Method of Lagrange multipliers for exploitation of the entropy principle
Method of Lagrange multipliers for exploitation of the entropy principle
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DOI：
10.1007/bf00250688
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发表时间：
1972
影响因子：
2.5
通讯作者：
I. Liu
中科院分区：
文献类型：
--
作者：
I. Liu
在热力学中，每当研究一种材料的性质时，熵原理就被用来对该材料的本构关系施加限制。迄今为止，还没有一种简单的方法可以从熵原理中推导出适用于所有不同材料的限制。事实上，直到最近，甚至还没有一个适用于所有物体的熵原理。穆勒[1][2][3]提出了这样一个普遍的熵原理，在这里，我建议一个简单的方法来利用它：拉格朗日乘子的方法。熵原理要求本构关系使得热力学场方程的每个解满足熵不等式。要满足这一要求并不容易，因为通常需要进行复杂的计算。本文提出的方法旨在促进这一问题的解决。大致可以描述如下：
In thermodynamics, whenever a material is subject to investigation of its properties, the entropy principle is used to impose restrictions on the constitutive relations for the material.There is not, so far, any simple method by which restrictions from the entropy principle can be derived for all kinds of different materials. Indeed, until very recently there was not even an entropy principle appropriate to all bodies. MULLER [1][2][3] has proposed such a general entropy principle, and here I suggest a simple method for its exploitation: the method of Lagrange multipliers. The entropy principle requires the constitutive relations to be such that every solution of the thermodynamic field equations satisfy the entropy inequality. To satisfy this requirement is not easy, since usually complicated calculations ensue. The method proposed here is intended to facilitate the solution of this problem. It can be described roughly as follows: