Hysteretic

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>

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)

Hysteretic.gif
Hysteretic2.png

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.

Examples

Effects of Hysteretic-Material Parameters 1


Code Developed by: Michael Scott (Oregon State University) & Filip Filippou (UC Berkeley)

Images Developed by: Silvia Mazzoni

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