极性连续介质力学
Polar continuum mechanics
摘要：
现有的极性连续统理论包含在偶应力张量的球面部分未解决的不确定性。这严重限制了它在微纳米尺度固体和流体力学研究中的应用，也许更重要的是，在涉及广泛尺度的流体湍流现象的研究中。在本文中，我们依靠能量方程，以及一些运动学的考虑，建立一个一致的偶应力理论的极性连续，解决所有的不确定性。在给出一般公式和得到守恒定律之后，我们专门集中于极性流体力学的偶应力理论。我们专门研究线性粘性流的理论，并考虑偶应力流体力学中的几个边值问题。更一般地说，由此产生的理论在这里可能提供一个基础，在最精细的尺度上的基本连续水平的研究。
英文摘要：
The existing polar continuum theory contains unresolved indeterminacies in the spherical part of the couple-stress tensor. This severely restricts its applicability in the study of micro and nano-scale solid and fluid mechanics and, perhaps more importantly, in the investigation of fluid turbulence phenomena, which involve a broad range of scales. In this paper, we rely on the energy equation, along with some kinematical considerations, to establish a consistent couple-stress theory for polar continua that resolves all indeterminacies. After presenting the general formulation and obtaining conservation laws, we concentrate exclusively on couple stress theory for polar fluid mechanics. We specialize the theory for linear viscous flow and consider several boundary value problems in couple-stress fluid mechanics. More generally, the resulting theory presented here may provide a basis for fundamental continuum-level studies at the finest scales.
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