Bulge testing is an experimental technique applied to the characterization of thin films, with which the mechanical properties are obtained employing numerical and analytical approaches. For rectangular and circular thin films, classical methods have been well adopted to calculate the stresses and strains at the central point without the dependency of its properties. It is due to that the equilibrium conditions are dependent on the curvatures generated at the maximum deflection point. Therefore, the kinematics of the bulged surface can be represented by a spherical cap and cylindrical shapes in these films. For square thin films, the deflected surface presents a complex displacement field that implies the development of analytical models for the estimation of these. In this sense, equations to represent the equibiaxial stress state (central point) for freestanding square thin films are developed and applied in this study. The curvatures are determined using a reviewed nonlinear deflection field. Virtual experiments were driven by applying finite element analysis to validate the stress and strain models through parametric analysis. In order to impose the residual stress in thin films, two approaches of modeling for the simulations are described. In order to validate the applicability of the proposed equations, different cases were presented for the linear elastic analysis, and two examples were developed to characterize elastoplastic behavior (bilinear and nonlinear) from load–deflection curves. The obtained results show that the developed models for square thin films are in good agreement with the finite element simulations since these predicted the stress and strain states with good accuracy.

凸起测试是一种应用于薄膜表征的实验技术，利用数值和分析方法可以获得机械性能。对于矩形和圆形薄膜，已经很好地采用经典方法来计算中心点处的应力和应变，而不受其特性的影响。这是由于平衡条件取决于在最大偏转点处产生的曲率。因此，鼓起表面的运动学可以由这些膜中的球形盖和圆柱形状来表示。对于方形薄膜，挠曲的表面呈现出一个复杂的位移场，这暗示了用于估计这些的分析模型的发展。在这个意义上，本研究开发并应用了代表独立方形薄膜的等双轴应力状态（中心点）的方程。使用回顾的非线性偏转场确定曲率。通过应用有限元分析来驱动虚拟实验，以通过参数分析验证应力和应变模型。为了在薄膜中施加残余应力，描述了两种用于模拟的建模方法。为了验证所提方程的适用性，提出了不同的线性弹性分析案例，并开发了两个实例来根据载荷-挠度曲线表征弹塑性行为（双线性和非线性）。