Manish Kumar

IITB Logo Manish Kumar
Assistant Professor

Department of Civil Engineering
Indian Institute of Technology Bombay, Mumbai

 

 

Elastomeric Bearings in Tension

Behavior of elastomeric bearings in tension can be categorized in two types

1.       Pure Tension

2.       Tension with shear(lateral displacement)

Case of pure tension has been observed to be more detrimental than tension combined with shear. Experiments have shown that elastomeric bearings in shear tension can sustain higher tensile strain without rupture than in pure tension (Iwabe et al 2000). Tension hysteretic curve shows non-linear behavior as tensile strain increases. Different models have been proposed to capture the nonlinear characteristics of the tension hysteresis curve and considers coupling of vertical and horizontal motion (Ryan et al 2005). It was found that vertical stiffness decreases with increasing lateral deformation. Possibility of tension buckling in multilayer elastomeric bearings was explored by Kelly (2003). It was observed that many experiments in which isolators were given vertical tensile displacement along with the lateral movement, isolators did not fail although tensile strain was much higher than the strain at cavitation. It was claimed analytically that there is possibility of buckling in tension. Tension in buckling was found to be mirror image of compression buckling in terms of critical load and buckled shape. For all practical applications, tensile buckling load is not achievable as the force required for cavitation in rubber is much smaller than critical buckling load; however, it helps in understanding the behavior of isolator bearings subjected to tensile load with lateral displacement. It was explained that elastomer could sustain the tension load because rotation at the middle of the bearing transfers part of vertical tension to the shear in the rotated direction. High tensile strain capacity of elastomers in tension-shear loading can also be explained by the fact that vertical stiffness of bearings decreases with lateral displacement and isolators do not build the tension stresses that could be produced with pure tension loading for same tensile strain. Yang et al (2010) proposed two tensile stress-strain models for rubber isolators: 1) Double stiffness stress-strain model, 2) Origin tensile stiffness stress-strain model to calculate the tensile stiffness and tensile deformations in pure tension and tension-shear loading. Material and geometrical nonlinearities were taken into accounts in these models. Experimental results showed good agreement with proposed analytical expressions for elastomeric bearings.

Some points that can be explored further while defining the stress strain curve of elastomeric bearings in tension are:

1)      Coupling of horizontal and vertical motion: Previous research has shown effects of lateral displacement on vertical motion. It needs to be discussed if element, that is to be defined in software, should capture this or if it can be ignored considering it will yield conservative results from design point of view.

2)      Hysteric behavior: Experiments show some hysteric behavior of elastomeric bearings in tension, however energy dissipated in tension would be very less compared to compression. Inclusion of tension hysteresis needs to be discussed.

3)      Loading history: Subsequent loading following the cavitation of rubber and how to capture loading history in the software, needs to be discussed. 

Vertical loading behavior of elastomeric bearings can be divided in compression and tension loading.

Compression

Behavior of elastomeric bearings in compression has been extensively studied and well established. Compression behavior that has been considered here is based on spring column model (Koh and Kelly, 1987; Kelly J.,1993; Constantinou et al, 2007). This model takes into consideration the effects of axial loads and contribution from shear deformation of bearings. For the model, that is to be developed here, hysteretic behavior in compression has been neglected, which is well supported by the experiments (Iwabe et al, 2000)

Tension

Tensile loading in elastomeric is characterized by appearance of cracks at a well-defined and comparatively small load. This phenomenon, known as cavitation of rubber, can be explained as elastic instability of preexisting holes in rubber in which unbounded elastic expansion of cavities leads to large deformations at a critical value of tension known as cavitation force. No fracture energy involves in this process and conversion of potential energy to strain energy takes place(Mark et al, 2005). It has been shown that large tensile strains are followed by rupture in rubber layers (Iwabe et al, 2000). All design codes limit the maximum tension force in elastomeric bearings to the cavitation force. However, some recent experiments have shown that elastomeric bearings can cavitate and sustain tensile strains as much as 100 percent(Iwabe et al, 2000). These experiments also showed the experimental behavior of tensile loading in bearings after cavitation. How to model the behavior of elastomeric bearings after cavitation is still not very clear. One area of interest might be the role of actual area of rubber (total area decreased by cavities) at the initiation of cavitation in affecting different properties of rubber. Literature on rubber so far, does not mention the concept of true area in reference to cavitation.

