UVCmultiaxial (Updated Voce-Chaboche)

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This command is used to construct an Updated Voce-Chaboche (UVC) material for general multiaxial stress states (e.g., for solid/brick elements). This material is a refined version of the classic nonlinear isotropic/kinematic hardening material model based on the Voce isotropic hardening law and the Chaboche kinematic hardening law. The UVC model contains an updated isotropic hardening law, with parameter constraints, to simulate the permanent decrease in yield stress with initial plastic loading associated with the discontinuous yielding phenomenon in mild steels.

Details regarding the model, its implementation, and calibration can be found in the references cited at the end. The plane-stress (e.g., for quad/plate/shell elements) and uniaxial (e.g., for beam elements) versions are also available. The plane-stress and uniaxial implementations have the exact same hardening rules as this general multiaxial model, and only differ in their purpose and numerical implementation.

Available in OpenSees version 3.1.0+.

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nDMaterial UVCmultiaxial $matTag $E $nu $fy $QInf $b $DInf $a $N $C1 $gamma1 <$C2 $gamma2 $C3 $gamma3 … $C8 $gamma8>

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$matTag	Integer tag identifying the material.
$E	Elastic modulus of the steel material.
$nu	Poisson's ratio for the steel material.
$fy	Initial yield stress of the steel material.
$QInf	Maximum increase in yield stress due to cyclic hardening (isotropic hardening).
$b	Saturation rate of QInf, b > 0.
$DInf	Decrease in the initial yield stress, to neglect the model updates set DInf = 0.
$a	Saturation rate of DInf, a > 0. If DInf == 0, then a is arbitrary (but still a > 0).
$N	Number of backstresses to define, N >= 1.
$C1	Kinematic hardening parameter associated with backstress component 1.
$gamma1	Saturation rate of kinematic hardening associated with backstress component 1.
<$C2 $gamma2 $C3 $gamma3 … $C8 $gamma8>	Additional backstress parameters, up to 8 may be specified. If C is specified, then the corresponding gamma must also be specified. Note that only the first N backstresses will be read by the parser.

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Examples, validation, and UVC model parameters

For the user, the only practical difference between the uniaxial and multiaxial/plane-stress implementations is the specification of Poisson's ratio in the list of input parameters.

Further information on the UVC model is centralized at the UVCuniaxial web page. On the UVCuniaxial page you will find examples validating the model, and UVC model parameters for common structural steels that are applicable for all stress states.

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References:

Please use Reference [1] when citing the UVC model.

[1] Hartloper, A. R., de Castro e Sousa A., and Lignos D.G. (2019). "Constitutive Modeling of Structural Steels: A Nonlinear Isotropic/Kinematic Hardening Material Model and its Calibration", https://doi.org/10.1061/(ASCE)ST.1943-541X.0002964.

[2] Hartloper, A. R., de Castro e Sousa A., and Lignos D.G. (2019). "Sensitivity of Simulated Steel Column Instabilities to Plasticity Model Assumptions". 12th Canadian Conference on Earthquake Engineering, Quebec City, QC, Canada. https://infoscience.epfl.ch/record/267788

[3] Hartloper, A. R., de Castro e Sousa A., and Lignos D.G. (2019). "A Nonlinear Isotropic/Kinematic Hardening Model for Materials with Discontinuous Yielding". Report No. 271062, Resilient Steel Structures Laboratory (RESSLab), EPFL, Lausanne, Switzerland. https://infoscience.epfl.ch/record/271062.

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Code developed, implemented, and maintained by: Alex Hartloper (EPFL). Issues, bugs, and feature requests can be opened at the github repository.