Maxwell Material

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This command is used to construct a ViscousDamper material, which represents the Maxwell Model (linear spring and nonlinear dashpot in series). The Maxwell material simulates the hysteretic response of viscous dampers.

uniaxialMaterial ViscousDamper $matTag $K $Cd $alpha

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$matTag	integer tag identifying material
$K	Elastic stiffness of linear spring (to model the axial flexibility of a viscous damper (brace and damper portion)
$Cd	Viscous parameter of damper
$alpha	Viscous damper exponent

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Examples:

1. Input parameters:

Assume a viscous damper with axial stiffness K=300.0kN/mm, viscous parameter Cd=280.3kN(s/mm)0.3, and exponent a=0.30.

The input parameters for the material should be as follows:

uniaxialMaterial ViscousDamper 1 300 280.3 0.30

Using these properties, Figure 1 shows the hysteretic response of this damper for sinusoidal displacement increments of 12, 24 and 36mm and a frequency f = 0.5Hz.

The sensitivity of the viscous damper with respect to its axial stiffness is shown in Figures 2 to 5 for the following set of parameters:

Figure 1. Viscous Damper with K=300.0 kN/mm, Cd=73.0kN(s/mm)0.6, a=0.60 , Figure 2. Viscous Damper with K=300.0 kN/mm, Cd=12.0kN(s/mm)1.0, a=1.0

Figure 2. Viscous Damper with K=300.0 kN/mm, Cd=683.0kN(s/mm)0.1, a=0.1 , Figure 2. Viscous Damper with K=300.0 kN/mm, Cd=1017.7kN(s/mm)0.01, a=0.01

2. Tcl input file for Viscous Damper Calibration.

3. OpenSees Example of 1-story steel moment frame with a viscous damper: (to be posted)

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References:

[1]	Olsson, A.K., and Austrell, P-E., (2001), "A fitting procedure for viscoelastic-elastoplastic material models," Proceedings of the Second European Conference on Constitutive Models for Rubber, Germany, 2001.
[2]	Ottosen, N.S., and Ristinmaa, M., (1999). "The mechanics of constitutive modelling, (Numerical and thermodynamical topics)," Lund University,Division of Solid Mechanics, Sweden, 1999.

Code Developed by : Prof. Kazuhiko Kasai (Tokyo Institute of Technology) and implemented by Sarven Akcelyan & Prof. Dimitrios G. Lignos, (McGill University)