Benchmark Problems of Hyper-Elasticity Analysis in Evaluation of FEM

The paper proposes benchmark problems on exact solutions of hyper-elastic analysis, which can be used to evaluate analysis capabilities of rubber-like materials provided by a finite element program or other approximate solution methods. Special attention was concentrated on analysis and derivation of the exact solutions for the thick-walled rubber cylinders under internal pressure and axial extension, the thick-walled rubber balloons under internal pressure and the rubber cylinders under torsion or tension-torsion. Deformation and stress analysis on the above three cases were conducted to provide equations and methods for data processing. Exact standard solutions of the problems combined with the strain energy function of generalized high-order polynomials are given. Numerical examples and evaluation results of two commercial packages that are in common use (ABAQUS and ANSYS) are presented. Good agreements are found in the comparisons between the present exact standard solutions and the simulation results.