Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible visco-hyperelastic a
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Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible visco-hyperelastic approach H. Khajehsaeid • M. Baghani • R. Naghdabadi
Received: 25 June 2013 / Accepted: 29 September 2013 / Published online: 16 October 2013 Ó Springer Science+Business Media Dordrecht 2013
Abstract 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,
H. Khajehsaeid R. Naghdabadi (&) Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran e-mail: [email protected] M. Baghani School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran R. Naghdabadi Institute for Nano-Science and Technology, Sharif University of Technology, Tehran, Iran
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. Keywords Visco-hyperelasticity Numerical analysis Elastomeric bushing Compressibility
1 Introduction Elastomers (rubber-like materials) as a great category of polymers have amorphous structure and are consisted of cross-linked long molecular chains in three-dimensional configurations. Highly non-linear, time dependent and hysteretic behavior is of their characteristics. Their behavior is dominantly governed by changes in the molecular network entropy where the chains reorient in response to the applied macroscopic deformations (Brinson and Brinson 2008; Treloar 1973). Thorough investigations have been made to study and model the elastomers quasi-static (Bechir et al. 2006; Gent 1996; Yeoh and Fleming 1997) and time dependent (Aniskevich et al. 2010; Diani et al. 2006; Drozdov and Kalamkarov 1996; Holzapfel 1996; Lion 1997; Reese 2003; Shim et al. 2004) behavior. These materials have wide and ever increasing applications
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in several industries such as automotive industry where rubbers are used as mechanical
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