A single prolate. 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 then contracted isovolumically with differing fibre angles. The relationship between fibre angles and stress is plotted.
# Example 5535
# A single axisymetric prolate LV model is used to investigate
# the local feedback mechanisms affecting the fibre
# orientation.
# (Tissue Remodelling with Micro Structurally Based
# Material Laws, Peter Hunter & Theo Arts 1997)
#
# Muscle Fibre Orientation
# PROBLEM_1: Sheet angles are all zero, fibre angles are zero at
# the apex nodes, -90 at the endocardial base, and the
# epicardial base node fibre angle is varied from 20 to 90 degs.
# PROBLEM_2: Endocardial sheet angles are -45 epicardial are 45,
# Endocardial fibre angles are 65 epicardial
# are varied from -20 to -90 degs.
$TRUE = 1
$FALSE = 0
# Choose which problem to run
$PROBLEM_1 = $TRUE
$PROBLEM_2 = $FALSE
$MIN_ANGLE = 20
$MAX_ANGLE = 90
$INC_ANGLE = 10
system "rm plot.dat"
set echo
for ($ANGLE=$MIN_ANGLE;$ANGLE<=$MAX_ANGLE;$ANGLE+=$INC_ANGLE)
{
print "\n\n\n\$ANGLE = $ANGLE\n";
fem
fem define parameters;r;profib;example
fem define coordinate;r;profib;example #Defines 3 GLOBAL PROLATE SPHEROIDAL
# ! coordinates.
# ! Transmural interpolation is in
# ! Focus^3.Cosh(Lamda).Sinh^2(Lamda).
fem define node;r;;example #Focus = 37.5. Reads 4 NODES, 3 COORDS,
# ! 1 VERSION per node per nj, 0
# ! DERIVATIVES for all coords. Nodal
# ! coordinates, Xj, are (lamda,mu,theta):
# ! 1=(0.43,0,0);2=(0.43,120,0);
# ! 3=(0.72,0,0); 4=(0.72,120,0).
fem define base;r;;example #Defines 3 basis functions:
# ! 1) Lagrange/Hermite with 3 Xi coords,
# ! Linear Lagrange interpolant and 1
# ! Gauss point in Xi1 dirctn (theta-
# ! circumferential) but 3 in Xi2 (mu-
# ! longitudinal) and Xi3 (lamda-
# ! transmural);
# ! 2) An auxiliary basis with 5 auxiliary
# ! element parameters, pressure basis
# ! same number of Gauss points as for
# ! basis function 1, and polynomial
# ! degrees of: 0 for Xi1 and Xi2 for
# ! all 5 parameters; 0 in Xi3 for
# ! parameter 1; 1 for parameter 2; 2
# ! for parameter 3; -1 for parameter
# ! 4 (Xi3=0 face pressure bc); & -2
# ! for parameter 5 (Xi3=1 face
# ! pressure bc).
# ! 3) 2 Xi coords with linear Lagrange
# ! interpolant, and 3 Gauss points
# ! in Xi1 and Xi2 directions.
fem define element;r;;example #Defines 1 prolate spheroidal element.
set echo
if($PROBLEM_1)
{
fem define fibre;r;problem_1/profib$ANGLE;example
} elsif($PROBLEM_2)
{
fem define fibre;r;problem_2/profib$ANGLE;example
}
set echo
# #Defines fibre angle orientation wrt Xi1
# ! direction (theta) in degrees.
# ! degrees at outer nodes 3,4.
fem define element;r;profib;example fibre #Defines fibre elements.
fem define window #Defines window
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.
