Experimental observations have revealed a change in the concavity of the resultant force-displacement plot in the extension test for pantographic sheets. In this paper, we aim to relate these macroscopically observed mechanical properties with the microscale properties of the hinges (or pivots) connecting the pantographic fibers. The material constituting the hinges is modeled at the microscale as an isotropic elastoplastic 3D Cauchy continuum. The elastic regime is assumed to be linear, while the plastic regime exhibits either saturating or non-saturating hardening. In the case of circular homogeneous cylindrical hinges, monotonic loading is considered to derive a mesoscale constitutive relation linking the torsional angle to the total applied torque. It is demonstrated that (non-)saturating hardening at the microscale results in (non-)saturating hardening of the twist angle/torque plot at the mesoscale, which itself is responsible for the change of concavity in bias extensional test of pantographic sheets.

实验观察表明，受电弓拉伸试验中合成力-位移图的凹度发生了变化。在本文中，我们的目标是将这些宏观观察到的机械性能与连接缩放纤维的铰链（或枢轴）的微观性能联系起来。构成铰链的材料在微观尺度上建模为各向同性弹塑性 3D 柯西连续体。假设弹性状态是线性的，而塑性状态表现出饱和或非饱和硬化。在圆形均质圆柱形铰链的情况下，考虑单调载荷以导出将扭转角与总施加扭矩联系起来的介观本构关系。结果表明，微观尺度的（非）饱和硬化会导致中尺度扭转角/扭矩图的（非）饱和硬化，这本身就是受电弓偏置拉伸试验中凹度变化的原因。