一族线性屈服破坏函数对应的耗散势

在材料塑性本构理论中应用热动力学原理一般有两种方法,一是在引入的屈服(包括硬化)、破坏函数和塑性势概念的基础上,从数学上或者根据试验规律,假设(拟合)其函数形式,然后将热力学定律或准热力学公设作为附加约束引入本构模型:二是直接从热动力学出发,通过构造能量函数(热力学势)、耗散函数及较少的限制条件给出全部的塑性本构理论,而得到的本构理论自动满足热动力学原理.长期以来,针对各种不同材料提出的大量屈服破坏函数,许多都是按照第一种方法给出的,却并未见到进行过严格的热动力学限制的验证.研究从塑性本构理论中上述两种研究方式在热力学定律的满足上的一致性出发,将求屈服函数对应的耗散势的问题归结为关于耗散势的偏微分方程求解问题,从理论上演绎出塑性理论中一族率无关线性屈服破坏函数对应的耗散势函数,从而将屈服破坏函数的热动力学验证问题转化为其对应耗散势的正负判断问题,也沟通了塑性理论中屈服破坏函数同热动力学中耗散势在概念上的联系,对于理解屈服破坏函数的热动力学内涵有重要理论意义.特别地,文中给出的求耗散势的方法具有一般性,不仅适合于线性的屈服破坏函数,也适合于非线性的屈服破坏函数.最后,利用热力学第2定律给出了一族线性屈服破坏函数具体的热力学限制条件.

Dissipation potential corresponding a class of yield/failure functions

Plasticity theory must satisfy the thermodynamic restriction conditions, of which Second Law of Thermodynamics is the most important. Yield /failure function is the original concept of plasticity theory, and it concerns the dissipation process described with Second Law nearly. Entropy or dissipation potential is a key state variable defined from Second Law of Thermodynamics to describe this irreversible process. So yield /failure function must have a close relation with the dissipation potential. In this research, dissipation potential corresponding to class of yield /failure functions in plasticity theory is deduced through solving the dissipation differential equation transformed from the yield /failure functions. Especially, the methodology of getting the dissipation potential is applicable for both the linear and nonlinear yield /failure functions. Thus the thermodynamic consistency of these yield /failure functions can be verified from this dissipation potential expediently. Moreover, the thermodynamic restriction conditions on the yield /failure function are deduced using the dissipation potential corresponding to a class of yield /failure functions and second law.