Maxwell Material

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

uniaxialMaterial Maxwell $matTag $K $C $a $L

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$matTag	integer tag identifying material
$K	Elastic stiffness of linear spring (to model elastic stiffness of viscous damper)
$C	Viscous parameter of damper
$a	Viscous damper exponent
$L	Viscous damper length

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Examples:

1. Input parameters:

Assume a viscous damper with axial stiffness K=150.0kN/mm, viscous parameter C = 100.0kN(s/mm)0.3, an exponent a=0.3 and length equal to 5000mm.

The input parameters for the material should be as follows:

uniaxialMaterial Maxwell 1 150.0 100.0 0.30 5000.0

Using these properties a comparison between simulated responses from OpenSees and a MATLAB based program are shown in Figure 1.

The sensitivity of the viscous damper with respect to its axial stiffness is shown in Figure 2 for the following set of parameters: K=500.0kN/mm, C=100.0kN(s/mm)0.3, a=0.30.

Figure 1. Viscous Damper with K=150.0kN/mm, C=100.0kN(s/mm)0.3, a=0.30

Figure 2. Viscous Damper with K=500.0kN/mm, C=100.0kN(s/mm)0.3, a=0.30

2. Tcl input file for Viscous Damper Calibration: (to be posted)

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 : by Dr. Dimitrios G. Lignos, (McGill University)