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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

$matTag integer tag identifying material
$alpha ratio of post-yield stiffness to the initial elastic stiffenss (0< α <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 γ and β 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 γ is usually in the range from -1 to 1 and parameter β is usually in the range from 0 to 1. Depending on the values of γ and β softening, hardening or quasi-linearity can be simulated. The hysteresis loop will exhibit softening for the following cases: (a) β + γ > 0 and β - γ > 0, (b) β+γ >0 and β-γ <0, and (c) β+γ >0 and β-γ = 0. The hysteresis loop will exhibit hardening if β+γ < 0 and β-γ > 0, and quasi-linearity if β+γ = 0 and β-γ > 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.

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