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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 Ogden (hyperelastic model) ： ウィキペディア英語版 Ogden (hyperelastic model) The Ogden material model is a hyperelastic material model used to describe the non-linear stress-strain behaviour of complex materials such as rubbers, polymers, and biological tissue. The model was developed by Ray W. Ogden in 1972.〔Ogden, R. W., (1972). ''Large Deformation Isotropic Elasticity – On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids'', Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 326, No. 1567 (1 February 1972), pp. 565–584.〕 The Ogden model, like other hyperelastic material models, assumes that the material behaviour can be described by means of a strain energy density function, from which the stress–strain relationships can be derived. == Ogden material model == In the Ogden material model, the strain energy density is expressed in terms of the principal stretches $\backslash ,\backslash !\backslash lambda\_j$, $\backslash ,\backslash !j=1,2,3$ as: :$$ W\left( \lambda_1,\lambda_2,\lambda_3 \right) = \sum_^N \frac\left( \lambda_1^ + \lambda_2^ + \lambda_3^ -3 \right) where $N$, $\backslash ,\backslash !\backslash mu\_p$ and $\backslash ,\backslash !\backslash alpha\_p$ are material constants. Under the assumption of incompressibility one can rewrite as $$ W\left( \lambda_1,\lambda_2 \right) = \sum_^N \frac\left( \lambda_1^ + \lambda_2^ + \lambda_1^\lambda_2^ -3 \right) In general the shear modulus results from $$ 2\mu = \sum_^ \mu_p \alpha_. With $N=3$ and by fitting the material parameters, the material behaviour of rubbers can be described very accurately. For particular values of material constants the Ogden model will reduce to either the Neo-Hookean solid ($N=1$, $\backslash alpha\; =\; 2$) or the Mooney-Rivlin material ($N=2$, $\backslash alpha\_1=2$, $\backslash alpha\_2=-2$, with the constraint condition $\backslash lambda\_1\backslash lambda\_2\backslash lambda\_3=1$). Using the Ogden material model, the three principal values of the Cauchy stresses can now be computed as $$ \sigma_ = p + \lambda_\frac = \lambda_P_. 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「Ogden (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.