论文标题
使用Riemann-Cartan几何形状的连续性兼容条件
Compatibility conditions of continua using Riemann-Cartan geometry
论文作者
论文摘要
在差异几何形状的框架中，特别是Riemann-Cartan几何形状研究了广义连续性的兼容条件。我们表明，线性弹性理论中Vallée的兼容性条件等效于消失的三维爱因斯坦张量。此外，我们表明，NYE的张量满足的兼容性条件也来自三维的爱因斯坦张量，这似乎在前面未提及的连续性力学中起着关键作用。我们讨论了可以使用我们的几何方法获得的进一步兼容条件，并将其应用于微观理论。
The compatibility conditions for generalised continua are studied in the framework of differential geometry, in particular Riemann-Cartan geometry. We show that Vallée's compatibility condition in linear elasticity theory is equivalent to the vanishing of the three dimensional Einstein tensor. Moreover, we show that the compatibility condition satisfied by Nye's tensor also arises from the three dimensional Einstein tensor which appears to play a pivotal role in continuum mechanics not mentioned before. We discuss further compatibility conditions which can be obtained using our geometrical approach and apply it to the micro-continuum theories.
