Measurement of in-plane elasticity of thin sheets often leverages out-of-plane poking or bulging, also known as indentation or bulge tests. For linear elastic sheets, a load-cubic deflection relation has been frequently assumed so that the stiffness of the sheet could be readily extracted. However, we find that recent results of indentation and bulge tests on 2D materials do not support the assumption, which can be attributed to the slippage of 2D materials against their supporting substrates. Besides, the interfacial slippage could cause instabilities in the sheet such as radial wrinkles in suspended region, with finite lengths. To gain a quantitative understanding, we assume constant interfacial shear traction and study the wrinkling extent and the effective stiffness of thin sheets upon poking and bulging. We identify a single dimensionless parameter governing these mechanical responses—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage). We discuss several useful asymptotic behaviors emerging at small and large sliding numbers. These understandings inspire when the effect of the interfacial slippage (as well as other substrate-associated subtleties) can be neglected in these tests. For instance, traditional bulge and indentation tests suffer from complexities caused by the slippage, pretension, Poisson's ratio, substrate roughness, and various interfacial traction-separation laws. Based on such understandings, we propose a simple poking/bulging methodology immune to all of these complexities, enabling an alternative way to measure the sheet stiffness.

薄板的平面内弹性的测量通常利用平面外戳或凸出，也称为压痕或凸出测试。对于线性弹性片材，经常假设载荷-立方挠度关系，以便可以容易地提取片材的刚度。但是，我们发现2D材料的压痕和凸出测试的最新结果不支持该假设，这可以归因于2D材料相对于其支撑基板的滑动。此外，界面滑移可能会引起片材的不稳定性，例如在有限长度的悬浮区域中出现径向皱纹。为了获得定量的理解，我们假设界面剪切力是恒定的，并研究在戳和鼓胀时薄片的起皱程度和有效刚度。我们确定了控制这些机械响应的单个无量纲参数，即滑动数，该参数是通过将薄片张力（驱动滑移）与界面牵引力（抵抗滑移）进行比较来定义的。我们讨论了在小和大滑动数下出现的几种有用的渐近行为。当在这些测试中可以忽略界面滑移（以及其他与基材相关的细微变化）的影响时，这些理解会激发灵感。例如，传统的隆起和压痕测试由于打滑，预紧，泊松比，基体粗糙度和各种界面牵引-分离定律而导致复杂性。基于这样的理解，我们提出了一种不受所有这些复杂因素影响的简单戳入/凸出方法，从而提供了一种替代的方法来测量纸张的刚度。