#
#
# INFLATION
#
#
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 1, and parameter 5 (Xi3=1
# ! face outside prolate) with increment
# ! magnitude 0. No force bcs.
fem define solve;r;profib;example # Read in solution information.
fem solve increment 0.2 iter 8 #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 solve increment 0.3 iter 8
fem solve increment 0.5
#
#
#
fem draw lines def dotted #Draw deformed mesh on window.
fem def initial;w;profib_def
fem eval reac
# ############################################
# Inflated solution is converged OK!
# ############################################
#
#
# COUPLING SET UP
#
#
$WALL = 1
$CAVITY = 2
#
# Set up cavity region geometry
fem define region;r;coupled;example
fem define coord;r;cavity;example region $CAVITY
#
fem define;add base;r;cavity;example
fem define node;r;cavity;example region $CAVITY
fem define element;r;cavity;example region $CAVITY
#
# Set up equations, material properties and initial conditions
# for cavity region
fem define equation;r;coupled;example region $WALL,$CAVITY lock
fem define material;r;cavity_isovol;example region $CAVITY
fem define initial;r;cavity;example region $CAVITY
#
# Define cavity-to-wall coupling and solution procedure information
fem define coupling;r;coupled;example
fem define solve;r;coupled;example coupled region $WALL,$CAVITY
#
# Transfer wall deformation from the inflation problem to
# geometric dependent variables for the cavity region
fem update solution coupled source_region $WALL
#
# Set up the reference state for the cavity region to be the deformed
# configuration from the inflation problem. To set up the
# 'inflated cavity', the x-coord ('in 1' represents the 1st RC coord)
# for the central cavity node (node 6) is set to the average of the
# x-coords for the adjacent interface nodes (node 2 - this could
# be a list of nodes)
fem update solution cavity_reference average 6 in 1 node 2 region $CAVITY
#
# List undeformed (pre-inflation) and inflated cavity volumes
fem list element total region $CAVITY
fem list element deformed total region $CAVITY
# ############################################
# cavity volume inflated from 40ml to 60ml.
# ############################################
#
fem draw lines region $WALL,$CAVITY
fem draw lines dot def region $WALL,$CAVITY
#
# Check that the current coupled solution is converged (as expected!)
fem evaluate residuals wrt geom_params coupled
# ############################################
# inflated state is a converged solution for the coupled problem!
# ############################################
#
#
# ISOVOLUMIC CONTRACTION
#
#
# Increment intracell calcium conc and solve for isovolumic contraction
fem define material;r;profib_active;example
if($PROBLEM_1)
{
fem define active;r;problem_1/profib_contract_Ca20;example
} elsif($PROBLEM_2)
{
fem define active;r;problem_2/profib_contract_Ca10;example
}
fem solve coupled increment 0.0
# ############################################
# Converged solution for the coupled wall/cavity problem.
# ############################################
#fem define initial;r;profib_endisovolcontr region WALL,CAVITY
#
# Save deformed configurations for end ejection
fem define initial;w;profib_endisovolcontr region $WALL,$CAVITY
#
fem draw lines deformed dotted rgb=blue region $WALL,$CAVITY
#
# Check that cavity volume has not changed
fem list element deformed total region $CAVITY
# ############################################
# This contraction phase was indeed isovolumic!
# ############################################
#
#
# POSTPROCESSING, VISUALISATION & PLOTTING
#
#
fem export nodes;heart$ANGLE as heart
fem export elements;heart$ANGLE as heart
fem export gauss;heart$ANGLE as gauss
fem evaluate field;fibre_angles$ANGLE geometric gauss # get fibre & sheet angles
