Example 5512: Inflation of an orthotropic trilinear prolate spheroid with fibres and sheets

A single prolate spheroidal element is defined with fibres oriented 65 degrees wrt the horizontal on the inside and -55 degrees wrt the horizontal on the outside. Sheet angles are defined as -45 degrees and +45 degrees at inner and outer nodes respectively. Geometry is interpolated isochorically (Focus^3.Cosh[lambda].Sinh^2[lambda]). Hydrostatic pressure is interpolated quadratically in Xi3 (element based) and the pole-zero law defines the incompressible material behaviour. The prolate is inflated with a pressure of 2kPa on the inside face while the the pressure is held at zero on the outside face.


The comfile run by this example is as follows:

#Example_5512  Inflation of an orthotropic prolate spheroid with fibres and sheets
 
fem
fem define coordinate;r;profib;example #Defines 3 GLOBAL PROLATE SPHEROIDAL
#                              !  coordinates.
#                              !  Transmural interpolation is in
#                              !  Focus^3.Cosh(Lamda).Sinh^2(Lamda).
fem define node;r;;example     #Focus = 37.5. Reads 4 NODES, 3 COORDS,
#                              !  1 VERSION per node per nj, 0
#                              !  DERIVATIVES for all coords. Nodal
#                              !  coordinates, Xj, are (lamda,mu,theta):
#                              !  1=(0.43,0,0);2=(0.43,120,0);
#                              !  3=(0.72,0,0); 4=(0.72,120,0).
fem define base;r;;example     #Defines 3 basis functions:
#                              !  1) Lagrange/Hermite with 3 Xi coords,
#                              !     Linear Lagrange interpolant and 1
#                              !     Gauss point in Xi1 dirctn (theta-
#                              !     circumferential) but 3 in Xi2 (mu-
#                              !     longitudinal) and Xi3 (lamda-
#                              !     transmural);
#                              !  2) An auxiliary basis with 5 auxiliary
#                              !     element parameters, pressure basis
#                              !     same number of Gauss points as for
#                              !     basis function 1, and polynomial
#                              !     degrees of: 0 for Xi1 and Xi2 for
#                              !     all 5 parameters; 0 in Xi3 for
#                              !     parameter 1; 1 for parameter 2; 2
#                              !     for parameter 3; -1 for parameter
#                              !     4 (Xi3=0 face pressure bc); & -2
#                              !     for parameter 5 (Xi3=1 face
#                              !     pressure bc).
#                              !  3) 2 Xi coords with linear Lagrange
#                              !     interpolant, and 3 Gauss points
#                              !     in Xi1 and Xi2 directions.
fem define element;r;;example  #Defines 1 prolate spheroidal element.
fem define fibre;r;;example    #Defines fibre angle orientation wrt Xi1
#                              !  direction (theta) in degrees. Uses
#                              !  basis 1 for fibre angle interpolation
#                              !  in all elements. No version prompts
#                              !  or derivs. Nodes 1,2 (inner nodes)
#                              !  are oriented at 65 degrees while the
#                              !  outer nodes 3,4 are -55 degrees from
#                              !  the axis. Defines sheet angles of -45 degrees
#                              !  at inner nodes 1,2 and +45
#                              !  degrees at outer nodes 3,4.
fem define element;r;;example fibre #Defines fibre elements.
fem define window;r;;example   #Defines window dimensions in X,Y,Z
#                              !  directions as (min,max):(-5,5),(-5,5),
#                              !  (-5,5).
fem draw lines                 #Makes line segments visible on window.
fem define equation;r;;example #Static 3D finite elasticity problem with
#                              !  geometric coords as the dependent
#                              !  variables. Solution is by Galerkin
#                              !  finite elements in a nonlinear
#                              !  analysis of a nonlinear equation.
#                              !  Incompressible material with basis 1
#                              !  in all elements for dep vars 1,2,3
#                              !  and basis 2 in all elements for dep
#                              !  var 4 (hydrostatic pressure).
fem define material;r;;example #Stresses in constitutive law are
#                              !  referred to body coords.  Defines a
#                              !  hyperelastic constitutive law for
#                              !  which the strain energy function, W,
#                              !  is a function of fibre/transverse
#                              !  strains that is pole-zero in strains
#                              !  with 16 constant constitutive law
#                              !  parameters. The Lagrangian strain
#                              !  components are referred to the
#                              !  undeformed fibre coordinate system
#                              !  where the 1-direction is aligned with
#                              !  fibre axis, 2-direction is the sheet
#                              !  axis (in the plane of the sheet,
#                              !  perpendicular to the fibres), and the
#                              !  3-direction is the sheet-normal coordinate.
fem define initial;r;;example  #Boundary pressure increments are entered
#                              !  and hydrostatic pressure is matched
#                              !  across boundaries with adjacent Xi3
#                              !  faces. Initial displacements are all
#                              !  zero. For dependent variable 2
#                              !  (mu-dirn) fix all nodes (1..4);
#                              !  Dependent variable 3 (theta-dirn),
#                              !  fix node 2. No force bcs.
#                              !  Dependent variable 4 (hyd press) fix
#                              !  element 1, parameter 4 (Xi3=0 face
#                              !  inside prolate) with increment
#                              !  magnitude 2, and parameter 5 (Xi3=1
#                              !  face outside prolate) with increment
#                              !  magnitude 0. No force bcs.
fem export nodes;heart1 field as heart #export the undeformed nodes
fem export elements;heart1 field as heart #export the undeformed elements
fem define solve;r;profib;example #  Read in solution information.
fem solve increment 0.2 iter 3 #Solve the problem.
#                              !Incrementing of the ventricular
#                              !  pressure is neccessary to avoid
#                              !  unstable solutions. This depends on
#                              !  the constitutive law and pressure
#                              !  the constitutive law and pressure
#                              !  magnitude, as the wall is gradually
#                              !  stiffened.
fem export nodes;heart2 field as heart #export the deformed nodes
fem export elements;heart2 field as heart #export the deformed elements
#
fem solve increment 0.3 iter 3 
fem export nodes;heart3 field as heart 
fem export elements;heart3 field as heart 
#                              
fem solve increment 0.5        
fem export nodes;heart4 field as heart
fem export elements;heart4 field as heart
#                              
#                              
#                              
fem draw lines def dotted      #Draw deformed mesh on window.
fem list strain at 1 ref       #List strain information wrt reference
#                              !  coordinates.
fem list stress at 1 ref       #List stress information wrt reference
#                              !  coordinates.
#
#
# Use the file view.com to view 3d animation in cmgui

