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:

KikuchiAikenLRB_sample.tcl

KikuchiAikenLRB ForceStrain.png


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