与马德隆应力张量耦合的应变张量
A strain tensor that couples to the Madelung stress tensor
摘要：
通常情况下，应力张量，推导出一个马德隆流体不被视为耦合到应变张量，这是符合流体假设。然而，基于先前关于量子势的几何性质的工作，人们实际上可以定义一个应变张量，然而，这不是由于空间区域的变形，而是由于该区域上的框架场的变形。当人们将马德隆应力张量表示为应变张量及其导数的函数时，人们就定义了马德隆介质的本构律，这可能会导致其基本结构的更详细的描述。它指出，由此产生的本构关系是强烈类似的法律，由开尔文和泰特的弯曲和扭转的弹性线和板，以及爱因斯坦方程的引力，如果一个人采取的观点度量弹性。
英文摘要：
Ordinarily, the stress tensor that one derives for a Madelung fluid is not regarded as being coupled to a strain tensor, which is consistent with the fluid hypothesis. However, based upon earlier work regarding the geometric nature of the quantum potential, one can, in fact, define a strain tensor, which is not, however, due to a deformation of a spatial region, but to a deformation of a frame field on that region. When one expresses the Madelung stress tensor as a function of the strain tensor and its derivatives, one then defines a constitutive law for the Madelung medium that might lead to a more detailed picture of its elementary structure. It is pointed out that the resulting constitutive law is strongly analogous to laws that were presented by Kelvin and Tait for the bending and torsion of elastic wires and plates, as well as the Einstein equations for gravitation if one takes the viewpoint of metric elasticity.
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