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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 Flow plasticity theory ： ウィキペディア英語版 Flow plasticity theory Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material. In flow plasticity theories it is assumed that the total strain in a body can be decomposed additively (or multiplicatively) into an elastic part and a plastic part. The elastic part of the strain can be computed from a linear elastic or hyperelastic constitutive model. However, determination of the plastic part of the strain requires a flow rule and a hardening model. == Small deformation theory == Typical flow plasticity theories (for small deformation perfect plasticity or hardening plasticity) are developed on the basis of the following requirements: # The material has a linear elastic range. # The material has an elastic limit defined as the stress at which plastic deformation first takes place, i.e., $\backslash sigma\; =\; \backslash sigma\_0$. # Beyond the elastic limit the stress state always remains on the yield surface, i.e., $\backslash sigma\; =\; \backslash sigma\_y$. # Loading is defined as the situation under which increments of stress are greater than zero, i.e., $d\backslash sigma\; >\; 0$. If loading takes the stress state to the plastic domain then the increment of plastic strain is always greater than zero, i.e., $d\backslash varepsilon\_p\; >\; 0$. # Unloading is defined as the situation under which increments of stress are less than zero, i.e., . The material is elastic during unloading and no additional plastic strain is accumulated. # The total strain is a linear combination of the elastic and plastic parts, i.e., $d\backslash varepsilon\; =\; d\backslash varepsilon\_e\; +\; d\backslash varepsilon\_p$. The plastic part cannot be recovered while the elastic part is fully recoverable. # The work done of a loading-unloading cycle is positive or zero, i.e., $d\backslash sigma\backslash ,d\backslash varepsilon\; =\; d\backslash sigma\backslash ,(d\backslash varepsilon\_e\; +\; d\backslash varepsilon\_p)\; \backslash ge\; 0$. This is also called the Drucker stability postulate and eliminates the possibility of strain softening behavior. The above requirements can be expressed in three dimensions as follows. * Elasticity (Hooke's law). In the linear elastic regime the stresses and strains in the rock are related by :::$$ \boldsymbol = \mathsf:\boldsymbol :::where the stiffness matrix $\backslash mathsf$ is constant. * Elastic limit (Yield surface). The elastic limit is defined by a yield surface that does not depend on the plastic strain and has the form :::$$ f(\boldsymbol) = 0 \,. * Beyond the elastic limit. For strain hardening rocks, the yield surface evolves with increasing plastic strain and the elastic limit changes. The evolving yield surface has the form :::$$ f(\boldsymbol, \boldsymbol_p) = 0 \,. * Loading. It is not straightforward to translate the condition $d\backslash sigma\; >\; 0$ to three dimensions, particularly for rock plasticity which is dependent not only on the deviatoric stress but also on the mean stress. However, during loading $f\; \backslash ge\; 0$ and it is assumed that the direction of plastic strain is identical to the normal to the yield surface ($\backslash partial\; f/\backslash partial\backslash boldsymbol$) and that $d\backslash boldsymbol\_p:d\backslash boldsymbol\; \backslash ge\; 0$, i.e., :::$$ d\boldsymbol:\frac:\frac = d\boldsymbol_e + d\boldsymbol_p \,. * Stability postulate: The stability postulate is expressed as :::$$ d\boldsymbol:d\boldsymbol \ge 0 \,. 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「Flow plasticity theory」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.