Maxwell Material: Difference between revisions

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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.
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.


{|  
{|  
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial Maxwell $matTag  $K $C $a $L'''
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial ViscousDamper $matTag  $K $Cd $alpha'''
|}
|}


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|  style="width:150px" | '''$matTag ''' || integer tag identifying material
|  style="width:150px" | '''$matTag ''' || integer tag identifying material
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|  '''$K ''' || Elastic stiffness of linear spring (to model elastic stiffness of viscous damper)
|  '''$K ''' || Elastic stiffness of linear spring (to model the axial flexibility of a viscous damper (brace and damper portion)
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|-
|  '''$C ''' || Viscous parameter of damper
|  '''$Cd ''' || Viscous parameter of damper
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|-
|  '''$a ''' || Viscous damper exponent
|  '''$alpha ''' || Viscous damper exponent
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|  '''$L''' || Viscous damper length
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|}
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| '''''1. Input parameters:'''''
| '''''1. Input parameters:'''''
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| Assume a viscous damper with axial stiffness K=150.0kN/mm, viscous parameter C = 100.0kN(s/mm)<sup>0.3</sup>, an exponent a=0.3 and length equal to 5000mm.  
| Assume a viscous damper with axial stiffness K=300.0kN/mm, viscous parameter Cd=280.3kN(s/mm)<sup>0.3, and exponent a=0.30.  
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|-
| The input parameters for the material should be as follows:
| The input parameters for the material should be as follows:
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| uniaxialMaterial Maxwell           1  150.0     100.0      0.30     5000.0
| uniaxialMaterial ViscousDamper           1  300      280.3     0.30
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| Using these properties a comparison between simulated responses from OpenSees and a MATLAB based program are shown in Figure 1.  
| 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.  
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|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)<sup>0.3</sup>, a=0.30.
|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:   
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| [[File:Fig1.png|425px|thumb|left|Figure 1. Viscous Damper with K=150.0kN/mm, C=100.0kN(s/mm)<sup>0.3</sup>, a=0.30]]  
| [[File:Fig1.png|425px|thumb|left|Figure 1. Viscous Damper with K=300.0 kN/mm, Cd=73.0kN(s/mm)<sup>0.6</sup>, a=0.60]] , [[File:Fig2.png|425px|thumb|left|Figure 2. Viscous Damper with K=300.0 kN/mm, Cd=12.0kN(s/mm)<sup>1.0</sup>, a=1.0]]  
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| [[File:Fig2.png|425px|thumb|left|Figure 2. Viscous Damper with K=500.0kN/mm, C=100.0kN(s/mm)<sup>0.3</sup>, a=0.30]]  
| [[File:Fig1.png|425px|thumb|left|Figure 2. Viscous Damper with K=300.0 kN/mm, Cd=683.0kN(s/mm)<sup>0.1</sup>, a=0.1]] , [[File:Fig2.png|425px|thumb|left|Figure 2. Viscous Damper with K=300.0 kN/mm, Cd=1017.7kN(s/mm)<sup>0.01</sup>, a=0.01]]  
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Code Developed by : <span style="color:blue"> by Dr. Dimitrios G. Lignos, (McGill University) </span>
Code Developed by : <span style="color:blue"> Prof. Kazuhiko Kasai and implemented by Sarven Akcelyan & Prof. Dimitrios G. Lignos, (McGill University) </span>

Revision as of 18:12, 21 August 2013



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
$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

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)

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 and implemented by Sarven Akcelyan & Prof. Dimitrios G. Lignos, (McGill University)

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