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Hertz Contact 2D

Tested with CGX 2.19 / CCX 2.19

  • Plane strain model
  • Linear elasticity
  • Surface-to-surface Penalty contact
  • 2 steps:
    1. displacement control,
    2. force (pressure) control

The model was inspired by this post by user dichtstoff in the CalculiX user forum. Here, essentially, parametrization with the CGX valu command and mesh bias were added.

File Contents
pre.fbd Pre-processing script for CGX (parametrized with valu)
Hertz.inp CCX input, surface-to-surface penalty contact
post.fbd CGX post-processing script
plots.fbd CGX post-processing script (path plots)
plots.gnu Gnuplot script for path plots
test.py Python script to run the example

Preprocessing

Parameter Value Description
radius 50 radius in mm
height 60 thickness of the block in mm
width 120 width of the block in mm

The prescribed displacement (first step) or the pressure (second step) are applied to the flat equatorial surface of the cylinder.

The values for both variants are chosen independently, thus they can't be compared directly.

> cgx -b pre.fbd

Two separate parts are generated and meshed with plane strain elements.

Sets and Contact surfaces:

Solving

> ccx Hertz
> monitor.py Hertz

Postprocess

> cgx -b post.fbd

The solution shows the expected feature of Hertz contact with the maximum of the equivalent stress somewhat below the contact surface.

Results with displacement control (first step)

Results with pressure control (second step)

> cgx -b plots.fbd

Stress plots along the symmetry line with x=0 at the contact location:

Results with displacement control (first step)

Results with pressure control (second step)