Inflation, extension and torsion analysis of compressible functionally graded hyperelastic tubes

Abstract

Problems of inflation, extension and torsion of hyperelastic rods and tubes are of great interest for modelling and characterizing rubber-like materials and soft biological tissues. For incompressible and compressible hyperelastic tubes, analytical solutions for the problem of inflation, extension and torsion have not been proposed. In this research, the problem of inflation, extension and torsion of a functionally graded compressible hyperelastic tube is formulated as a one-dimensional problem and is solved using the finite difference method. First, the proposed method is verified against existing analytical and three-dimensional finite element method solutions. After that, by analyzing a number of problems over a wide range of variables, the interactions of inflation, extension and torsion are investigated.