The radial compaction of a hyperelastic tube as a benchmark in compressible finite elasticity

The stress solution to the radial compaction of a hyperelastic tube is developed analytically for both incompressible and slightly compressible material response. The solution is explicit for the incompressible behaviour and implicit for the compressible one. It is shown that proper combination of tube geometry and total compaction leads to stress results very sensitive to small variations of Poisson's ratio. This makes the problem a good benchmark for the performance of numerical methods in the area of compressible finite elasticity. As an example, the commercial finite element code ABAQUS is applied to a demanding tube configuration for Poisson's ratios in the range from 0.49 to 0.5.