Example d25: Hertz contact problem using linear elasticity

This example illustrates the Hertz contact problem using linear elasticity.

Before contact After contact mechanics solution
Fig. 1 Before contact Fig. 2 After contact mechanics solution


The comfile run by this example is as follows:

#############################################################
# This illustrates the classical Hertz contact problem of a 
# rigid cylinder indenting an elastic half-space. The 
# governing equation is linear elasticity and the constitutive 
# law is a simple compressible linear isotropic function 
# requiring a Young's modulus (E) and Poisson's ratio (v). 
# The half-space is trilinear and the cylinder is bicubic-linear. 
# Even though the problem is linear, the addition of contact makes 
# the problem non-linear requiring a Newton-Raphson solution approach. 
#############################################################

# Define parameters, regions, coordinate system and bases
fem def para;r;hertz;example
fem def region;r;two;example
fem def coord 3,1
fem def bases;r;collapsed;example

# Read in half-space described by trilinear elements
fem def nodes;r;half;example reg 1
fem def elem;r;half;example reg 1

# Refine half-space with dense mesh in region of contact 
fem refine xi 1 element 101 ntimes 2 reg 1
fem refine xi 1 element 101,103 ntimes 2 reg 1
fem refine xi 1 element 101,107,105,108 ntimes 1 reg 1
fem refine xi 1 element 101,107,111,112 ntimes 1 reg 1
fem refine xi 3 ntimes 3 reg 1

# Define fibre directions
fem def fibre;r;half;example reg 1
fem def elem;r;half;example fibre reg 1

# Read in rigid cylinder described by bicubic-linear elements
fem def nodes;r;cylinder;example reg 2
fem def elem;r;cylinder;example reg 2

# Update derivatives and scale-factors
fem up node deriv 1 linear reg 2
fem up node deriv 2 linear reg 2
fem up node deriv 3 linear reg 2
fem up scale_factors normalise reg 2

# Align cylinder for contact
fem change nodes rotate by -90 reg 2
fem change nodes translate by -2,2,0 reg 2

# Define fibre directions
fem def fibre;r;cylinder;example reg 2
fem def elem;r;cylinder;example fibre reg 2
 
## Export cylinder (master surface)
#fem export nodes;cylinder as cylinder reg 2
#fem export elem;cylinder as cylinder reg 2

# Node groups for fixed boundary conditions
fem group nodes 101,305,221,301,179,297,217,293,107,103,303,219,299,177,295,215,291,105 as fixedx reg 1
fem group nodes 105,161,145,169,129,165,149,173,121,153,133,157,113,137,125,141,109,117,106 as fixedy1 reg 1
fem group nodes 107,162,146,170,130,166,150,174,122,154,134,158,114,138,126,142,110,118,108 as fixedy2 reg 1
fem group nodes 101..442 as fixedz reg 1
fem group nodes 1..20 as cylinderfixedz reg 2
fem group nodes 1..20 as cylinderfixedy reg 2
fem group nodes 1..20 as cylinderfixedx reg 2

# Define equations
fem def equa;r;half;example reg 1
fem def equa;r;cylinder;example reg 2

# Define material properties
fem def mat;r;half;example reg 1
fem def mat;r;cylinder;example reg 2

# Define initial fixed boundary conditions
fem def init;r;half;example reg 1
fem def init;r;cylinder;example reg 2

# Move cylinder through prescribed displacement
fem change nodes translate by 0,-0.02,0 nodes cylinderfixedy reg 2

# define contact parameters
fem def contact;r;contact;example

# Define solve for problem reg 1
fem def solve;r;half;example reg 1

$j=0;
$CONVERGED=0;
while ($CONVERGED==0) 
{
$j++;
######################################Projection

# Set contact xi points on specified faces (8x8)
fem def xi;c contact_points faces 381,575,531,593,479,584,548 points 8 reg 1