Elastomeric bearings when tested for first time, shows higher value of characteristic strength and stiffness. If bearings are loaded repeatedly in tension, load-deformation curve shows stress-softening behavior (Mullin’s effect), which is characterized by lower characteristic strength and stiffness. This softening behavior is shown for deformations lower than maximum deformation applied before and once it exceeds the maximum past deformation, it traces back the new path while unloading. It has been claimed that properties of rubber tested for the first time, known as virgin properties, can be recovered significantly with high temperature or solvent pressure applied for a long time (Mullins L, 1948; Harwood and Payne, 1966; Rigbi Z,1980; Laraba-Abbes et al, 2003; Diani et al, 2009). However, for all practical loading conditions during earthquakes, heating in elastomeric bearings can be neglected and repeated loading of elastomeric bearings can be characterized by Mullin’s effect. Although, many efforts have been made for the physical interpretation of this effect using molecular theory, there is still no general agreement on the origin of this effect at microscopic level. Many theories have been proposed to describe this phenomenon, such as bond rupture, molecules slipping, filler rupture, disentanglement, double layer model (Diani et al, 2009). Considering complexity involved in modeling the stress-strain behavior of rubber, most of the models that have been suggested to capture the stress softening behavior, are phenomenological in nature. These models capture the Mullins effect using the energy density and damage index approach suggested by Simo(1987) and Kachanov(1958).

 

Proposed Models

A vertical stiffness model(spine model) has been proposed here to simulate vertical load deformation behavior of elastomeric bearings. Basic assumptions for both models are as follows:

1.       Considering the variability involved with measurement of shear modulus (G) of rubber with deformation, it has been taken as the nominal value at large shear deformations.

2.       No hysteresis in compression has been considered for both models.

3.       Possibility of tension buckling has not been considered as cavitation force is much less than the buckling load.

4.       Cavitation force has been fixed at 3GA.

5.       Initial modulus before cavitation(tension) or buckling(compression) is given by compression modulus Ec and it has been assumed that rubber loses confinement effect after cavitation and modulus after cavitation is given by elastic modulus E=3G

Spine Model

Spine model approximate the vertical load deformation curve as elastic and neglects any hysteresis in compression or tension.

Elastomeric Bearings vertical loading curve

Figure 1.  Elastic Spine Model

 

References

1.       Constantinou, M.C., Whittaker, A.S., Kalpakidis, Y., Fenz, D.M. and Warn, G.P. (2007a), “Performance of Seismic Isolation Hardware under Service and Seismic Loading,” Report No. MCEER-07-0012, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.

2.       Harwood J.A.C., Payne A.R.. Stress softening in natural rubber vulcanizates. IV. Unfilled vulcanizates. J Appl Polymer Sci 1966;10:1203–11.

3.       Iwabe N., Takayama M., Kani N., Wada A., “Experimental study on the effect of tension for rubber bearings”, Proceedings, 12th World Conference on Earthquake Engineering (2000).

4.       Julie D, Bruno F, Pierre G. A review on the Mullins effect. European Polymer Journal 45 (2009) 601–612

5.       Kachanov L.M., Time of the rupture process under creep conditions. Izvestiya Akad Nauk SSR Otd Tekh Nauk 1958;58:26–31.

6.       Kelly, J.M., Earthquake-Resistant Design with Rubber, Springer-Verlag, London(1993).

7.       Koh, C.G. and Kelly, J.M. (1987), “Effects of Axial Load on Elastomeric Bearings”, Report No. UCB/EERC-86/12, Earthquake Engineering Research Center, University of California, Berkeley.

8.       Laraba-Abbes F., Ienny P., Piques R., A new ‘Taylor-made’ methodology for the mechanical behaviour analysis of rubber-like materials: II. Application to the hyperelastic behaviour characterization of a carbon-black filled natural rubber vulcanizate. Polymer 2003;44:821–40.

9.       Mark, J. E., Erman, B., Elrich, F. R., Science and Technology of Rubber, ELSEVIER Academic Press(2005)

10.   Rigbi Z., Reinforcement of rubber by carbon black. Adv Polym Sci 1980;36:21–68.

11.   Yamamoto S, Kikuchi M, Ueda M , Aiken I D. A mechanical model for elastomeric seismic isolation bearings including the influence of axial load. Earthquake Engng Struct. Dyn. 2009; 38:157–180

12.   Simo JC. On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects. Comput Methods Appl Mech Engrg 1987;60:153–73.