拉格朗日应变张量与欧拉应变张量的变换性质
Transformation Properties of the Lagrangian and Eulerian Strain Tensors
摘要：
基于平行传播子、世界函数和位移矢量场作为三点张量，给出了有限变形理论的欧拉和拉格朗日应变张量的坐标独立推导.推导明确表明，欧拉和拉格朗日应变张量是两点张量，每个空间和材料坐标的函数。欧拉应变是两点张量，其在空间坐标的变换下变换为二阶张量，并且在材料坐标的变换下变换为标量。拉格朗日应变是两点张量，其在空间坐标变换下变换为标量，并且在材料坐标变换下变换为二阶张量。当应变张量从一个参考系变换到另一个运动系时，需要这些变换性质。
英文摘要：
A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates. The Eulerian strain is a two-point tensor that transforms as a second rank tensor under transformation of spatial coordinates and transforms as a scalar under transformation of the material coordinates. The Lagrangian strain is a two-point tensor that transforms as scalar under transformation of spatial coordinates and transforms as a second rank tensor under transformation of the material coordinates. These transformation properties are needed when transforming the strain tensors from one frame of reference to another moving frame.
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