fem list stress;stresses$ANGLE fibre # get stresses
system "echo \"\# Fibre angle ${ANGLE} degrees\" >> plot.dat"
system "awk -v angle=${ANGLE} -f ${example}extract_fibre_angles_stress.awk ${example}elements.txt fibre_angles${ANGLE}.opfiel stresses${ANGLE}.opstre >> plot.dat"
}
system "gnuplot ${example}angle_stress.gnu"
fem list initial region $WALL,$CAVITY
Name Modified Size
example_5535.com 07-Jul-2003 11k angle_stress.gnu 10-Apr-2000 1.3k cavity.ipbase 10-Apr-2000 1.1k cavity.ipcoor 10-Apr-2000 707 cavity.ipelem 10-Apr-2000 404 cavity.ipinit 12-Dec-2002 1.4k cavity.ipnode 10-Apr-2000 1.3k cavity_eject.ipmate 10-Apr-2000 386 cavity_isovol.ipmate 10-Apr-2000 390 coupled.ipcoup 21-Aug-2002 437 coupled.ipcoup.old 10-Apr-2000 386 coupled.ipregi 10-Apr-2000 94 coupled.irequa 02-May-2004 3.8k coupled.irsolv 16-Aug-2010 3.1k coupled.irsolv.old 13-Apr-2007 2.9k elements.txt 10-Apr-2000 2 extract_fibre_angles_stress.awk 10-Apr-2000 2.4k extract_fibre_wall_strains.awk 10-Apr-2000 2.7k problem_1/ 03-Mar-2004 - problem_2/ 03-Mar-2004 - profib.ipacti 03-Mar-2004 735 profib.ipbase 10-Apr-2000 4.2k profib.ipcoor 10-Apr-2000 707 profib.ipelem 10-Apr-2000 409 profib.ipelfb 10-Apr-2000 349 profib.ipelfd 10-Apr-2000 276 profib.ipequa 02-May-2004 2.0k profib.ipfibr 30-Jan-2001 1.3k profib.ipfiel 10-Apr-2000 601 profib.ipfit 13-Apr-2007 1.5k profib.ipinit 12-Dec-2002 1.8k profib.ipmate 12-Dec-2002 5.7k profib.ipnode 10-Apr-2000 1.2k profib.ippara 12-Nov-2002 5.9k profib.ipsolv 16-Aug-2010 2.3k profib.ipsolv.old 13-Apr-2007 2.1k profib.ipwind 10-Apr-2000 262 profib_active.ipmate 12-Dec-2002 6.2k profib_contract.ipacti 03-Mar-2004 717 profib_def.ipinit 12-Dec-2002 6.2k profib_endeject.irinit 12-Dec-2002 11k profib_endisovolcontr.irinit 12-Dec-2002 11k prol.ippara 12-Nov-2002 5.9k test_output.com 20-Nov-2001 38 view.com 20-Nov-2001 3.2k
Name Modified Size
examples_5_55_553_5535.tar.gz 17-Aug-2010 24k
| Status | Tested | Real time (s) | |
| i686-linux | |||
| cm | Failure | Sun Mar 6 00:31:22 2016 | 15 |
| last break | Tue Aug 12 00:37:00 2014 | 28 | |
| last success | Sun Apr 17 01:02:00 2011 | 31 | |
| cm-debug | Failure | Sun Mar 6 00:46:00 2016 | 30 |
| last break | Tue Aug 12 00:40:00 2014 | 47 | |
| last success | Thu Apr 7 01:10:00 2011 | 54 | |
| mips-irix | |||
| cm | Success | Sun Aug 19 03:01:05 2007 | 99 |
| cm-debug | Success | Wed Aug 15 03:11:35 2007 | 260 |
| cm-debug-clear-malloc | Success | Sat Aug 18 03:44:28 2007 | 298 |
| cm-debug-clear-malloc7 | Success | Mon Aug 20 03:45:44 2007 | 301 |
| cm64 | Success | Sun Aug 19 03:03:38 2007 | 116 |
| cm64-debug | Success | Tue Aug 21 04:13:40 2007 | 267 |
| cm64-debug-clear-malloc | Success | Fri May 20 10:36:11 2005 | 146 |
| rs6000-aix | |||
| cm | Success | Wed Mar 4 01:15:21 2009 | 13 |
| cm-debug | Success | Mon Mar 2 01:28:40 2009 | 81 |
| cm64 | Success | Wed Mar 4 01:16:01 2009 | 13 |
| cm64-debug | Success | Tue Mar 3 01:32:30 2009 | 75 |
| x86_64-linux | |||
| cm | Failure | Sun Mar 6 00:02:17 2016 | 7 |
| last break | Tue Aug 12 00:19:00 2014 | 10 | |
| last success | Sun Apr 17 00:30:00 2011 | 11 | |
| cm-debug | Failure | Sun Mar 6 00:03:52 2016 | 14 |
| last break | Tue Aug 12 00:40:00 2014 | 18 | |
| last success | Fri Apr 8 00:13:00 2011 | 19 |
| 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. |
| i686-linux | |||
| Failure | cm: | ndiff test: significant differences with generic answer. | |
| Failure | cm-debug: | ndiff test: 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 | |||
| Failure | cm: | ndiff test: significant differences with generic answer. | |
| Failure | cm-debug: | ndiff test: significant differences with generic answer. |
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