OpenSEES-BoucWenGG

Implementation in OpenSEES of the Bouc-Wen model modified by Gerolymos and Gazetas (2005).

Author: Andrea Marchi (andrea.marchi@uniroma1.it)

References:

Gerolymos N. and Gazetas G. Constitutive model for 1-D cyclic soil behaviour applied to seismic analysis of layered deposits. Soils and Foudations, 45-147 (2005).
Marchi A. Improved Bouc-Wen model implementation in OpenSees. Proceedings of the 2022 Eurasian OpenSees Days. EOS 2022. Lecture Notes in Civil Engineering, vol 326, 31-38. Springer, Cham. https://doi.org/10.1007/978-3-031-30125-4_3

Usage (TLC):

Include BoucWenGG.dll file inside the same folder of the TCL model file to use the material. The material can be defined by the TCL command:

uniaxialMaterial BoucWenGG $matTag $alpha $k0 $strainY $n $gamma $beta $s1 $s2 $mkur

parameter	description
`matTag`	integer tag identifying the material
`alpha`	ratio of the post-yielding stiffness to the initial elastic stiffness
`k0`	initial elastic stiffness
`strainY`	yielding strain $\varepsilon_y$
`n`	parameter that controls the transition between the initial and post-yielding branch. As $n$ increases the transition becomes sharper (when $n\to\infty$ the model is piece-wise linear).
`gamma`, `beta`	parameters that control the shape of the hysteresis loop
`s1`, `s2`	control the stiffness degradation upon reversal
`mkur`	account for stress and tangent stiffness modification proposed by Drosos et al. (2012). `mkur`=1 modification is aplied, `mkur`=0 modification is not applied

$F(u(t)) = \alpha \ k_0 \ u(t) + (1-\alpha) \ k_0 \ u_y \ \zeta(t)$

$\dot{\zeta}(t) = \frac{\dot{u}(t)}{u_y} [(\gamma+\beta) - |\zeta(t)|^n \ (\gamma + \beta \ sgn(\dot{u}(t) \ \zeta(t))) ] $