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:

Testing status by file:

• cmiss_test.log
  

  i686-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  mips-irix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc7:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  Success	cm64-debug-clear-malloc:	cmiss_test.log.retain.
  rs6000-aix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  x86_64-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.

  
  
• cmiss_test.out
  

  i686-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  mips-irix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  rs6000-aix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  x86_64-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.

  
  

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

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