Ibarra Medina Krawinkler model - eesd-epfl/OpenSees GitHub Wiki
Any uniaxial model can be used in combination with the macroelement, if the coupling between axial load and shear force capacity is disregarded, through the flag "fiberSectionShearModel1d". Among existing uniaxial models, the Ibarra–Medina–Krawinkler model can be used to simulate all the main features of the complex hysteretic shear response of a masonry wall in shear.
A complete description of the model, developed for simulating moment-rotation relationships in steel and concrete members modelled through concentrated plasticity approaches, is given in Ibarra et al. (2005). Further detail are provided in the OpenSees documentation and the references reported there. A useful video tutorial by prof. D. Lignos is also provided.
The "peak-oriented" version of the model can be used, or alternatively a second one capturing also the pinching response, if this aspect is relevant. The hysteretic response is defined by 23 parameters, many of which would need extensive calibration based on experimental data—particularly the parameters defining the cyclic loading strength/stiffness degradation.
However, if cyclic degradation phenomena are not accounted for, the whole response depends solely on the backbone curve (which therefore must represent the cyclic response envelope), that can be defined based on few parameters directly derived from code provisions, literature, or reasonable assumptions. The following code presents a simple calibration a the Ibarra–Medina–Krawinkler model for masonry elements, assuming already that the response is symmetric (for the generic definition of the model refer to its documentation).
uniaxialMaterial ModIMKPeakOriented $matTag $G $as $as $Vy -$Vy \
$Lambda_S $Lambda_C $Lambda_A $Lambda_K \
$c_S $c_C $c_A $c_K \
$theta_p $theta_p $theta_pc $theta_pc \
$Res $Res $theta_u $theta_u $D $D
Where:
| matTag | tag of the material model |
| G | elastic shear modulus |
| Vy, as | shear force at "yielding" and hardening ratio after yielding (i.e. the ratio between the tangent stiffness after and before the yielding point) |
| Lambda_S, Lambda_C, Lambda_A, Lambda_K | Cyclic deterioration parameters corresponding, respectively, to deterioration of strength, postpeak strength, reloading stiffness, and unloading stiffness. The set (0, 1, 0, 0) can be used to disable cyclic deterioration (Lambda_C must not be 0). |
| c_S, c_C, c_A, c_K | Rate of strength deterioration for the 4 modes. Use the set (1, 1000, 1, 1) if the effect of postpeak strength deterioration must be hidden; use 1 instead for all if the effect is modelled. |
| theta_p | Displacement at peak force, minus the yielding displacement |
| theta_pc | Displacement at "zero" postpeak capacity, minus the displacement at peak force |
| Res | Residual strength ratio (reasonably 10-30%, or more for spandrel elements) |
| D | Asymmetric deterioration parameter, use 1 |
If the backbone is defined in terms of maximum force Vmax, force at cracking Vy (which can be assumed equal, if no indication is available, to Vmax), and drifts at peak force δmax and drift at a force drop ξ, δu, with ξ usually assumed equal to 20%. These parameters are defined as (for a height h of the element):
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The input file for obtaining these figures can be downloaded here. The definition of all parameters of the shear model is given in the input file as a function of the parameters defining the standard shear model of the macroelement.