3.1.5.19. IMKPinching Material

This command is used to construct a material with a pinched hysteretic response based on the modified Ibarra-Medina-Krawinkler deterioration model.

uniaxialMaterial IMKPinching $Mat_Tag $Ke $dp_pos $dpc_pos $du_pos $Fy_pos $FmaxFy_pos $FresFy_pos $dp_neg $dpc_neg $du_neg $Fy_neg $FmaxFy_neg $FresFy_neg $Lamda_S $Lamda_C $Lamda_A $Lamda_K $c_S $c_C $c_A $c_K $D_pos $D_neg $kappaF $kappaD

Argument

Type

Description

$matTag

integer

integer tag identifying material

$Ke

float

Elastic stiffness

$dp_pos

float

Pre-capping deformation in positive loading direction

$dpc_pos

float

Post-capping deformation in positive loading direction

$du_pos

float

Ultimate deformation in positive loading direction

$Fy_pos

float

Yield strength in positive loading direction

$FmaxFy_pos

float

Maximum-to-yield strength ratio in positive loading direction

$FresFy_pos

float

Residual-to-yield strength ratio in positive loading direction

$dp_neg

float

Pre-capping deformation in negative loading direction

$dpc_neg

float

Post-capping deformation in negative loading direction

$du_neg

float

Ultimate deformation in negative loading direction

$Fy_neg

float

Yield strength in negative loading direction

$FmaxFy_neg

float

Maximum-to-yield strength ratio in negative loading direction

$FresFy_neg

float

Residual-to-yield strength ratio in negative loading direction

$Lamda_S

float

Cyclic deterioration parameter for yield strength deterioration

$Lamda_C

float

Cyclic deterioration parameter for post-capping stiffness deterioration

$Lamda_A

float

Cyclic deterioration parameter for accelerated reloading stiffness deterioration

$Lamda_K

float

Cyclic deterioration parameter for unloading stiffness deterioration

$c_S

float

Rate of yield strength deterioration

$c_C

float

Rate of post-capping stiffness deterioration

$c_A

float

Rate of accelerated reloading stiffness deterioration

$c_K

float

Rate of unloading stiffness deterioration

$D_pos

float

rate of cyclic deterioration in the positive loading direction. This parameter is used to create asymmetric hysteretic behavior as in the case of a composite beam (0< D_pos <1). For symmetric hysteretic response use 1.0.

$D_neg

float

rate of cyclic deterioration in the negative loading direction. This parameter is used to create asymmetric hysteretic behavior as in the case of a composite beam (0< D_pos <1). For symmetric hysteretic response use 1.0.

$kappaF

float

Pinching parameter defining the break point with respect to the maximum force experienced in the direction of loading (0 <kappaF <1).

$kappaD

float

Pinching parameter defining the break point with respect to the maximum permanent deformation experienced in the direction of loading (0 <kappaD <1).

Note

All material model parameters (in both the positive and negative direction) shall be specified as positive values.

Lamda is used to compute the reference energy based on the following equation Ref_Energy = Lamda * Fy

IbarraEtAl2005

Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Engineering & Structural Dynamics, 34(12), 1489-1511, Doi: 10.1002/eqe.495.

../../../../_images/IMKPinching.jpg

Fig. 3.1.5.13 IMKPinching backbone curve

../../../../_images/IMKPinching_sample_responses_validations.jpg

Fig. 3.1.5.14 IMKPinching sample responses and validations

Example

The following is used to construct a IMKPeakOriented material with symmetric hysteretic response.

set Ke      10000.;
set dp      0.01;
set dpc     0.05;
set du      0.08;
set My      100.;
set Mc_My   1.10;
set Mres_My 0.10;
set lambda  0.50;
set c_S     1.00;
set c_C     1.00;
set c_K     1.00;
set c_A     1.00;
set D_pos   1.00;
set D_neg   1.00;

uniaxialMaterial IMKPeakOriented   1 $Ke $dp $dpc $du $My $Mc_My $Mres_My $dp $dpc $du $My $Mc_My $Mres_My $lambda $lambda $lambda $lambda $c_S $c_S $c_A $c_K $D_pos $D_neg $kappaF $kappaD;

For code inquires or bug reporting, please contact: - Kazuki Ichinohe, University of Tokyo, e-mail: z-ichinohe@g.ecc.u-tokyo.ac.jp - Ahmed Elkady, University of Southampton, e-mail: a.elkady@soton.ac.uk