摘要
在不可逆热力学框架内引入了四条基本假设,建立了宏观本构关系的新的逻辑系统.在假设3中通过引入一种新的运算,把内变量演化方程定义在时间的点集上.结合讨论Clausius-Duhem不等式,得到了假设4,它把时间点集的性质与系统状态联起来.以此为基础,证明了一致性条件成立的判别准则和加卸载准则,并成功地解释了实验现象:存在有一个应变速率的临界值,当加载应变速率低于该值时,材料的应力-应变关系基本上与速率无关;当高于该值时,则明显与速率相关.更富有力学含义地给出了不可逆系统稳定性的一种定义,并证明了判别稳定性的一个准则.此外,还得出系统稳定是不可逆行为与时间无关的前提条件.
By introducing four basic assumptions into the framework of irreversible thermodynamics, a new logical system of constitutive relations are formed. In assumption 3 a new operation is introduced and the evolution equations of internal variables are denned in the point set of time. By discussing Clausius-Duhem's inequality, assumption 4 is obtained and therefore the properties of the point set of time are related to the states of the system. Based on the analysis above, the judgement criterion of consistency condition and the criterion of loading-unloading are proven and the experimental phenomenon is successfully explained, namely, there is a critical strain rate, the stress-strain relationships of materials basically have nothing to do with the rate for a loading strain rate less than the critical strain rate and the stress-strain relationships of materials are obviously related to the rate for a loading strain rate greater than the critical strain rate. Mechanically, a definition of stability of an irreversible system is given and the corresponding judgement criterion of stability is proven. Furthermore, it is obtained that the preconditions of time-independent irreversible behavior is the stability of the system.
出处
《力学学报》
EI
CSCD
北大核心
2003年第3期377-384,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金重点项目基金资助项目(50139010
50279001)
大连理工大学海岸和近海工程国家重点实验室访问学者基金资助项目
关键词
不可逆热力学
本构关系
内变量演化方程
时间无关
稳定性
irreversible thermodynamics, constitutive relationship, evolution equation of internal variables, time-independent, stability
