Example 522: Uniform biaxial extension of a unit cube

A 3D unit cube of incompressible Mooney-Rivlin material is displacement loaded on the X=1 face by 10% in the X direction and Y=1 face by 10% in the Y direction while keeping the X=0 and Y=0 faces fixed (biaxial extension).


The comfile run by this example is as follows:

#Example_522  Uniform biaxial extension of a unit cube
 
fem
fem define coordinate;r;biaxial;example #Defines 3D rectangular cartesian
fem define node;r;;example           #Defines 8 nodes as in uniaxial example
fem define base;r;;example	         #Defines 3 basis functions:
#                                !  1) Lagrange/Hermite with 3 Xi coords;
#                                !  2) Auxiliary bsis with 3 Xi coords;
#                                !  3) Linear Lagrange with 2 Xi coords.
fem define element;r;;example        #Defines 1 element.
fem define window                #Define 2D window.
fem draw lines                   #Make line segments visible on window.
fem define fibre;d               #Use the default fibre angle
fem define element;r;;example fibre
fem define equation;r;;example       #Defines a finite elasticity problem.
fem define material;r;;example       #Defines a hyperelastic constitutive
#                                !  law.
fem define initial;r;;example        #Define NO PRESSURE BOUNDARY CONDITIONS
#                                !  or INITIAL DISPLACEMENTS. Dependent
#                                !  variable 1 fixes nodes 1,3,5,7 by an
#                                !  increment of 0.0, and nodes 2,4,6,8
#                                !  with displacement 0.1.  Nodes 1,2,5,6
#                                !  are fixed with 0.0 for dependent
#                                !  variable 2, and nodes 3,4,7,8 have a
#                                !  displacement of 0.1.Fix nodes 1,2,3,4
#                                !  for dependent variable 3. No bcs are
#                                !  prescribed for dependent variable 4,
#                                !  and there are no force bcs.
fem define solve;r;;example          #Defines a Newton-Raphson iteration.
fem solve step 1                 #Solve the problem (should converge in
#                                !  about 3 iterations).
fem list initial                 #Note the Lagrange multiplier, p=-11.28
#                                !  Thus hydrostatic pressure=0.5p=5.64.
fem draw line deformed dotted    #Draw deformed mesh on window.
fem list strain at 1 ref         #List strain information wrt reference
#                                !  coordinates at 1st gauss point.
#                                !  Strain invariants:I1=3.103,I2=3.117,
#                                !  I3=1.  Stretch ratios: lamda(1)=
#                                !  lamda(2)=1.1, lamda(3)=0.8264.
#                                !  Lagrangian strains: E11=E22=0.105,
#                                !  E33 =-0.1585.
fem list stress at 1 ref         #List stress information wrt reference
#                                !  coordinates at 1st gauss point.
#                                !  Cauchy stress in the Xi 1 direction,
#                                !  T11=T22=9.76.  Other components
#                                !  should be close to 0.

Additional testing commands:

# There are repeated eigenvalues so Euler angles and eigenvectors are not unique.
fem list stress at 1 ref
fem list strain at 1 ref

Files used by this example are:

Name                Modified     Size

example_522.com 10-Apr-2000 2.9k biaxial.ipbase 10-Apr-2000 3.4k biaxial.ipcoor 10-Apr-2000 611 biaxial.ipelem 10-Apr-2000 450 biaxial.ipelfb 10-Apr-2000 279 biaxial.ipequa 02-May-2004 2.1k biaxial.ipinit 05-Dec-2002 1.6k biaxial.ipmate 05-Dec-2002 2.3k biaxial.ipnode 10-Apr-2000 1.9k biaxial.ipsolv 16-Aug-2010 2.2k biaxial.ipsolv.old 13-Apr-2007 2.1k test_output.com 10-Apr-2000 132

Download the entire example:

Name                      Modified     Size

examples_5_52_522.tar.gz 14-Aug-2014 6.9k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:01:56 20160
cm-debugSuccessSat Mar 5 00:02:13 20160
mips-irix
cmSuccessSun Aug 19 01:22:55 20073
cm-debugSuccessWed Aug 15 01:21:56 20075
cm-debug-clear-mallocSuccessSat Aug 18 01:25:04 20079
cm-debug-clear-malloc7SuccessMon Aug 20 01:22:30 20078
cm64SuccessSun Aug 19 01:24:52 20073
cm64-debugSuccessTue Aug 21 01:20:01 20076
cm64-debug-clear-mallocSuccessTue Feb 1 09:44:04 20053
rs6000-aix
cmSuccessWed Mar 4 01:07:19 20090
cm-debugSuccessMon Mar 2 01:06:08 20091
cm64SuccessWed Mar 4 01:07:19 20090
cm64-debugSuccessTue Mar 3 01:11:42 20091
x86_64-linux
cmSuccessSun Mar 6 00:01:03 20160
cm-debugSuccessSat Mar 5 00:01:13 20160

Testing status by file:


Html last generated: Sun Mar 6 05:50:21 2016

Input last modified: Thu Aug 14 10:03:13 2014


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