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)).

Model.uniaxial(“BoucWen”, name, alpha, ko, n, a, b, c)

alpha float ratio of post-yield stiffness to the initial elastic stiffenss ($0< \alpha < 1$)

ko float initial elastic stiffness

n int parameter that controls transition from linear to nonlinear range (as n increases the transition becomes sharper; n is usually grater or equal to 1)

a

[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)

`gamma`	`float`
`beta`	`float`

b

[Ao,deltaA], parameters that control tangent stiffness

`Ao`	`float`
`deltaA`	`float`

c

[deltaNu,deltaEta], parameters that control material degradation

`deltaNu`	`float`
`deltaEta`	`float`

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:
1. $\beta + \gamma \gt 0$ and $\beta - \gamma \gt 0$,
2. $\beta + \gamma \gt 0$ and $\beta - \gamma \lt 0$, and
3. $\beta + \gamma \gt 0$ and $\beta - \gamma = 0$.
The hysteresis loop will exhibit hardening if $\beta + \gamma \lt 0$ and $\beta - \gamma \gt 0$, and quasi-linearity if $+ = 0 and $\beta - \gamma \gt 0$.
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.