Technical Brief

Failure of Rubber Bearings Under Combined Shear and Compression

[+] Author and Article Information
P. Mythravaruni

Faculty of Civil and Environmental Engineering,
Haifa 3200003, Israel
e-mail: varuni.mythra@gmail.com

K. Y. Volokh

Faculty of Civil and Environmental Engineering,
Haifa 3200003, Israel
e-mail: cvolokh@technion.ac.il

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 8, 2018; final manuscript received April 17, 2018; published online May 15, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(7), 074503 (May 15, 2018) (4 pages) Paper No: JAM-18-1136; doi: 10.1115/1.4040018 History: Received March 08, 2018; Revised April 17, 2018

Rubber bearings, used for seismic isolation of structures, undergo large shear deformations during earthquakes as a result of the horizontal motion of the ground. However, the bearings are also compressed by the weight of the structure and possible traffic on it. Hence, failure analysis of rubber bearings should combine compression and shear. Such combination is considered in the present communication. In order to analyze failure, the strain energy density is enhanced with a limiter, which describes rubber damage. The inception of material instability and the onset of damage are marked by the violation of the condition of strong ellipticity, which is studied in the present work. Results of the studies suggest that horizontal cracks should appear because of the dominant shear deformation in accordance with the experimental observations. It is remarkable that compression delays failure in terms of the critical stretches.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Gent, A. N. , 2001, Engineering With Rubber, 2nd ed., Hanser, Munich, Germany. [PubMed] [PubMed]
Kurashige, M. , 1981, “ Instability of a Transversely Isotropic Elastic Slab Subjected to Axial Loads,” ASME J. Appl. Mech., 48(2), pp. 351–356. [CrossRef]
Triantafyllidis, N. , and Abeyaratne, R. , 1983, “ Instability of a Finitely Deformed Fiber-Reinforced Elastic Material,” ASME J. Appl. Mech., 50(1), pp. 149–156. [CrossRef]
Danescu, A. , 1991, “ Bifurcation in the Traction Problem for a Transversely Isotropic Material,” Math. Proc. Camb. Philos. Soc., 110(2), pp. 385–394. [CrossRef]
Merodio, J. , and Ogden, R. W. , 2002, “ Material Instabilities in Fiber-Reinforced Nonlinearly Elastic Solids Under Plane Deformation,” Arc. Mech., 54(5–6), pp. 525–552. http://am.ippt.pan.pl/am/article/view/v54p525
Dorfmann, L. , and Ogden, R. W. , eds., 2015, Nonlinear Mechanics of Soft Fibrous Materials, Springer, Wien, Austria.
Simo, J. C. , 1987, “ On a Fully Three-Dimensional Finite Strain Viscoelastic Damage Model: Formulation and Computational Aspects,” Comp. Meth. Appl. Mech. Eng., 60(2), pp. 153–173. [CrossRef]
Govindjee, S. , and Simo, J. C. , 1991, “ A Micro-Mechanically Based Continuum Damage Model of Carbon Black-Filled Rubbers Incorporating the Mullins Effect,” J. Mech. Phys. Solids, 39(1), pp. 87–112. [CrossRef]
Johnson, M. A. , and Beatty, M. F. , 1993, “ A Constitutive Equation for the Mullins Effect in Stress Controlled in Uniaxial Extension Experiments,” Cont. Mech. Therm., 5(4), pp. 301–318. [CrossRef]
Miehe, C. , 1995, “ Discontinuous and Continuous Damage Evolution in Ogden-Type Large-Strain Elastic Materials,” Eur. J. Mech. A, 14(5), pp. 697–720.
De Souza Neto, E. A. , Peric, D. , and Owen, D. R. J. , 1998, “ Continuum Modeling and Numerical Simulation of Material Damage at Finite Strains,” Arch. Comp. Meth. Eng., 5(4), pp. 311–384. [CrossRef]
Ogden, R. W. , and Roxburgh, D. G. , 1999, “ A Pseudo-Elastic Model for the Mullins Effect in Filled Rubber,” Proc. Roy. Soc. London Ser. A, 455(1988), pp. 2861–2877. [CrossRef]
Menzel, A. , and Steinmann, P. , 2001, “ A Theoretical and Computational Framework for Anisotropic Continuum Damage Mechanics at Large Strains,” Int. J. Solids Struct., 38(52), pp. 9505–9523. [CrossRef]
Guo, Z. , and Sluys, L. , 2006, “ Computational Modeling of the Stress-Softening Phenomenon of Rubber Like Materilas Under Cyclic Loading,” Eur. J. Mech. A, 25(6), pp. 877–896. [CrossRef]
De Tommasi, D. , Puglisi, G. , and Saccomandi, G. , 2008, “ Localized Vs Diffuse Damage in Amorphous Materials,” Phys. Rev. Lett., 100(8), p. 085502. [CrossRef] [PubMed]
Dal, H. , and Kaliske, M. , 2009, “ A Micro-Continuum-Mechanical Material Model for Failure of Rubberlike Materials: Application to Ageing-Induced Fracturing,” J. Mech. Phys. Solids, 57(8), pp. 1340–1356. [CrossRef]
Volokh, K. Y. , 2013, “ Review of the Energy Limiters Approach to Modeling Failure of Rubber,” Rubber. Chem. Technol., 86(3), pp. 470–487. [CrossRef]
Volokh, K. Y. , 2017, “ Loss of Ellipticity in Elasticity With Energy Limiters,” Eur. J. Mech. A, 63, pp. 36–42. [CrossRef]
Rajagopal, K. R. , and Wineman, A. S. , 1987, “ New Universal Relations for Nonlinear Isotropic Elastic Materials,” J. Elast., 17(1), pp. 75–83. [CrossRef]
Mihai, L. A. , Budday, S. , Holzapfel, G. A. , Kuhl, E. , and Goriely, A. , 2017, “ A Family of Hyperelastic Models for Human Brain Tissue,” J. Mech. Phys. Solids, 106, pp. 60–79. [CrossRef]
Volokh, K. Y. , 2016, Mechanics of Soft Materials, Springer, Singapore. [CrossRef]
Volokh, K. Y. , 2014, “ On Irreversibility and Dissipation in Hyperelasticity With Softening,” ASME J. Appl. Mech., 81(7), p. 074501. [CrossRef]
Takahashi, Y. , 2012, “ Damage of Rubber Bearings and Dambers of Bridges in 2011 Great East Japan Earthquake,” International Symposium on Engineering Lessons Learned From the 2011 Great East Japan Earthquake, Tokyo, Japan, Mar. 1–4, pp. 1333–1342. http://www.jaee.gr.jp/event/seminar2012/eqsympo/pdf/papers/36.pdf


Grahic Jump Location
Fig. 2

Convergence of f2(γ) to zero for various amounts of compression

Grahic Jump Location
Fig. 1

Cauchy stress versus stretch for uniaxial tension. Dashed line is for the model without failure and solid line is for the model with failure.

Grahic Jump Location
Fig. 3

Shear versus the orientation of the superposed acoustic wave. Curves f1=0 (β=1) and f2=0 are presented for various values of compression stretch. The minimum shear indicates the inception of instability through the loss of strong ellipticity.

Grahic Jump Location
Fig. 4

Shear stress versus amount of shear for various values of compression. Limit points designate the material strength and the elliptical markers on the curves indicate the loss of the strong ellipticity.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In