Impact Material: Difference between revisions

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This material is based on an approximation to the Hertz contact model proposed by Muthukumar (See REFERENCES below). The energy dissipated during impact is:
This material is based on an approximation to the Hertz contact model proposed by Muthukumar (See REFERENCES below). The energy dissipated during impact is:


E = kh * δm ^ (n+1_(1-e^2) / (N+1)  
E = kh * δm^(n+1) * (1-e^2) / (N+1)  


where kh is the impact stiffness parameter, with a typical value of EA/L or 25,000 k-in.-3/2; n is typically taken as 3/2 for the exponent associated with the Hertz power rule; e is the coefficient of restitution, with typical values from 0.6-0.8; and δm is the maximum penetration during the pounding event.  The effective stiffness, Keff, is:
where kh is the impact stiffness parameter, with a typical value of EA/L or 25,000 k-in.-3/2; n is typically taken as 3/2 for the exponent associated with the Hertz power rule; e is the coefficient of restitution, with typical values from 0.6-0.8; and δm is the maximum penetration during the pounding event.  The effective stiffness, Keff, is:
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The yield displacement is:
The yield displacement is:


δy = a δm
δy = a * δm


where a is typically taken as 0.1.  The initial stiffness, K1, and secondary stiffness, K2, are then selected such that the Impact model dissipates an amount of energy during a pounding event that is consistent with the associated energy dissipated in the Hertz model.
where a is typically taken as 0.1.  The initial stiffness, K1, and secondary stiffness, K2, are then selected such that the Impact model dissipates an amount of energy during a pounding event that is consistent with the associated energy dissipated in the Hertz model.


K1 = Keff + E/(a*δm^2)
K1 = Keff + E / (a*δm^2)


K2 = Keff - E/((1-a)*δm^2)
K2 = Keff - E / ((1-a)*δm^2)


Response of Impact Material during a pounding event.
Response of Impact Material during a pounding event.

Latest revision as of 22:35, 20 November 2009

This command is used to construct an impact material object

uniaxialMaterial ImpactMaterial $matTag $K1 $K2 $δy $gap


$matTag integer tag identifying material
$K1 initial stiffness
$K2 secondary stiffness
$δy yield displacement
$gap initial gap*

NOTES:

This material is implemented as a compression-only gap material. Delta_y and gap should be input as negative values.


DESCRIPTION:

This material is based on an approximation to the Hertz contact model proposed by Muthukumar (See REFERENCES below). The energy dissipated during impact is:

E = kh * δm^(n+1) * (1-e^2) / (N+1)

where kh is the impact stiffness parameter, with a typical value of EA/L or 25,000 k-in.-3/2; n is typically taken as 3/2 for the exponent associated with the Hertz power rule; e is the coefficient of restitution, with typical values from 0.6-0.8; and δm is the maximum penetration during the pounding event. The effective stiffness, Keff, is:

Keff = kh * sqrt(δm)

The yield displacement is:

δy = a * δm

where a is typically taken as 0.1. The initial stiffness, K1, and secondary stiffness, K2, are then selected such that the Impact model dissipates an amount of energy during a pounding event that is consistent with the associated energy dissipated in the Hertz model.

K1 = Keff + E / (a*δm^2)

K2 = Keff - E / ((1-a)*δm^2)

Response of Impact Material during a pounding event.

Response of Impact Material for displacement cycles of increasing amplitude.



EXAMPLE:



REFERENCES:

Muthukumar, S., and DesRoches, R. (2006). “A Hertz Contact Model with Non-linear Damping for Pounding Simulation.” Earthquake Engineering and Structural Dynamics, 35, 811-828.

Muthukumar, S. (2003). “A Contact Element Approach with Hysteresis Damping for the Analysis and Design of Pounding in Bridges.” PhD Thesis, Georgia Institute of Technology. http://smartech.gatech.edu/

Nielson, B. (2005). “Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones.” PhD Thesis, Georgia Institute of Technology. http://smartech.gatech.edu/



Code Developed by: Mathew Dryden, UC Berkeley