Thermomechanical coupling effects on path-dependent thickness evolution in finite-strain spinning disks

Abstract This study investigates finite deformations in hyperelastic rotating disks subjected to concurrent thermomechanical loading. A simplified semi-analytical formulation is developed for relatively thin disks by introducing a refined displacement field that addresses a limitation in existing literature: the unrealistic assumption of constant axial displacement through the disk's thickness, independent of radial position. While this common simplification avoids solving the axial equation of motion and reduces computational complexity, it yields physically inaccurate predictions for rotating systems. The proposed framework couple’s mechanical and thermal responses while accounting for deformation- and temperature-dependent thickness variations. Results demonstrate strong agreement with fully 3D finite element simulations, with maximum errors of 5–6% in mechanical predictions under extreme conditions and ≤3% in temperature distributions. Quantitatively, the model validates that soft disks undergoing large deformations require intrinsically coupled solutions of solid mechanics and heat transfer equations to capture realistic thermomechanical behavior. The work establishes that disregarding radial variations in axial displacement – though analytically convenient – fundamentally compromises solution fidelity and provides a validated alternative for accurate performance assessment of thin rotating hyperelastic disks under combined thermal and centrifugal loads.