Example 524: 10% uniaxial extension of a unit cube with fibres (0 degrees)

A 3D unit cube of incompressible transversely isotropic material (exponential material law) where the fibre direction is aligned with the X axis, is displacement loaded on the X=1 face by 10% in the X direction while keeping the X=0 face fixed (uniaxial extension).

The comfile run by this example is as follows:

#Example_524  10% uniaxial extension of a unit cube with fibres (0 degrees)
              #The problems in this set investigate the effects of
              #adding fibres in different orientations with respect
              #to the applied extension.
 
fem
fem define coordinates;r;unifib0;example #Defines 3D rectangular cartesian.
fem define node;r;;example            #Defines 8 nodes.
fem define base;r;;example	      #Defines 3 basis functions.
fem define element;r;;example         #Defines 1 element.
fem define fibre;r;;example           #Define fibre orientations in the 1-2
#                                 !  plane wrt Xi 1 coordinate.  For all 8
#                                 !  nodes with
#                                 !  NO VERSION prompting and 0
#                                 !  DERIVATIVES for the fibre angle,
#                                 !  enter fibre angles as 0 degrees.
fem define element;r;;example fibre  #Define the fibre elements. Enter
#                                 !  angles in DEGREES and define the
#                                 !  basis function for the fibre angle
#                                 !  to be the SAME for each element and
#                                 !  use BASIS 1.
fem define window
fem draw lines
fem draw fibres
fem define equation;r;;example        #Read in equation information.
fem define material;r;;example	  #Stresses in the constitutive law are
#               !  referred to FIBER/TRANSVERSE coordinates.
#               !  Choose a HYPERELASTIC CONSTITUTIVE LAW for which the
#               !  strain energy function, W, is an EXPONENTIAL function
#               !  of FIBRE/TRANSVERSE STRAINS (Ef,Es,En)that has
#               !  5 CONSTANT PARAMETERS: W=alpha(1)*exp(Q) where
#               !  Q=2*alpha(2)*(Ef+Es+En)+alpha(3)*(Ef^2)+
#               !    alpha(4)*(Es^2+En^2+2*Esn^2)+2*alpha(5)*(Efs^2+Enf^2)
#               !  and the constants alpha(i) are: alpha(1)=1,
#               !  alpha(2)=5, alpha(3)=10, alpha(4)=0, alpha(5)=5.
#
fem define initial;r;;example         #Defines initial conditions.
fem define solve;r;;example           #Defines solution information.
fem solve step 1 error 1.D-10     #Solve the problem.
fem list initial                  #Note the Lagrange multiplier, p=-2.922
#                                 !  ie. hydrostatic pressure=0.5p=-1.461.
fem draw line deformed dotted
fem list strain at 1 ref     #List strain information wrt reference
#                            !  coordinates at 1st gauss point. Stretch
#                            !  ratios: lamda(1)=1.1, lamda(2)=lamda(3)
#                            !  =0.9535. Lagrangian strains:
#                            !  E11=0.105, E22=E33=-0.04545.
fem list stress at 1 ref     #List stress information wrt reference
#                            !  coordinates at 1st gauss point.  Cauchy
#                            !  stress in the Xi 1 direction, T11=3.567
#                            !  and should be the only nonzero stress
#                            !  component.
#
#                !The strains are the same as in the 10% uniaxial
#                !  extension problem because the material properties
#                !  chosen (1st two constants) were the same.  The
#                !  material, however, is no longer isotropic, but since
#                !  no shearing occurs, the stiffness in the transverse
#                !  direction being different from the fibre direction
#                !  does not affect the strains.  Although the strain
#                !  values are the same, the stress is different because
#                !  the material is anisotropic.  Here, the fibre
#                !  direction is the X-direction because the fibres are
#                !  oriented 0 degrees wrt X-axis.

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_524.com     10-Apr-2000  3.7k
test.com            10-Apr-2000  3.7k
test_output.com     10-Apr-2000  132 
unifib0.ipbase      10-Apr-2000  3.5k
unifib0.ipcoor      10-Apr-2000  633 
unifib0.ipelem      10-Apr-2000  471 
unifib0.ipelfb      10-Apr-2000  275 
unifib0.ipequa      02-May-2004  2.1k
unifib0.ipfibr      30-Jan-2001  1.1k
unifib0.ipinit      05-Dec-2002  2.9k
unifib0.ipmate      13-Oct-2003  3.0k
unifib0.ipnode      10-Apr-2000  1.9k
unifib0.ipsolv      16-Aug-2010  2.4k
unifib0.ipsolv.old  13-Apr-2007  2.2k

Download the entire example:

Name                      Modified     Size


examples_5_52_524.tar.gz  14-Aug-2014  7.8k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:01:57 20160
cm-debugSuccessSat Mar 5 00:02:14 20160
mips-irix
cmSuccessSun Aug 19 01:24:57 20073
cm-debugSuccessWed Aug 15 01:22:43 20075
cm-debug-clear-mallocSuccessSat Aug 18 01:25:56 200710
cm-debug-clear-malloc7SuccessMon Aug 20 01:24:11 20079
cm64SuccessSun Aug 19 01:23:27 20073
cm64-debugSuccessTue Aug 21 01:20:55 20076
cm64-debug-clear-mallocSuccessTue Feb 1 09:44:13 20053
rs6000-aix
cmSuccessWed Mar 4 01:07:20 20090
cm-debugSuccessMon Mar 2 01:06:20 20091
cm64SuccessWed Mar 4 01:07:20 20090
cm64-debugSuccessTue Mar 3 01:11:43 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 05:50:22 2016

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

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