Axisymmetric deformations of circular rings made of linear and Neo-Hookean materials under internal and external pressure: A benchmark for finite element codes

• Linear, incompressible and compressible Neo-Hookean materials are used.
• Analytical benchmark solution to test commercial programs.
• Two commercial FE programs give incorrect results for large strains and linear elastic material.

The axisymmetric deformations of thick circular rings are investigated. Four materials are explored: linear material, incompressible Neo-Hookean material and Ogden's and Bower's forms of compressible Neo-Hookean material. Radial distributed forces and a displacement-dependent pressure are the external loads. This problem is relatively simple and allows analytical, or semi-analytical, solution; therefore it has been chosen as a benchmark to test commercial finite element software for various material laws at large strains. The solutions obtained with commercial finite element software are almost identical to the present semi-analytical ones, except for the linear material, for which commercial finite element programs give incorrect results.