Evans E A
Biophys J. 1976 Jun;16(6):597-600. doi: 10.1016/S0006-3495(76)85714-1.
The intention of this note is to correct a subtle and somewhat esoteric error that the author discovered in his previous publications on membrane elastic behavior. The consitutive relation between membrane force resultants and large, elastic deformations of a membrane surface involves a strain tensor, characterizing the finite deformations. The original strain tensor that appeared in the equations was the Lagrangian strain tensor; however, the proper strain representation (also Lagrangian in nature because it is "measured" relative to the undeformed material state) is transformed by rotations of coordinates in the deformed material state (whereas the Lagrangian strain tensor is transformed by rotations of coordinates in the undeformed state). The principal membrane tensions are unchanged by this correction; the material elastic constants remain the same; and therefore, the material behavior in shear and isotropic tension is the same. However, the tensor, constitutive relation can be properly applied to coordinate systems other than the principal axis system.
本注释的目的是纠正作者在先前关于膜弹性行为的出版物中发现的一个细微且有些深奥的错误。膜面内力与膜面大弹性变形之间的本构关系涉及一个应变张量，用于表征有限变形。方程中最初出现的应变张量是拉格朗日应变张量；然而，正确的应变表示（本质上也是拉格朗日的，因为它是相对于未变形材料状态“测量”的）在变形材料状态下会因坐标旋转而变换（而拉格朗日应变张量在未变形状态下因坐标旋转而变换）。这种修正不会改变主膜张力；材料弹性常数保持不变；因此，材料在剪切和各向同性拉伸时的行为是相同的。然而，张量本构关系可以适用于主轴系统以外的坐标系。
