**Author details**

A. R. Bhuiyan

*Department of Civil Engineering, Chittagong University of Engineering and Technology, Chittagong, Bangladesh* 

#### Y.Okui

332 Earthquake Engineering

**5. Summary** 

the viscosity induced overstress ( *oe*

levels was clearly demonstrated in the test results.

confirmed this condition.

This chapter discusses an experimental scheme to characterize the mechanical behavior of three types of bearings and subsequently demonstrates the modeling approaches of the stress responses identified from the experiments. The mechanical tests conducted under horizontal shear displacement along with a constant vertical compressive load demonstrated the existence of Mullins' softening effect in all the bearing specimens. However, with the passage of time a recovery of the softening effect was observed. A preloading sequence had been applied before actual tests were carried out to remove the Mullins' effect from other inelastic phenomena. Cyclic shear tests carried out at different strain rates gave an image of the significant strain-rate dependent hysteresis property. The strain-rate dependent property in the loading paths was appeared to be reasonably stronger than in the unloading paths. The simple and multi-step relaxation tests at different strain levels were carried out to investigate the viscosity property in the loading and unloading paths of the bearings. Moreover, in order to identify the equilibrium hysteresis, the multistep relaxation tests were carried out with different maximum strain levels. The dependence of the equilibrium hysteresis on the experienced maximum strain and the current strain

The mechanical tests indicated the presence of strain-rate dependent hysteresis with high strain hardening features at high strain levels in the HDRB. In the other bearing specimens, strain-rate dependent phenomenon was seen less prominent; however, the strain hardening features at high strain levels in the RB showed more significant than any other bearings. In this context, an elasto-plastic model was proposed for describing strain hardening features along with equilibrium hysteresis of the RB, LRB and HDRB. The performance of the proposed model in representing the strain rate-independent responses of the bearings was evaluated. In order to model the strain-rate dependent hysteresis observed in the experiments, an evolution equation based on viscosity induced overstress was proposed for the bearings. In doing so, the Maxwell's dashpot-spring model was employed in which a nonlinear viscosity law is incorporated. The nonlinear viscosity law of the bearings was deduced from the experimental results of MSR and SR loading tests. The performance of the proposed evolution equation in representing the rate-dependent responses of the bearings was evaluated using the relaxation loading tests. On the basis of the physical interpretation of the strain-rate dependent hysteresis along with other inelastic properties observed in the bearings, a chronological method comprising of experimentation and computation was proposed to identify the constitutive parameters of the model. The strain-rate independent equilibrium response of the bearing was identified using the multi-step relaxation tests. After identifying this response, the elasto-plastic model (the top two branches of the rheology model) was used to find out the parameters for the elasto-plastic response. A series

) are non-negative. The parameters of Table 3 have

*Department of Civil and Environmental Engineering, Saitama University, Saitama, Japan* 
