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.