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首页> 外文期刊>Journal of the Mechanics and Physics of Solids >Conservation laws and path-independent integrals in mechanical-diffusion-electrochemical reaction coupling system
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Conservation laws and path-independent integrals in mechanical-diffusion-electrochemical reaction coupling system

机译：机械扩散-电化学反应耦合系统中的守恒律和与路径无关的积分

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In this study, the conservation laws οf dissipative mechanical-diffusion-electrochemical reaction system are systematically obtained based on Noether's theorem. According to linear, irreversible thermodynamics, dissipative phenomena can be described by an irreversible force and an irreversible flow. Additionally, the Lagrange function, L and the generalized Hamilton least-action principle are proposed to be used to obtain the conservation integrals. A group of these integrals, including the J-, M-, and L-integrals, can be then obtained using the classical Noether approach for dissipative processes. The relation between the J-integral and the energy release rate is illustrated. The path-independence of the J-integral is then proven. The J-integral, derived based on Noether's theorem, is a line integral, contrary to the propositions of existing published works that describe it both as a line and an area integral. Herein, we prove that the outcomes are identical, and identify the physical meaning of the area integral, a concept that was not explained previously. To show that the J-integral can dominate the distribution of the corresponding field quantities, an example of a partial, stress-diffusion coupling process is disscussed.
机译：在这项研究中，基于Noether定理系统地获得了耗散机械扩散-电化学反应系统的守恒律。根据线性，不可逆的热力学，耗散现象可以用不可逆的力和不可逆的流动来描述。此外，提出了拉格朗日函数，L和广义汉密尔顿最小作用原理来获得守恒积分。然后，使用耗散过程的经典Noether方法可以获得一组这些积分，包括J-，M-和L-积分。示出了J积分与能量释放速率之间的关系。然后证明了J积分的路径独立性。基于Noether定理得出的J积分是线积分，这与现有已发表作品将其描述为线和面积积分的命题相反。在这里，我们证明了结果是相同的，并确定了面积积分的物理含义，这一概念以前没有解释过。为了表明J积分可以控制相应场量的分布，讨论了一个局部应力扩散耦合过程的示例。

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