Finite Difference Investigation of Nonlinear Deformation in Torsionally Loaded Cylindrical Hyperelastic Solids

This research investigates the finite deformation of a compressible hyperelastic cylindrical body under torsional loading, analyzed using the Finite Difference Method (FDM). A mathematical model incorporating the deformation gradient tensor and the Blatz–Ko strain energy function is developed to capture the nonlinear elastic behavior associated with large, reversible deformations. The governing equations are numerically solved in Wolfram Mathematica to obtain the displacement field and to assess the influence of material compressibility under varying external pressures. Results demonstrate that materials with lower initial compressibility exhibit greater deformability, making them suitable for flexible applications such as elastomeric seals, while higher compressibility materials show increased resistance to excessive deformation, appropriate for load-bearing components like drive shafts. The Blatz–Ko formulation effectively reproduces compression–expansion cycles consistent with the Poynting effect; however, numerical oscillations at high compressibility and pressure indicate limitations of the FDM scheme. Moreover, the persistence of consistent deformation patterns near the cylinder’s origin across all compressibility levels emphasizes the significance of boundary conditions in governing mechanical response.