Thermodynamical Frameworks for Higher Grade Material Theories with Internal Variables or Additional Degrees of Freedom
Thermodynamical Frameworks for Higher Grade Material Theories with Internal Variables or Additional Degrees of Freedom
复制标题
具有内部变量或附加自由度的高级材料理论的热力学框架
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Forest
中科院分区：
文献类型：
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作者：
C. Papenfuss;S. Forest
摘要本研究的目的是比较几种热力学框架，考虑应变梯度、内变量梯度、内变量梯度和温度梯度对材料本构行为的影响。特别地，导出了热力学第二定律的限制。利用方法包括两个步骤：利用Liu的著名方法和利用剩余不等式的新方法。第一个例子为本构函数引入了一组扩大的变量，特别是包括应变梯度、内部变量、其梯度和温度梯度。在第二个例子中，内力的幂被充实以纳入广义应力测量。在第三个例子中，经典的热力学设置被一个附加变量的平衡型微分方程所补充。最后，展望了n级材料理论。结果表明，自由能密度只在引入附加平衡方程的情况下才与梯度有关。我们还证明，对于各向同性材料，热力学第二定律意味着，对于一类大的状态空间，熵通量等于热通量除以温度。
Abstract The objective of the present work is to compare several thermomechanical frameworks, taking into account the influence of strain gradient, internal variables, gradient of internal variables, and temperature gradient on the constitutive behavior of materials. In particular, the restrictions by the second law of thermodynamics are derived. The method of exploitation consists of two steps: an application of the well-known method by Liu and a new method of exploiting the residual inequality. The first example introduces an enlarged set of variables for the constitutive functions including in particular the strain gradient, an internal variable, its gradient, and the temperature gradient. In the second example, the power of internal forces is enriched to incorporate generalized stress measures. In the third example, the classical thermomechanical setting is complemented by a balance-type differential equation for an additional variable. Finally, material theories of grade n are envisaged. It is shown that the free energy density may depend on gradients only in the case that an additional balance equation is introduced. We also demonstrate that for isotropic materials the second law of thermodynamics implies for a large class of state spaces that the entropy flux equals the heat flux divided by temperature.