From 1D to fully coupled 2D stress-analysis of thick rotating disks at finite deformation

Rotating hyperelastic disks are key elements in high-performance systems, where large deformations and complex stress fields challenge standard models. Many analytical treatments simplify the problem by assuming uniform thickness or restricting deformation to radial-only kinematics, limiting accuracy for thick disks and realistic geometries with thickness variation. This work presents a two-dimensional semi-analytical formulation for an incompressible hyperelastic disk with naturally evolving (non-prescribed) thickness under centrifugal loading, retaining coupled axial and radial deformation within a Neo-Hookean framework. The formulation is validated through direct comparison with finite-element simulations and shows accuracy gains over classical one-dimensional theories, especially at large thickness ratios and rotation speeds. It predicts tensile thickening near the outer edge and compressive thinning toward the center, along with shear and axial stress components that radial-only models cannot capture. Quantitatively, the approach delivers up to a 14% improvement in strain prediction for thickness ratios above 0.8 and identifies when axial–radial coupling becomes important (L/R ≥ 0.4). It also predicts a non-monotonic edge profile at high thickness ratios (R/L ≥ 1.4), with localized mid-thickness indentation from nonlinear equilibrium—behavior not reproduced by existing 1D or constrained formulations. Overall, the model is an efficient alternative to full simulation for global and localized nonlinear features.