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

Ivan Breslavsky (1) , Marco Amabili (1) , Mathias Legrand (2, 1) , Farbod Alijani (1)

1 Department of Mechanical Engineering [Montréal]
2 Structural Dynamics and Vibration Laboratory [Montréal]

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.

Highlights:

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

Mots clés: Circular rings; Pressure; Hyperelasticity; Non-linear deformations

Domaines: Sciences de l'ingénieur [physics]

Ivan Breslavsky, Marco Amabili, Mathias Legrand, Farbod Alijani. Axisymmetric deformations of circular rings made of linear and Neo-Hookean materials under internal and external pressure: A benchmark for finite element codes. International Journal of Non-Linear Mechanics, 2016, 84, pp.39-45. ⟨10.1016/j.ijnonlinmec.2016.04.011⟩. ⟨hal-01339533⟩