Hysteretic Material

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This command is used to construct a uniaxial bilinear hysteretic material object with pinching of force and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility.

uniaxialMaterial Hysteretic $matTag $s1p $e1p $s2p $e2p <$s3p $e3p> $s1n $e1n $s2n $e2n <$s3n $e3n> $pinchX $pinchY $damage1 $damage2 <$beta>

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$matTag	integer tag identifying material
$s1p $e1p	stress and strain (or force & deformation) at first point of the envelope in the positive direction
$s2p $e2p	stress and strain (or force & deformation) at second point of the envelope in the positive direction
$s3p $e3p	stress and strain (or force & deformation) at third point of the envelope in the positive direction (optional)
$s1n $e1n	stress and strain (or force & deformation) at first point of the envelope in the negative direction
$s2n $e2n	stress and strain (or force & deformation) at second point of the envelope in the negative direction
$s3n $e3n	stress and strain (or force & deformation) at third point of the envelope in the negative direction (optional)
$pinchx	pinching factor for strain (or deformation) during reloading
$pinchy	pinching factor for stress (or force) during reloading
$damage1	damage due to ductility: D1(mu-1)
$damage2	damage due to energy: D2(Eii/Eult)
$beta	power used to determine the degraded unloading stiffness based on ductility, mu-beta (optional, default=0.0)

NOTE:

1. In cases $s3p > $s2p and abs($s3n) > abs($s2n), the envelope of the hysteretic material after $e3p or $e3n follows the slope defined by 2nd and 3rd point of the envelope.
2. In cases $s3p <= $s2p and abs($s3n) <= abs($s2n) the envelope of the hysteretic material after $e3p or $e3n is a flat line with a constant stress (or force) equal to $s3p or $s3n.

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Code Developed by: Micheal Scott & Filip Filippou, UC Berkeley

Images Developed by: Silvia Mazzoni