Abstract Although the Hughes-Winget rotation tensor is not strongly objective when stretching occurs during a time step it is very accurate when the incremental stretching during the time step is small, a condition that is almost always met in practice. Two types of evolution equations based on the Jaumann derivative are examined which show that the main source of error in the numerical algorithms is due to the approximation of the average deformation rate during the time step. A new strongly objective expression for the average deformation rate during a time step is developed and shown to correct the observed errors in tests of strong objectivity.

中文翻译：

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应用于数值积分算法的平均变形率的强客观表达式

摘要 虽然 Hughes-Winget 旋转张量在时间步长拉伸时不是很强的客观性，但在时间步长的增量拉伸很小时是非常准确的，这个条件在实践中几乎总是满足。研究了基于 Jaumann 导数的两种类型的演化方程，它们表明数值算法中的主要误差来源是由于时间步长期间平均变形率的近似。一个时间步长期间平均变形率的新的强客观表达式被开发出来，并被证明可以纠正强客观测试中观察到的错误。