Poking with a sharp probe has been one of the most popular method to characterize mechanical properties of materials in film form including atomically thin two-dimensional materials. Herein, we propose an approximate analytical framework for describing the deflection of films under anisotropic tension and central concentrated load, which is expected to provide a more flexible selection and more robust reference for corresponding experiments. Specifically, first, we point out the high similarity of the deflection among the square, circular and elliptic substrate-free films, which allows us to transform the discussion of square and circular films into that of elliptic films. Then, the deflection of the elliptic film is analytically described by considering the film as a combination of an elliptical annular membrane and a tiny elliptic plate in the center. Finally, the analytical solution is verified to have high accuracy in describing the deflection of an elliptic film, and be applicable to square and circular substrate-free films from nano to macro scales.

用锋利的探针戳一直是表征薄膜形式材料（包括原子级薄二维材料）机械性能的最流行方法之一。在此，我们提出了一个近似的分析框架来描述薄膜在各向异性张力和中心集中载荷下的挠度，有望为相应的实验提供更灵活的选择和更可靠的参考。具体来说，首先，我们指出方形、圆形和椭圆形无基板薄膜之间的偏转高度相似，这使我们能够将方形和圆形薄膜的讨论转化为椭圆形薄膜的讨论。然后，椭圆膜的挠度通过将膜视为椭圆环膜和中心微小椭圆板的组合来解析描述。最后验证了该解析解在描述椭圆薄膜的挠度方面具有较高的准确性，适用于从纳米尺度到宏观尺度的方形和圆形无衬底薄膜。