Pinching4 Material

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This command is used to construct a uniaxial material that represents a 'pinched' load-deformation response and exhibits degradation under cyclic loading. Cyclic degradation of strength and stiffness occurs in three ways: unloading stiffness degradation, reloading stiffness degradation, strength degradation.

uniaxialMaterial Pinching4 $matTag $ePf1 $ePd1 $ePf2 $ePd2 $ePf3 $ePd3 $ePf4 $ePd4 <$eNf1 $eNd1 $eNf2 $eNd2 $eNf3 $eNd3 $eNf4 $eNd4> $rDispP $rForceP $uForceP <$rDispN $rForceN $uForceN > $gK1 $gK2 $gK3 $gK4 $gKLim $gD1 $gD2 $gD3 $gD4 $gDLim $gF1 $gF2 $gF3 $gF4 $gFLim $gE $dmgType

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$matTag	integer tag identifying material
$ePf1 $ePf2 $ePf3 $ePf4	floating point values defining force points on the positive response envelope
$ePd1 $ePd2 $ePd3 $ePd4	floating point values defining deformation points on the positive response envelope
$eNf1 $eNf2 $eNf3 $eNf4	floating point values defining force points on the negative response envelope
$eNd1 $eNd2 $eNd3 $eNd4	floating point values defining deformation points on the negative response envelope
$rDispP	floating point value defining the ratio of the deformation at which reloading occurs to the maximum historic deformation demand
$fFoceP	floating point value defining the ratio of the force at which reloading begins to force corresponding to the maximum historic deformation demand
$uForceP	floating point value defining the ratio of strength developed upon unloading from negative load to the maximum strength developed under monotonic loading
$rDispN	floating point value defining the ratio of the deformation at which reloading occurs to the minimum historic deformation demand
$fFoceN	floating point value defining the ratio of the force at which reloading begins to force corresponding to the minimum historic deformation demand
$uForceN	floating point value defining the ratio of strength developed upon unloading from negative load to the minimum strength developed under monotonic loading
$gK1 $gK2 $gK3 $gK4 $gKLim	floating point values controlling cyclic degradation model for unloading stiffness degradation
$gD1 $gD2 $gD3 $gD4 $gDLim	floating point values controlling cyclic degradation model for reloading stiffness degradation
$gF1 $gF2 $gF3 $gF4 $gFLim	floating point values controlling cyclic degradation model for strength degradation
$gE	floating point value used to define maximum energy dissipation under cyclic loading. Total energy dissipation capacity is defined as this factor multiplied by the energy dissipated under monotonic loading.
$dmgType	string to indicate type of damage (option: "cycle", "energy")
$beta	power used to determine the degraded unloading stiffness based on ductility, m-b (optional, default=0.0)
$curveTag	an integer tag for the LimitCurve defining the limit surface
$curveType	an integer defining the type of LimitCurve (0 = no curve, 1 = axial curve, all other curves can be any other integer)

NOTES:

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EXAMPLE:

LimitStateMaterialExample

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DESCRIPTION:

Stiffness and strength are assumed to deteriorate due to the imposed "load" history. The same basic equations are used to describe deterioration in strength, unloading stiffness and reloading stiffness:

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REFERENCES:

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Code Developed by: Nilinjan Mitra, University of Washington