Closed-Form Analysis of Stress and Deformation in Functionally Graded Multi-Layer Hyperelastic Cylinders Under Internal Pressure

This study presents a closed-form analytical solution for large-deformation pressure-induced stress and displacement fields in thick-walled, functionally graded (FG) hyperelastic polyvinyl chloride (PVC) cylinders subjected to internal pressure. The formulation inherently satisfies incompressibility—an aspect not guaranteed by standard finite element methods (FEMs)—and provides explicit expressions for all stress and deformation components. Using a Mooney–Rivlin model with an exponential–logarithmic gradation law, the study examines bi-layer and tri-layer configurations under varying property-changing scenarios. The governing equations are reduced to a single nonlinear scalar relation for the radial mapping constant, ensuring computational efficiency. Analytical predictions demonstrate excellent agreement with FEM results (errors < 1%) and recover homogeneous limits, and demonstrate that continuous gradation significantly reduces stress concentrations compared to discrete layering. The proposed model offers an efficient tool for designing pressure-resistant FG hyperelastic components for engineering applications such as pipes, hoses, biomedical devices, and protective casings.