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|
- 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.
- The material can only define stress-strain relationship.
Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." REER report, PEER-2003/14 .
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.