Modified Ibarra-Medina-Krawinkler Deterioration Model with Peak-Oriented Hysteretic Response (ModIMKPeakOriented Material)

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This command is used to construct a ModIMKPeakOriented material. This material simulates the modified Ibarra-Medina-Krawinkler deterioration model with peak-oriented hysteretic response. Note that the hysteretic response of this material has been calibrated with respect to 200 experimental data of RC beams in order to estimate the deterioration parameters of the model. This information was developed by Lignos and Krawinkler (2012). NOTE: before you use this material make sure that you have downloaded the latest OpenSees version.. A youtube video presents a summary of this model including the way to be used within openSees (http://youtu.be/YHBHQ-xuybE).

uniaxialMaterial ModIMKPeakOriented $matTag $K0 $as_Plus $as_Neg $My_Plus $My_Neg $Lamda_S $Lamda_C $Lamda_A $Lamda_K $c_S $c_C $c_A $c_K $theta_p_Plus $theta_p_Neg $theta_pc_Plus $theta_pc_Neg $Res_Pos $Res_Neg $theta_u_Plus $theta_u_Neg $D_Plus $D_Neg
$matTag integer tag identifying material
$K0 elastic stiffness
$as_Plus strain hardening ratio for positive loading direction
$as_Neg strain hardening ratio for negative loading direction
$My_Plus effective yield strength for positive loading direction
$My_Neg effective yield strength for negative loading direction (negative value)
$Lamda_S Cyclic deterioration parameter for strength deterioration [E_t=Lambda*M_y, see Lignos and Krawinkler (2011); set Lambda = 0 to disable this mode of deterioration]
$Lamda_C Cyclic deterioration parameter for post-capping strength deterioration [E_t=Lambda*M_y, see Lignos and Krawinkler (2011); set Lambda = 0 to disable this mode of deterioration]
$Lamda_A Cyclic deterioration parameter for acceleration reloading stiffness deterioration [E_t=Lambda*M_y, see Lignos and Krawinkler (2011); set Lambda = 0 to disable this mode of deterioration]
$Lamda_K Cyclic deterioration parameter for unloading stiffness deterioration [E_t=Lambda*M_y, see Lignos and Krawinkler (2011); set Lambda = 0 to disable this mode of deterioration]
$c_S rate of strength deterioration. The default value is 1.0.
$c_C rate of post-capping strength deterioration. The default value is 1.0.
$c_A rate of accelerated reloading deterioration. The default value is 1.0.
$c_K rate of unloading stiffness deterioration. The default value is 1.0.
$theta_p_Plus pre-capping rotation for positive loading direction (often noted as plastic rotation capacity)
$theta_p_Neg pre-capping rotation for negative loading direction (often noted as plastic rotation capacity) (must be defined as a positive value)
$theta_pc_Plus post-capping rotation for positive loading direction
$theta_pc_Neg post-capping rotation for negative loading direction (must be defined as a positive value)
$Res_Pos residual strength ratio for positive loading direction
$Res_Neg residual strength ratio for negative loading direction (must be defined as a positive value)
$theta_u_Plus ultimate rotation capacity for positive loading direction
$theta_u_Neg ultimate rotation capacity for negative loading direction (must be defined as a positive value)
$D_Plus rate of cyclic deterioration in the positive loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0.
$D_Neg rate of cyclic deterioration in the negative loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0.


Image from: Lignos and Krawinkler (2012)

The deterioration model parameters can be calibrated based on actual experimental data of RC beams in terms of load - displacement or moment - rotation. Examples of such calibrations can be found in Lignos (2008) and Lignos and Krawinkler (2012).

References:

[1] Lignos, D.G., Krawinkler, H. (2012). “Development and Utilization of Structural Component Databases for Performance-Based Earthquake Engineering", Journal of Structural Engineering, ASCE, doi: 10.1061/(ASCE)ST.1943-541X.0000646.
[2] Lignos, D.G., and Krawinkler, H. (2011). “Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading”, Journal of Structural Engineering, ASCE, Vol. 137 (11), 1291-1302.
[3] Lignos, D.G. and Krawinkler, H. (2012). “Sidesway collapse of deteriorating structural systems under seismic excitations,” Rep.No.TB 177, The John A. Blume Earthquake Engineering Research Center, Stanford University, Stanford, CA. [electronic version: https://blume.stanford.edu/tech_reports]
[4] Lignos, D.G. (2008). “Sidesway collapse of deteriorating structural systems under seismic excitations,” Ph.D. Dissertation, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA.
[5] Ibarra L.F., and Krawinkler, H. (2005). “Global collapse of frame structures under seismic excitations”, Rep. No. TB 152, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA. [electronic version: https://blume.stanford.edu/tech_reports]
[6] Ibarra L.F., Medina R. A., and Krawinkler H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration”, Earthquake Engineering and Structural Dynamics, 34(12), 1489-1511.

Code Developed by : by Dr. Dimitrios G. Lignos, McGill University

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