Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible visco-hyperelastic approach

Elastomers have wide and ever increasing applications in several industries. In this work a compressible visco-hyperelastic approach is employed to investigate the behavior of elastomeric materials. The time-discrete form of the material model is developed to be used in numerical simulations. This formulation provides a recursive relation to update the stress in any time step regarding the deformation history. By means of analytical solutions derived for pure torsion of a solid circular cylinder, the numerical implementation is validated and then, the response of an elastomeric bushing is investigated in torsional, axial and combined deformations. These bushings are used in suspension systems to reduce amplitude of vibrations as well as shocks. It is shown that, the numerical model well simulates the non-linear time dependent response of the bushing in different deformation rates. Also, a multi-step relaxation test is simulated to identify the hysteretic behavior. Finally, fully relaxed response of the bushing for torsional and combined torsional–axial deformations is predicted and compared with those of experiment as well as three other constitutive models. The comparisons reveal that, the proposed approach well predicts the coupling effect of axial displacement on torsional moment where it is not the case for other compared models.