Large Deformation Analysis of Rotating Variable-Thickness Homogeneous and FGM Hyperelastic Disks using PINNs

This study presents a Physics-Informed Neural Network (PINN) framework for analyzing the nonlinear deformation of rotating variable-thickness hyperelastic disks made of both homogeneous and Functionally Graded Materials (FGMs). The formulation incorporates large-deformation kinematics, the incompressibility constraint, and the neo-Hookean constitutive law within a hybrid loss function that combines physical residuals with sparse high-fidelity data. Three disk geometries — rectangular, trapezoidal, and parabolic profiles — are examined under steady-state rotation for both homogeneous and radially graded materials characterized by power-law variations in shear modulus and density. The hybrid PINN framework yields mesh-free and physics-consistent predictions for the displacement and stress fields. Quantitative comparison with Finite Element Method (FEM) benchmarks demonstrates excellent agreement across all geometries: the relative differences remain below approximately 2% in radial displacement, the mean absolute deviation within about 3[Formula: see text]MPa in the maximum principal stress, and the predicted shift in peak-stress location less than 3% of the outer radius for both positive and negative gradation indices ([Formula: see text]). These results, derived directly from the validated graphical and numerical comparisons, confirm the accuracy, stability, and robustness of the proposed hybrid PINN formulation for the nonlinear analysis of rotating variable-thickness hyperelastic disks made of both homogeneous and graded materials.