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首页> 外文期刊>International journal of engineering research and industrial applications >A POLAR CONTINUUM THEORY FOR FLUENT CONTINUA
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A POLAR CONTINUUM THEORY FOR FLUENT CONTINUA

机译：流体连续性的极连续性理论

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摘要

Polar decomposition of the changing velocity gradient tensor in a deforming fluent continua into pure stretch rates and rates of rotations shows that a location and its neighboring locations can experience different rates of rotation during evolution. Alternatively, we can also consider decomposition of the velocity gradient tensor into symmetric and skew symmetric tensors. The skew symmetric tensor is also a measure of pure rates of rotations whereas the symmetric tensor is a measure of strain rates. The measures of the internal rates of rotation due to deformation in the two approaches describe the same physics but in different forms. Polar decomposition gives the rate of rotation matrix and not the rates of rotation angles whereas the skew symmetric part of the velocity gradient tensor yields rates of rotation angles that are explicitly defined in terms of velocity gradients. These varying rates of rotation arise due to varying deformation of the continua, hence are internal to the volume of matter and are explicitly defined by deformation, hence do not require additional rotational degrees of freedom. If the internal varying rates of rotations are resisted by the continua, then there must exist internal moments corresponding to these. The internal rates of rotations and the corresponding moments can result in additional rate of energy storage or rate of dissipation.
机译：将变形流体连续体中变化的速度梯度张量的极分解为纯拉伸速率和旋转速率，表明某个位置及其邻近位置在进化过程中会经历不同的旋转速率。或者，我们也可以考虑将速度梯度张量分解为对称和偏斜对称张量。偏斜对称张量也是纯旋转速率的量度，而对称张量是应变速率的量度。两种方法中由于变形引起的内部旋转速率的度量描述了相同的物理原理，但形式不同。极坐标分解给出的是旋转矩阵的速率，而不是旋转角度的速率，而速度梯度张量的斜对称部分产生的旋转角度的速率是根据速度梯度明确定义的。这些变化的旋转速率是由于连续体的变化而产生的，因此在物质体积内部，并且由变形明确地定义，因此不需要附加的旋转自由度。如果内部变化的旋转速度受到连续性的抵制，那么必须存在与之相对应的内部力矩。内部旋转速度和相应的力矩会导致额外的能量存储速度或耗散速度。

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