Identification of the location and magnitude of a concentrated force applied to a hyperelastic plate using gradient-based and machine learning methods

Analyzing the problem of identifying a concentrated force applied to a hyperelastic plate can provide valuable insights into the behavior of this class of materials. This analysis also supports research in crucial fields, such as biomechanics, particularly in the design and fabrication of human organs. For instance, in cardiac tissue modeling, accurately mapping external forces on heart valves or ventricular walls informs the design of biocompatible prosthetics or surgical planning tools. In soft robotics, identifying localized forces is essential for optimizing actuators. While significant progress has been made in force identification for linear elastic materials, the nonlinearity behavior of hyperelastic materials introduces unique complexities that remain inadequately addressed in current literature. Existing inverse methods for hyperelastic plates often simplify the problem by estimating either the magnitude or its location independently. To identify both unknowns simultaneously, this study employs two gradient-based methods and two machine learning algorithms. The finite element method and the first-order shear deformation theory are used to analyze the hyperelastic plates. In the inverse problem, the lateral displacements at several measurement points are considered as measured data. The first gradient-based method updates both unknowns simultaneously, while the second method optimizes them separately in each stage of the method. Comparisons show that the second algorithm is more systematic. Increasing the number of measurement data reduces the fluctuations but increases the computational cost. Accuracy decreases with higher measurement error. While training machine learning models is time-consuming, once trained, they can quickly identify the unknown force.