论文标题
弹性理论总体相对论
Elasticity Theory in General Relativity
论文作者
论文摘要
从拉格朗日（Lagrangian）而不是欧拉（Eulerian）的角度来审查弹性的一般相对论理论。超弹性体的运动和应力 - 能量量张量的方程是从DeWitt首先考虑的量规不变动作原理得出的。该动作是单个相对论粒子的动作的自然扩展。拉格朗日治疗中的中心对象是Landau-Lifshitz雷达度量标准，它是右cauchy绿色变形张量的相对论版本。我们还介绍了变形梯度，绿色应变以及第一和第二Piola-kirchhoff应力张量的相对论定义。还提出了相对论超弹性的量规描述，并且随着光的速度变得无限。
The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action principle first considered by DeWitt. This action is a natural extension of the action for a single relativistic particle. The central object in the Lagrangian treatment is the Landau-Lifshitz radar metric, which is the relativistic version of the right Cauchy-Green deformation tensor. We also introduce relativistic definitions of the deformation gradient, Green strain, and first and second Piola-Kirchhoff stress tensors. A gauge-fixed description of relativistic hyperelasticity is also presented, and the nonrelativistic theory is derived in the limit as the speed of light becomes infinite.
