时空系的标架变换规律和受内约束简单物质的响应泛函

The Frame-Change Law of Space-time and the Response Functionals of Simple Materials with Internal Constraints

讨论了标架无关性的定义,指出Hunter(1983)[1]和王自强(2000)[2]的定义及时空系标架变换规律与理论力学[3]中有关复合运动的有关概念一致,这表明Truesdell和Noll(1965)的时空标架变换规律及客观量标架变换规律只有被理解为矩阵方程而不是张量方程才是正确的.还讨论了受内约束简单物质的响应泛函.利用Vianello(1990)[4]的方法证明总是存在正规化方法选取满足正规化条件的可决定应力响应泛函使它同时满足标架无关性和物质对称性要求.这就从理论上说明,对受内约束简单物质,可以引入正规化条件消除响应泛函的不确定性,确定可决定应力响应泛函.

In this paper,the definition of frame-indifference is discussed and it is pointed out that the definition of frame-indifference and frame-change law of space-time in Hunter(1983) and Wang(2000) agree to the related concepts when the compound motions are concerned in theoretical mechanics.This shows that Truesdell and Noll's frame-change laws of space-time and frame-indifferent variables must be regarded as matrix equations rather than tensorial equations.The response functionals are also discussed in the present paper.By use of the approach of Vianello(1990) it is proved that there exists an approach to select a normalized extra stress response functional so that it satisfies the frame-indifference and invariance of material symmetry.Therefore,for any simple material with internal constraints,theoretically the indeterminacy of the determinate stress response functional can be removed by normalization so that the extra stress response functional is determined.