.. include:: sub.txt

==================================================================================================================
 Modified Ibarra-Medina-Krawinkler Deterioration Model with Pinched Hysteretic Response (ModIMKPinching Material)
==================================================================================================================

.. function:: uniaxialMaterial('ModIMKPinching', matTag, K0, as_Plus, as_Neg, My_Plus, My_Neg, FprPos, FprNeg, A_pinch, 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)
   :noindex:

   This command is used to construct a ModIMKPinching material. This material simulates the modified Ibarra-Medina-Krawinkler deterioration model with pinching hysteretic response. 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 `youtube link <http://youtu.be/YHBHQ-xuybE>`_.


   ===================================   ===========================================================================
   ``matTag`` |int|                      integer tag identifying material
   ``K0`` |float|                        elastic stiffness
   ``as_Plus`` |float|                   strain hardening ratio for positive loading direction
   ``as_Neg`` |float|                    strain hardening ratio for negative loading direction
   ``My_Plus`` |float|                   effective yield strength for positive loading direction
   ``My_Neg`` |float|                    effective yield strength for negative loading direction (Must be defined as a negative value)
   ``FprPos`` |float|                    Ratio of the force at which reloading begins to force corresponding to the maximum historic deformation demand (positive loading direction)
   ``FprNeg`` |float|                    Ratio of the force at which reloading begins to force corresponding to the absolute maximum historic deformation demand (negative loading direction)
   ``A_pinch`` |float|                   Ratio of reloading stiffness
   ``Lamda_S`` |float|                   Cyclic deterioration parameter for strength deterioration [E_t=Lamda_S*M_y, see Lignos and Krawinkler (2011); set Lamda_S = 0 to disable this mode of deterioration]
   ``Lamda_C`` |float|                   Cyclic deterioration parameter for post-capping strength deterioration [E_t=Lamda_C*M_y, see Lignos and Krawinkler (2011); set Lamda_C = 0 to disable this mode of deterioration]
   ``Lamda_A`` |float|                   Cyclic deterioration parameter for accelerated reloading stiffness deterioration [E_t=Lamda_A*M_y, see Lignos and Krawinkler (2011); set Lamda_A = 0 to disable this mode of deterioration]
   ``Lamda_K`` |float|                   Cyclic deterioration parameter for unloading stiffness deterioration [E_t=Lamda_K*M_y, see Lignos and Krawinkler (2011); set Lamda_K = 0 to disable this mode of deterioration]
   ``c_S`` |float|                       rate of strength deterioration. The default value is 1.0.
   ``c_C`` |float|                       rate of post-capping strength deterioration. The default value is 1.0.
   ``c_A`` |float|                       rate of accelerated reloading deterioration. The default value is 1.0.
   ``c_K`` |float|                       rate of unloading stiffness deterioration. The default value is 1.0.
   ``theta_p_Plus`` |float|              pre-capping rotation for positive loading direction (often noted as plastic rotation capacity)
   ``theta_p_Neg`` |float|               pre-capping rotation for negative loading direction (often noted as plastic rotation capacity) (must be defined as a positive value)
   ``theta_pc_Plus`` |float|             post-capping rotation for positive loading direction
   ``theta_pc_Neg`` |float|              post-capping rotation for negative loading direction (must be defined as a positive value)
   ``Res_Pos`` |float|                   residual strength ratio for positive loading direction
   ``Res_Neg`` |float|                   residual strength ratio for negative loading direction (must be defined as a positive value)
   ``theta_u_Plus`` |float|              ultimate rotation capacity for positive loading direction
   ``theta_u_Neg`` |float|               ultimate rotation capacity for negative loading direction (must be defined as a positive value)
   ``D_Plus`` |float|                    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`` |float|                     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.
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.. seealso::


   `Notes <http://opensees.berkeley.edu/wiki/index.php/Modified_Ibarra-Medina-Krawinkler_Deterioration_Model_with_Pinched_Hysteretic_Response_(ModIMKPinching_Material)>`_