linear elasticity damping

[sillypants]

I'm doing a transient simulation of an electrostatically driven cantilever. I simulate contact with the substrate using a soft limiter on displacement, but after the cantilever hits that boundary condition, it starts flailing. Is there a way to add a damping term to make it settle down?

[raback]

Hi

How severe is this? Does it make the simulation totally useless? Are using StressSolve or ElasticSolve? I must admit that the soft limiters were introduced as a generic way to limit any field, and we haven't probably dealt cases like this ourselves. Our own uses has been for cavitation pressure and melting temperature type of limits.There might be some enhancements needed to robustly treat transient cases like this.

-Peter

[sillypants]

I'm using StressSolve, mostly for the solver speed, and the flailing was pretty severe, only making the first few timesteps usable. Adding "damping = .7" definitely helped it settle down, but I think I may have found the root issue - when the cantilever (ground) deflects down toward the applied voltage, the Electrostatics/Electric Force combination is calculating a lesser force instead of a greater force, so StressSolve pulls the cantilever back up and the cycle begins again.

I went back to using steady state instead of transient and see the same issue. What am I missing? Is Mesh Solver required or does it just speed up solving? When I tried using it I got segmentation fault, so I left it out.

Here's my sif and cantilever.grd for reference if you have a moment:

Code: Select all

Header
  CHECK KEYWORDS Warn
  Mesh DB "." "cantilever"
  Include Path ""
  Results Directory ""
End

Simulation
  Max Output Level = 4
  Coordinate System = Cartesian
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Steady State
  Steady State Max Iterations = 10
  Output Intervals = 1
  Timestepping Method = BDF
  BDF Order = 1
  Post File = force_ss.ep
End

Constants
  Permittivity of Vacuum = 8.8542e-12
  Boltzmann Constant = 1.3807e-23
  Unit Charge = 1.602e-19
End

Body 1
  Target Bodies(1) = 1
  Name = "Air"
  Equation = 1
  Material = 1
End

Body 2
  Target Bodies(1) = 2
  Name = "Board"
  Equation = 2
  Material = 2
End

Solver 1
  Equation = Electrostatics
  Variable = -dofs 1 Potential
  Procedure = "StatElecSolve" "StatElecSolver"
  Calculate Electric Field = True
  Exec Solver = Always
  Stabilize = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Nonlinear System Convergence Tolerance = 1.0e-8
  Nonlinear System Max Iterations = 2
  Nonlinear System Newton After Iterations = 3
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Direct
  Linear System Direct Method = Banded
End

Solver 2
  Equation = Electric Force
  Procedure = "ElectricForce" "StatElecForce"
  Exec Solver = Always
End

Solver 3
  Equation = Linear elasticity
  Variable = -dofs 3 Displacement
  Procedure = "StressSolve" "StressSolver"
  Exec Solver = Always
  Stabilize = True
  Calculate Stresses = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Nonlinear System Convergence Tolerance = 1.0e-8
  Nonlinear System Max Iterations = 5
  Nonlinear System Newton After Iterations = 3
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Direct
  Linear System Direct Method = Banded
  Apply Limiter = True
  Limiter Value Tolerance = 1e-8
End

Equation 1
  Name = "Electrostatics and Force"
  Active Solvers(2) = 1 2
End

Equation 2
  Name = "Linear Elasticity"
  Active Solvers(1) = 3
End

Material 1
  Name = "Air"
  Relative Permittivity = 1.00059
End

Material 2
  Name = "Aluminium"
  Poisson ratio = 0.35
  Youngs modulus = 70.0e9
End

Boundary Condition 1
  Target Boundaries(1) = 4
  Name = "Applied Voltage"
  Potential = 10
End

Boundary Condition 2
  Target Boundaries(1) = 6
  Name = "Ground (Cantilever Bottom)"
  Potential = 0
  Calculate Electric Force = True
  Force 1 = Opposes Electric Force Density 1
  Force 2 = Opposes Electric Force Density 2
  Force 3 = Opposes Electric Force Density 3
  Displacement 3 Lower Limit = Real -4.8e-7
End

Boundary Condition 3
  Target Boundaries(1) = 2
  Name = "Fixed Surface"
  Displacement 1 = 0.0
  Displacement 2 = 0.0
  Displacement 3 = 0.0
End

Code: Select all

***** ElmerGrid input file for structured grid generation *****
Version = 210903
Coordinate System = Cartesian 3D
Subcell Divisions in 3D = 3 3 2
Subcell Limits 1 = 0 5e-6 25e-6 30e-6
Subcell Limits 2 = -2e-6 -1e-6 1e-6 2e-6 
Subcell Limits 3 = 0 .5e-6  .7e-6
Material Structure in 2D
1 1 1
1 2 1
1 1 1
End
Materials Interval = 1 2
Extruded Structure
! 1stmat   lastmat  newmat  
  1        2        1
  2        2        2
End
Boundary Definitions
! type     out      int      double   of the boundaries
! air boundary
  1        0        1        1
! fixed surface of cantiliever      
  2       -4        2        1
!other cantilever surfaces
  3       -1        2        1
  3       -2        2        1
  3       -3        2        1
End
Numbering = Horizontal
Element Degree = 2
Element Innernodes = False
Triangles = False
Coordinate Ratios = 1 1
Element Divisions 1 = 4 16 4
Element Divisions 2 = 4 8 4
Element Divisions 3 = 5 8

[raback]

Hi

If the displacement affects the electric field, MeshSolver is required. Then the problem is of course that at contact some of your elements may be of zero size. You could leave some small gap to overcome the problem.

There is also a 1D model for electrostatics that might not be as picky for contact.

Now what physical happens at the contact. It may be difficult to work with the singularities of the electrostatics together with contact. Long time ago when I did some modeling of the critical pull-in voltage I did a separation of the computation of shape and amplitude in order to overcome the nasty behavior. Then the contact problem was eliminated alltogether. Of course it is not an option if contact is what you are looking for.

-Peter

[sillypants]

Thank you! Actual contact is not necessary, and in real life, an insulator coats the electrode to avoid shorting. To this end, I left a small gap just as you suggested (about 2e-8).

Concerning MeshSolver, when I try to use it, ElectricForce always gives a segmentation fault on the second iteration. Any tips?