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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 Willam-Warnke yield criterion ： ウィキペディア英語版 Willam-Warnke yield criterion The Willam-Warnke yield criterion 〔Willam, K. J. and Warnke, E. P. (1975). ''Constitutive models for the triaxial behavior of concrete.'' Proceedings of the International Assoc. for Bridge and Structural Engineering , vol 19, pp. 1- 30.〕 is a function that is used to predict when failure will occur in concrete and other cohesive-frictional materials such as rock, soil, and ceramics. This yield criterion has the functional form :$$ f(I_1, J_2, J_3) = 0 \, where $I\_1$ is the first invariant of the Cauchy stress tensor, and $J\_2,\; J\_3$ are the second and third invariants of the deviatoric part of the Cauchy stress tensor. There are three material parameters ($\backslash sigma\_c$ - the uniaxial compressive strength, $\backslash sigma\_t$ - the uniaxial tensile strength, $\backslash sigma\_b$ - the equibiaxial compressive strength) that have to be determined before the Willam-Warnke yield criterion may be applied to predict failure. In terms of $I\_1,\; J\_2,\; J\_3$, the Willam-Warnke yield criterion can be expressed as :$$ f := \sqrt + \lambda(J_2,J_3)~(\tfrac - B) = 0 where $\backslash lambda$ is a function that depends on $J\_2,J\_3$ and the three material parameters and $B$ depends only on the material parameters. The function $\backslash lambda$ can be interpreted as the friction angle which depends on the Lode angle ($\backslash theta$). The quantity $B$ is interpreted as a cohesion pressure. The Willam-Warnke yield criterion may therefore be viewed as a combination of the Mohr-Coulomb and the Drucker-Prager yield criteria. == Willam-Warnke yield function == In the original paper, the three-parameter Willam-Warnke yield function was expressed as :$$ f := \cfrac~\cfrac + \sqrt}~\cfrac\cfrac - 1 \le 0 where $I\_1$ is the first invariant of the stress tensor, $J\_2$ is the second invariant of the deviatoric part of the stress tensor, $\backslash sigma\_c$ is the yield stress in uniaxial compression, and $\backslash theta$ is the Lode angle given by :$$ \theta = \tfrac\cos^\left(\cfrac~\cfrac where :$$ \begin u(\theta) := & 2~r_c~(r_c^2-r_t^2)~\cos\theta \\ v(\theta) := & r_c~(2~r_t - r_c)\sqrt \\ w(\theta) := & 4(r_c^2 - r_t^2)\cos^2\theta + (r_c-2~r_t)^2 \end The quantities $r\_t$ and $r\_c$ describe the position vectors at the locations $\backslash theta=0^\backslash circ,\; 60^\backslash circ$ and can be expressed in terms of $\backslash sigma\_c,\; \backslash sigma\_b,\; \backslash sigma\_t$ as :$$ r_c := \sqrt}\left() The parameter $z$ in the model is given by :$$ z := \cfrac ~. The Haigh-Westergaard representation of the Willam-Warnke yield condition can be written as :$$ f(\xi, \rho, \theta) = 0 \, \quad \equiv \quad f := \bar(\theta)~\rho + \bar~\xi - \sigma_c \le 0 where :$$ \bar := \cfrac ~;~~ \bar := \cfrac ~. 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「Willam-Warnke yield criterion」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.