BoucWen

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< <math></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 \(\gamma\) and \(\beta\) 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 \(\gamma\) is usually in the range from -1 to 1 and parameter \(\beta\) is usually in the range from 0 to 1. Depending on the values of \(\gamma\) and \(\beta\) softening, hardening or quasi-linearity can be simulated. The hysteresis loop will exhibit softening for the following cases: (a) <math></math> + <math></math> > 0 and \(\beta\) -

    \[\gamma&lt;/math&gt; &gt; 0, (b) &lt;math&gt;\beta&lt;/math&gt;+&lt;math&gt;\gamma&lt;/math&gt; &gt;0 and &lt;math&gt;\beta&lt;/math&gt;-&lt;math&gt;\gamma&lt;/math&gt; &lt;0, and (c) &lt;math&gt;\beta&lt;/math&gt;+&lt;math&gt;\gamma\]

    >0 and \(\beta\)-<math></math> = 0. The hysteresis loop will exhibit hardening if <math></math>+<math></math> < 0 and \(\beta\)-<math></math> > 0, and quasi-linearity if <math></math>+<math></math> = 0 and <math></math>-<math></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). for random vibration of hysteretic systems.” Journal of Engineering Mechanics Division, 102(EM2), 249-263.

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