonfleet (1955 film) ・ Moonflesh ・ Moonflower ・ Moonflower (album) ・ Moonflower Lane ・ Moonflower Plastic ・ Moonflowers Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mooney–Rivlin solid ： ウィキペディア英語版 Mooney–Rivlin solid In continuum mechanics, a Mooney–Rivlin solid〔Mooney, M., 1940, ''A theory of large elastic deformation'', Journal of Applied Physics, 11(9), pp. 582-592.〕〔Rivlin, R. S., 1948, ''Large elastic deformations of isotropic materials. IV. Further developments of the general theory'', Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 241(835), pp. 379-397.〕 is a hyperelastic material model where the strain energy density function $W\backslash ,$ is a linear combination of two invariants of the left Cauchy–Green deformation tensor $\backslash boldsymbol$. The model was proposed by Melvin Mooney in 1940 and expressed in terms of invariants by Ronald Rivlin in 1948. The strain energy density function for an incompressible Mooney–Rivlin material is〔Boulanger, P. and Hayes, M. A., 2001, '' Finite amplitude waves in Mooney–Rivlin and Hadamard materials'', in Topics in Finite Elasticity, ed. M. A Hayes and G. Soccomandi, International Center for Mechanical Sciences.〕〔C. W. Macosko, 1994, Rheology: principles, measurement and applications, VCH Publishers, ISBN 1-56081-579-5.〕 :$W\; =\; C\_\; (\backslash overline\_1-3)\; +\; C\_\; (\backslash overline\_2-3),\; \backslash ,$ where $C\_$ and $C\_$ are empirically determined material constants, and $I\_1$ and $I\_2$ are the first and the second invariant of the unimodular component of the left Cauchy–Green deformation tensor:〔The characteristic polynomial of the linear operator corresponding to the second rank three-dimensional Finger tensor (also called the left Cauchy–Green deformation tensor) is usually written :$p\_B\; (\backslash lambda)\; =\; \backslash lambda^3\; -\; a\_1\; \backslash ,\; \backslash lambda^2\; +\; a\_2\; \backslash ,\; \backslash lambda\; -\; a\_3\; \backslash ,$ In this article, the trace $a\_1$ is written $I\_1$, the next coefficient $a\_2$ is written $I\_2$, and the determinant $a\_3$ would be written $I\_3$.〕 :$$ \begin \bar_1 & = J^~I_1 ~;~~ I_1 = \lambda_1^2 + \lambda_2 ^2+ \lambda_3 ^2 ~;~~ J = \det(\boldsymbol) = \lambda_1\lambda_2\lambda_3 \\ \bar_2 & = J^~I_2 ~;~~ I_2 = \lambda_1^2 \lambda_2^2 + \lambda_2^2 \lambda_3^2 + \lambda_3^2 \lambda_1^2 \end where $\backslash boldsymbol$ is the deformation gradient. For an incompressible material, $J=1$. ==Derivation== The Mooney–Rivlin model is a special case of the generalized Rivlin model (also called polynomial hyperelastic model) which has the form :$$ W = \sum_^N C_ (\bar_1 - 3)^p~(\bar_2 - 3)^q + \sum_^M D_m~(J-1)^ with $C\_\; =\; 0$ where $C\_$ are material constants related to the distortional response and $D\_m$ are material constants related to the volumetric response. For a compressible Mooney–Rivlin material $N\; =\; 1,\; C\_\; =\; C\_2,\; C\_\; =\; 0,\; C\_\; =\; C\_1,\; M=1$ and we have :$$ W = C_~(\bar_2 - 3) + C_~(\bar_1 - 3) + D_1~(J-1)^2 If $C\_\; =\; 0$ we obtain a neo-Hookean solid, a special case of a Mooney–Rivlin solid. For consistency with linear elasticity in the limit of small strains, it is necessary that :$$ \kappa = 2 \cdot D_1 ~;~~ \mu = 2~(C_ + C_) where $\backslash kappa$ is the bulk modulus and $\backslash mu$ is the shear modulus. 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「Mooney–Rivlin solid」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.