On the predictive capability and stability of rubber material models

Abstract

Due to the high non-linearity and incompressibility constraint of rubber materials, the predictive capability and stability of rubber material models require specific attention for practical engineering analysis. In this thesis, the predictive capability of various rubber material models, namely the Mooney-Rivlin model, Arruda-Boyce model, Ogden model and the newly proposed Sussman-Bathe model, is investigated theoretically with continuum mechanics methods and tested numerically in various deformation situations using the finite element analysis software ADINA. In addition, a recently made available stability criterion of rubber material models is re-derived and verified through numerical experiments for the above four models with ADINA. Thereafter, the predictive capability and stability of material models are studied jointly for non-homogenous deformations. The Mooney-Rivlin model, Arruda-Boyce model, Ogden model have difficulties in describing the uniaxial compression data while the Sussman-Bathe model can fit both compression and extension data well. Thus, the Sussman-Bathe model has the best predictive capability for pure shear deformations. Furthermore, with respect to more complex non-homogenous deformations, a conclusion is drawn that all three major deformations, namely uniaxial deformation, biaxial deformation and pure shear deformation, must satisfy the stability criterion to obtain physically correct non-homogenous simulation results.