有理力学中固体、流体和气体作为连续介质的几何场表示
Geometrical Field Representation of Solid, Fluid, and Gas as Continuum in Rational Mechanics
摘要：
基于连续介质中运动变换的点集变换概念，将宏观经典应变表示为材料单元的本征伸缩和本征局部转动的相加。对于零经典应变（在其位形表面上没有观察到宏观变形，需要适当的容器来容纳液体和气体以构成宏观不变位形），结果表明：（1）对于固体，局部转角为零。物质元素没有内在的拉伸。(2)对于液体，局域转动不会改变基本规范张量。材料单元在旋转平面上具有内在平面拉伸。(3)对于气态，内禀局域转动将放大基本规范张量。材料元件具有沿旋转方向的固有拉伸。因此，在没有观察到宏观经典应变的条件下，材料元素具有三种不同的物理状态：固体（无内禀拉伸），流体（平面内禀拉伸）和气体（定向内禀拉伸）。此外，对于这三种状态，自由条件由零内禀拉伸定义。在此自由条件下，建立了多状态下材料的本构方程。
英文摘要：
Based on the points-set transformation concept about the motion transformation in continuum, the macro classical strain is expressed by the additive addition of the intrinsic stretching of material element and its intrinsic local rotation. For zero classical strain (no macro deformation observed on its configuration surface, suitable container is required for liquid and gas to make up macro invariant configuration), the results show that: (1) For solid, the local rotation angular is zero. The material element has no intrinsic stretching. (2) For liquid, the local rotation will not change the basic gauge tensor. The material element has intrinsic plane stretching on the rotation plane. (3) For gas state, the intrinsic local rotation will amplify the basic gauge tensor. The material element has intrinsic stretching along the rotation direction. Hence, under the condition of no macro classical strain be observed, the material element has three different physical states: solid (no intrinsic stretching), fluid (plane intrinsic stretching), and gas (directional intrinsic stretching). Furthermore, for the three states, the free conditions are defined by zero intrinsic stretching. Referring to this free condition, the constitutive equations for the materials at multiple states are established.
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