A thermodynamically consistent continuum modeling framework is developed to investigate the transient thermo-mechanical response of rotating bi-directional functionally graded (BD-FG) discs as a result of a friction heating regime from a gray cast iron (GCI) brake pad. The disc gradation is through-thickness from the ceramic phase ( \({Al}_{2}{O}_{3}\) ) at the inner surface to the metallic shear phase (GCI) at the outer surface, where friction takes place. Hence, the effects of material inhomogeneity can be analyzed in terms of heat conduction and mechanical deformation. The transient thermal field follows the Fourier law for the heat conduction mechanism, where the outer surface of the disc experiences a constant and uniform heat flux and the inner surface is adiabatic. The structural response is achieved through a quasi-3D refined zigzag theory where transverse shear deformation and non-uniform temperature distribution through the thickness can be described. Geometric nonlinearity is achieved using Von-Kármán-type kinematic relations, and nonlinear governing equations are established using an energy-based variational principle. The system of equations is discretized using the differential quadrature method for both spatial and temporal solutions, with time-domain problems solved using Newmark integration. Numerical results reveal the effect of functional gradation, rotational inertia, and thermal boundary conditions on the nonlinear bending performance of the disc. The work provides a predictive approach for the design of high-performance thermally loaded FG rotating structures subjected to complicated loading histories.