# Define data at xi positions 
fem def data;c from_xi reg 1

# Update slave info
fem update data field to slave

# Project onto target face 
fem def xi;c closest_face faces 623 region 2

# Store projection gap in data fields
fem update data field from gap region 2  

# Update master info
fem update data field to master 

# Place initial geometry YP(ny,3) into XP
if ($j>1) 
{
FEM up geom from sol YP_index 3 to 1..3 reg 1
}
#####################################Mechanics problem
# Solve contact problem
fem solve error 0.01 iterate 5 reg 1

FEM up geom from sol to 1..3 reg 1 
}

# Place initial geometry YP(ny,3) into XP
FEM up geom from sol YP_index 3 to 1..3 reg 1

# Only need displacements for stresses
fem update solution geometry subtract reg 1

# Fit stresses at Gauss points to nodal fields
fem def field;r;half;example
fem def elem;r;half;example field
fem up gauss stress ref 
fem de fit;r;half;example gauss
fem fit

## Export undeformed slave with stresses
#fem export nodes;half as half reg 1 
#fem export elem;half as half reg 1 

# Add undeformed geometry to displacements
fem update solution geometry add reg 1
# Update XP from YP
FEM up geom from sol to 1..3 reg 1

## Export deformed slave
#fem export nodes;half_def as half_def reg 1 offset 1000
#fem export elem;half_def as half_def reg 1 offset_elem 1000

## Export deformed master
#fem export nodes;cylinder_def as cylinder_def reg 2 offset 2000
#fem export elem;cylinder_def as cylinder_def reg 2 offset_elem 2000
 

Additional testing commands:



Files used by this example are:

Name                Modified     Size

example_d25.com 23-Apr-2008 4.7k collapsed.ipbase 01-Sep-2004 8.3k contact.ipcont 25-Sep-2008 626 contact.ipsolv 16-Aug-2010 2.7k contact.ipsolv.old 13-Apr-2007 2.5k coupled.irequa 01-Sep-2004 3.6k coupled.irsolv 13-Apr-2007 1.0k cylinder.ipelem 01-Sep-2004 3.3k cylinder.ipelfb 01-Sep-2004 2.4k cylinder.ipequa 29-Sep-2004 2.0k cylinder.ipfibr 01-Sep-2004 15k cylinder.ipinit 01-Sep-2004 2.4k cylinder.ipmate 01-Sep-2004 974 cylinder.ipnode 01-Sep-2004 18k cylinder.ipsolv 13-Apr-2007 1.1k half.ipbase 01-Sep-2004 3.3k half.ipelem 01-Sep-2004 506 half.ipelfb 01-Sep-2004 38k half.ipelfd 01-Sep-2004 38k half.ipequa 29-Sep-2004 2.0k half.ipfibr 01-Sep-2004 60k half.ipfiel 01-Sep-2004 68k half.ipfit 13-Apr-2007 1.8k half.ipinit 01-Sep-2004 875 half.ipmate 01-Sep-2004 973 half.ipnode 01-Sep-2004 2.1k half.ipsolv 13-Apr-2007 1.1k half.ipxi 01-Sep-2004 3.5k hertz.ipequa 01-Sep-2004 1.7k hertz.ippara 09-Nov-2008 6.0k hertz.ipsolv 13-Apr-2007 1.4k hertz.ircoor 01-Sep-2004 1.1k hertz.irsolv 13-Apr-2007 1.5k test_output.com 01-Sep-2004 0 two.ipregi 01-Sep-2004 93 view.com 01-Sep-2004 2.6k

Download the entire example:

Name                      Modified     Size

examples_d_d2_d25.tar.gz 17-Aug-2010 113k

Testing status by version:

StatusTestedReal time (s)
hpc_cmo64_irixSuccessSun Jul 31 01:35:44 200511
rs6000-aix
cm64SuccessWed Mar 4 01:12:07 20095
x86_64-linux
cmSuccessSun Mar 6 00:01:12 20162

Testing status by file:


Html last generated: Sun Mar 6 05:51:25 2016

Input last modified: Mon Aug 16 11:35:03 2010


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