We consider the complementing condition and Agmon’s condition for linearized elasticity in two-dimensions. With an elasticity tensor C $\mathsf{C}$ derived from a compressible, isotropic stored energy W $W$ , linearized about a homogeneous deformation f 0 $\mathbf{f}_{0}$ , we apply the complementing and Agmon’s conditions to a traction portion of the surface of a body with unit normal n $\mathbf{n}$ . We show these conditions are independent of n $\mathbf{n}$ for arbitrary W $W$ and f 0 $\mathbf{f}_{0}$ . We also consider the case of failure of the complementing condition for the pure traction problem.

中文翻译：

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有限弹性​​中的互补条件和阿格蒙条件

我们考虑了二维线性化弹性的互补条件和阿格蒙条件。弹性张量 C $\mathsf{C}$ 源自可压缩的各向同性储存能量 W $W$ ，关于均匀变形 f 0 $\mathbf{f}_{0}$ 线性化，我们应用补充和阿格蒙条件到具有单位法线 n $\mathbf{n}$ 的物体表面的牵引部分。我们表明，对于任意 W $W$ 和 f 0 $\mathbf{f}_{0}$ ，这些条件与 n $\mathbf{n}$ 无关。我们还考虑了纯牵引问题的补充条件失效的情况。