Additional testing commands:

fem list stress at 1 ref
fem list strain at 1 ref

Files used by this example are:

Name               Modified     Size

example_5512.com 17-Dec-2002 7.2k heart1.exelem 10-Apr-2000 5.5k heart1.exnode 10-Apr-2000 1.2k heart2.exelem 10-Apr-2000 5.5k heart2.exnode 10-Apr-2000 1.2k heart3.exelem 10-Apr-2000 5.5k heart3.exnode 10-Apr-2000 1.2k heart4.exelem 10-Apr-2000 5.5k heart4.exnode 10-Apr-2000 1.2k junk.ipdata 10-Apr-2000 1.3k profib.ipbase 10-Apr-2000 4.2k profib.ipcoor 10-Apr-2000 707 profib.ipelem 10-Apr-2000 409 profib.ipelfb 10-Apr-2000 353 profib.ipequa 02-May-2004 2.0k profib.ipfibr 30-Jan-2001 1.3k profib.ipinit 12-Dec-2002 1.7k profib.ipmate 12-Dec-2002 5.7k profib.ipnode 10-Apr-2000 1.2k profib.ipshee 10-Apr-2000 781 profib.ipsolv 16-Aug-2010 2.3k profib.ipsolv.old 13-Apr-2007 2.1k profib.ipwind 10-Apr-2000 262 test_output.com 17-Dec-2002 50 view.com 10-Apr-2000 2.0k

Download the entire example:

Name                           Modified     Size

examples_5_55_551_5512.tar.gz 14-Aug-2014 12k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:02:02 20160
cm-debugSuccessSat Mar 5 00:02:19 20161
mips-irix
cmSuccessSun Aug 19 01:32:01 20075
cm-debugSuccessWed Aug 15 01:28:41 200712
cm-debug-clear-mallocSuccessSat Aug 18 01:35:43 200717
cm-debug-clear-malloc7SuccessMon Aug 20 01:31:55 200716
cm64SuccessSun Aug 19 01:32:08 20076
cm64-debugSuccessTue Aug 21 01:28:09 200714
cm64-debug-clear-mallocSuccessTue Feb 1 09:45:26 20057
rs6000-aix
cmSuccessWed Mar 4 01:08:41 20091
cm-debugSuccessMon Mar 2 01:07:57 20094
cm64SuccessWed Mar 4 01:08:41 20091
cm64-debugSuccessTue Mar 3 01:12:59 20093
x86_64-linux
cmSuccessSun Mar 6 00:01:03 20160
cm-debugSuccessSat Mar 5 00:01:14 20160

Testing status by file:


Html last generated: Sun Mar 6 05:50:24 2016

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


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