Nonlinear stress and deformation analysis of pressurized thick-walled hyperelastic cylinders with experimental verifications and material identifications

Abstract

The main purpose of the present research is the investigation of the stress and displacement distributions of the internally pressurized thick-walled hyperelastic cylindrical vessels or pressure pipes. The governing equations are derived by incorporation of the incompressible neo-Hookean and Mooney-Rivlin hyperelastic constitutive models into the direct hyperelasticity theory in the von Karman framework of large deformations. In contrast to all the available researches, no simplifications or linearization are made. The non-linear governing equations are solved by utilizing a second-order point-collocation procedure and implementation of details of the proposed incremental iterative solution scheme in the Matlab code written by the authors. Another novelty of the present research is experimentally identifying the employed polymeric hyperelastic material and verification of the results through experiments conducted by the authors. Due to using both nonlinear constitutive laws and nonlinear stress-displacement relations, through-thickness distributions of the radial displacement and radial and circumferential stresses are extracted for various pressures. The experimental results reveal that while the neo-Hookean hyperelastic model cannot be used for materials with stress-softening, the Mooney-Rivlin model reproduces the experimental results with excellent accuracy. In addition to the experimental verification, the results are verified by the Abaqus finite element analysis code as well.