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Statements

Subject Item
dbr:Objective_stress_rate
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客观应力率 Objective stress rate
rdfs:comment
客观应力率（英語：objective stress rate）在连续介质力学中是指不依赖参考系的应力时间导数。一些本构关系可以表示为应力率与应变率之间的关系。由于物体的力学响应不应随参考系的变化而变化（即客观性），而由柯西应力张量求时间导数直接得到的应力率张量并不是客观的，故需要定义具有客观性的应力率。 在连续介质力学中有多种客观应力率的定义，它们都可以表示成李导数的形式。其中最常见的客观应力率包括 * 柯西应力张量的特鲁斯德尔（Truesdell）应力率 （其中为速度梯度张量） * 柯西应力张量的格林－纳厄迪（Green-Naghdi）应力率 （其中，为转动张量） * 柯西应力张量的耀曼（Jaumann）应力率 （其中为自旋张量，即速度梯度张量的反对称部分） In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. Many constitutive equations are designed in the form of a relation between a stress-rate and a strain-rate (or the rate of deformation tensor). The mechanical response of a material should not depend on the frame of reference. In other words, material constitutive equations should be frame-indifferent (objective). If the stress and strain measures are material quantities then objectivity is automatically satisfied. However, if the quantities are spatial, then the objectivity of the stress-rate is not guaranteed even if the strain-rate is objective.
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客观应力率（英語：objective stress rate）在连续介质力学中是指不依赖参考系的应力时间导数。一些本构关系可以表示为应力率与应变率之间的关系。由于物体的力学响应不应随参考系的变化而变化（即客观性），而由柯西应力张量求时间导数直接得到的应力率张量并不是客观的，故需要定义具有客观性的应力率。 在连续介质力学中有多种客观应力率的定义，它们都可以表示成李导数的形式。其中最常见的客观应力率包括 * 柯西应力张量的特鲁斯德尔（Truesdell）应力率 （其中为速度梯度张量） * 柯西应力张量的格林－纳厄迪（Green-Naghdi）应力率 （其中，为转动张量） * 柯西应力张量的耀曼（Jaumann）应力率 （其中为自旋张量，即速度梯度张量的反对称部分） In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. Many constitutive equations are designed in the form of a relation between a stress-rate and a strain-rate (or the rate of deformation tensor). The mechanical response of a material should not depend on the frame of reference. In other words, material constitutive equations should be frame-indifferent (objective). If the stress and strain measures are material quantities then objectivity is automatically satisfied. However, if the quantities are spatial, then the objectivity of the stress-rate is not guaranteed even if the strain-rate is objective. There are numerous objective stress rates in continuum mechanics – all of which can be shown to be special forms of Lie derivatives. Some of the widely used objective stress rates are: 1. * the Truesdell rate of the Cauchy stress tensor, 2. * the Green–Naghdi rate of the Cauchy stress, and 3. * the Zaremba-Jaumann rate of the Cauchy stress. The adjacent figure shows the performance of various objective rates in a simple shear test where the material model is hypoelastic with constant elastic moduli. The ratio of the shear stress to the displacement is plotted as a function of time. The same moduli are used with the three objective stress rates. Clearly there are spurious oscillations observed for the Zaremba-Jaumann stress rate.This is not because one rate is better than another but because it is a misuse of material models to use the same constants with different objective rates. For this reason, a recent trend has been to avoid objective stress rates altogether where possible.
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