Computation of damping contribution

1

Hi CalculiX Users,

I was trying to plot the hysteresis cycle (stress-displacement) of a cube under a sinusoidal displacement boundary condition from the sum of traction forces and the mean displacement of the loaded face. I need those data to compute an overall ‘homogenized’ damping from the area of the cycle and the maximum force.

I assigned to the FE model an isotropic material (E, nu) with Rayleigh damping and I performed an implicit dynamic structural simulation.

I read on the manual (*NODE FILE section) that CalculiX does not consider the contribution of the damping forces for the computation of the reactions forces. So, I was wandering how to get the data on stress/forces to plot the cycle.

I tried to retrieve the reaction forces on the loaded face and then I computed the resultant, but I found that results are weird and they do depend on the number of integration points (the more integration points are present in the mesh, the bigger is the resultant reaction force and a plateau is never reached).

I also looked for an alternative way, by trying to get the elastic potential energy and the dissipated one. However, I could not find a way to retrieve the dissipated energy during the simulation.

Could you please help me?

Thanks,
Luca

2

Maybe integrate stress at the surface or connect the boundary condition with springs and sum their forces?

3

Monitor shows the work done by the external forces into the overall balance including non conservative ones like friction and work performed by the damping forces.

 initial energy (at start of step) = 0.000000e+00

 since start of the step: 
 external work = 4.609449e-05
 work performed by the damping forces = -4.456035e-05

 netto work = 1.534139e-06

 actual energy: 
 internal energy = 3.126866e-09
 kinetic energy = 1.527023e-06
 elastic contact energy = 0.000000e+00
 energy lost due to friction = 0.000000e+00
 total energy  = 1.530150e-06

 energy increase = 1.530150e-06

 energy balance (absolute) = -3.988753e-09 
 energy balance (relative) = 0.009212 %

Take a close look because I think that doesn’t include the energy decrease due to numerical damping.

Manual : “The parameter ALPHA takes an argument between -1/3 and 0. It controls
the dissipation of the high frequency response: lower numbers lead to increased
numerical damping ([62]). The default value is -0.05.”

That’s not the same Raileight’s ALPHA