# KikuchiAikenLRB Material

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This command is used to construct a uniaxial KikuchiAikenLRB material object. This material model produces nonlinear hysteretic curves of lead-rubber bearings.

 uniaxialMaterial KikuchiAikenLRB \$matTag \$type \$ar \$hr \$gr \$ap \$tp \$alph \$beta <-T \$temp> <-coKQ \$rk \$rq> <-coMSS \$rs \$rf>

 \$matTag integer tag identifying material \$type rubber type (see note 1) \$ar area of rubber [unit: m^2] \$hr total thickness of rubber [unit: m] \$gr shear modulus of rubber [unit: N/m^2] \$ap area of lead plug [unit: m^2] \$tp yield stress of lead plug [unit: N/m^2] \$alph shear modulus of lead plug [unit: N/m^2] \$beta ratio of initial stiffness to yielding stiffness \$temp temperature [unit: °C] \$rk \$rq reduction rate for yielding stiffness (\$rk) and force at zero displacement (\$rq) \$rs \$rf reduction rate for stiffness (\$rs) and force (\$rf) (see note 3)

NOTES:

1) Following rubber types for \$type are available:

 1 lead-rubber bearing, up to 400% shear strain [Kikuchi et al., 2010 & 2012]

2) This material uses SI unit in calculation formula. Input arguments must be converted into [m], [m^2], [N/m^2].

3) \$rs and \$rf are available if this material is applied to multipleShearSpring (MSS) element. Recommended values are \$rs=1/sum(i=0,n-1){ sin(pi*i/n)^2} and \$rf=1/sum(i=0,n-1){sin(pi*i/n)}, where n is the number of springs in the MSS. For example, when n=8, \$rs=0.2500 and \$rf=0.1989.

EXAMPLE:

REFERENCES:

M. Kikuchi, T. Nakamura, I. D. Aiken, "Three-dimensional analysis for square seismic isolation bearings under large shear deformations and high axial loads", Earthquake Engineering and Structural Dynamics, Vol. 39, 1513-1531, 2010.

M. Kikuchi , I. D. Aiken, A. Kasalanati , "Simulation analysis for the ultimate behavior of full-scale lead-rubber seismic isolation bearings", 15th World Conference on Earthquake Engineering, No. 1688, 2012.

Code Developed by: mkiku