BoucWen Material

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This command is used to construct a uniaxial Bouc-Wen smooth hysteretic material object. This material model is an extension of the original Bouc-Wen model that includes stiffness and strength degradation (Baber and Noori (1985)).

uniaxialMaterial BoucWen $matTag $alpha $ko $n $gamma $beta $Ao $deltaA $deltaNu $deltaEta

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$matTag	integer tag identifying material
$alpha	ratio of post-yield stiffness to the initial elastic stiffenss (0< <math>\alpha</math> <1)
$ko	initial elastic stiffness
$n	parameter that controls transition from linear to nonlinear range (as n increases the transition becomes sharper; n is usually grater or equal to 1)
$gamma $beta	parameters that control shape of hysteresis loop; depending on the values of <math>\gamma</math> and <math>\beta</math> softening, hardening or quasi-linearity can be simulated (look at the NOTES)
$Ao $deltaA	parameters that control tangent stiffness
$deltaNu $deltaEta	parameters that control material degradation

NOTES:

1. Parameter <math>\gamma</math> is usually in the range from -1 to 1 and parameter <math>\beta</math> is usually in the range from 0 to 1. Depending on the values of <math>\gamma</math> and <math>\beta</math> softening, hardening or quasi-linearity can be simulated. The hysteresis loop will exhibit softening for the following cases: (a) <math>\beta</math> + <math>\gamma</math> > 0 and <math>\beta</math> - <math>\gamma</math> > 0, (b) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> <0, and (c) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> = 0. The hysteresis loop will exhibit hardening if <math>\beta</math>+<math>\gamma</math> < 0 and <math>\beta</math>-<math>\gamma</math> > 0, and quasi-linearity if <math>\beta</math>+<math>\gamma</math> = 0 and <math>\beta</math>-<math>\gamma</math> > 0.
2. The material can only define stress-strain relationship.

REFERENCES:

Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." REER report, PEER-2003/14 [1].

Baber, T. T. and Noori, M. N. (1985). "Random vibration of degrading, pinching systems." Journal of Engineering Mechanics, 111(8), 1010-1026.

Bouc, R. (1971). "Mathematical model for hysteresis." Report to the Centre de Recherches Physiques, pp16-25, Marseille, France.

Wen, Y.-K. (1976). \Method for random vibration of hysteretic systems." Journal of Engineering Mechanics Division, 102(EM2), 249-263.