BoucWen Material

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< $\alpha$ <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) $\beta$ + $\gamma$ > 0 and $\beta$ - $\gamma$ > 0, (b) $\beta$+$\gamma$ >0 and $\beta$-$\gamma$ <0, and (c) $\beta$+$\gamma$ >0 and $\beta$-$\gamma$ = 0. The hysteresis loop will exhibit hardening if $\beta$+$\gamma$ < 0 and $\beta$-$\gamma$ > 0, and quasi-linearity if $\beta$+$\gamma$ = 0 and $\beta$-$\gamma$ > 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.