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) |
|
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) |
|
parameters that control tangent stiffness |
|
parameters that control material degradation |
NOTES:
-
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 \(\beta\) -
\[\gamma</math> > 0, (b) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> <0, and (c) <math>\beta</math>+<math>\gamma\]
>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. - 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.