Example 844: single cylindrical element finite elasticity problem coupled to coronary mesh

This example illustrates the solution to the coupled flow/solid mechanics problem. An eleven-element (linear in polar-cylindrical coordinate system) asymmetric coronary mesh is embedded within a homogeneous Mooney Rivlin cylinder with finite wall thickness. The cylinder is inflated and subject to an axial compressive force in the Z-direction in steps over a period of 0.005s. The transient flow equations are solved incorporating the additional force exerted on the embedded vessels walls due to the deformation of the cylinder. The fluid flow pressure at the inlet of the network is increased from 10.6 - 14.6 kPa linearly over the same period while the pressure at the exit or distal ends of all the daughter links are maintained constant at 10.6 kPa. For the theory and further details of this problem, see section 5.4 of the PhD thesis "Coronary flow mechanics" by N.P.Smith.

Simulation of coupled flow/solid mechanics

The comfile run by this example is as follows:

# Note : region 1 - solid: a cylinder with finite thickness; region 2 - fluid flow
#        class 1 - Finite elasticity problem ; class 2 - Flow through elastic tube

fem define para;r;cylinder_flow_mech;example
fem reallocate
fem define region;r;cylinder_flow_mech;example              # Defines no. of regions
fem define coordinate;r;cylinder_mech;example reg 1         # Defines coordinates for solid         
fem define node;r;cylinder_mech;example reg 1               # Reads in nodal information                
fem define base;r;cylinder_mech;example reg 1               # Defines basis functions (05)                
fem define element;r;cylinder_mech;example reg 1            # Reads in element information            
fem define fibre;r;cylinder_mech;example reg 1              # Reads in fibre information for solid  
fem define element;r;cylinder_mech;example fib reg 1        # Defines fibre interpolation          
fem define equation;r;cylinder_mech;example reg 1 class 1   # Defines equations for solid 
fem define material;r;cylinder_mech;example reg 1 class 1   # Reads in mech properties of solid   
fem define initial;r;cylinder_mech;example reg 1 class 1    # Defines initial & boundary conds.        
fem define solve;r;cylinder_mech;example reg 1 class 1      # Defines solution parameters     

fem define coordinate;r;cylinder_flow;example reg 2         # Defines coordinates for fluid flow        
fem define node;r;cylinder_flow;example reg 2               # Reads in nodal information                
fem define;add base;r;cylinder_flow;example                 # Defines basis functions (01)               
fem define element;r;cylinder_flow;example reg 2            # Reads in element information           

fem define xi;r;cylinder_flow;example node of 2 in 1        # Reads in xi positions of reg 2 wrt reg 1
fem update mesh position of 2 in 1 undeform                 # Updates relative positions

fem define field;r;cylinder_flow;example reg 2              # Reads in field information 
fem define element;r;cylinder_flow;example field reg 2      # Defines field interpolation       
fem define grid;r;cylinder_flow;example coronary reg 2      # Reads in spatial discretisation    
fem update grid geometry reg 2                              # Updates grid point coordinates 
fem define equation;r;cylinder_flow;example reg 2 class 2   # Defines equations for fluid flow  
fem define material;r;cylinder_flow;example reg 2 class 2   # Reads in phy. & mech. properties      
fem update material field material 4 no_field 1 reg 2 class 2
#                                                           # Updates unstressed radii
fem define time;r;cylinder_flow;example                     # Defines boundary conditions   
fem define initial;r;cylinder_flow;example reg 2 class 2    # Defines initial conditions                   
fem define solve;r;cylinder_flow;example reg 2 class 2      # Defines solution parameters                  

fem define coup;r;cylinder_flow_mech;example                # Defines solid & fluid mech. coupling                                     
$time_initial=0.000;
$time_final=0.005;
$time_step=0.0001;   
$write_out_period=0.0005;

fem export nodes;solid${time_initial} field as solid offset 500 reg 1 class 1
fem export elements;solid field as solid offset_elem 500 offset_node 500 reg 1 class 1 
fem export grid;fluid as flow offset_elem 0 offset_node 0 elastic_tube reg 2 class 2
fem export points;fluid${time_initial} grid as flow offset 0 reg 2 class 2

for ($time=$time_initial;$time<$time_final;$time=$time+$write_out_period)      
{
$w_time=$time+$write_out_period;
fem solve restart to $write_out_period delta_t $time_step reg 1,2 class 1,2;
fem update geometry from solution reg 1;
fem export nodes;solid${w_time} field as solid offset 500 reg 1 class 1;
fem update nodes derivative 1 linear reg 2 
fem update mesh position of 2 in 1 undeform
fem update grid geometry reg 2
fem export points;fluid${w_time} grid as flow offset 0 reg 2 class 2
}

Additional testing commands:

fem list nodes reg 2
fem list elem reg 2

Files used by this example are:

Name                           Modified     Size


example_844.com                02-Oct-2001  3.9k
cylinder_flow.ipbase           02-Oct-2001  929 
cylinder_flow.ipcoor           02-Oct-2001  681 
cylinder_flow.ipelem           02-Oct-2001  3.5k
cylinder_flow.ipelfd           02-Oct-2001  2.8k
cylinder_flow.ipequa           22-Nov-2005  1.3k
cylinder_flow.ipfiel           02-Oct-2001  3.0k
cylinder_flow.ipgrid           27-Nov-2001  258 
cylinder_flow.ipinit           01-Dec-2005  713 
cylinder_flow.ipmate           02-Oct-2001  6.8k
cylinder_flow.ipnode           02-Oct-2001  2.5k
cylinder_flow.ipsolv           27-Aug-2002  801 
cylinder_flow.iptime           02-Oct-2001  1.4k
cylinder_flow.ipxi             02-Oct-2001  792 
cylinder_flow_mech.ipcoup      21-Aug-2002  730 
cylinder_flow_mech.ipcoup.old  02-Oct-2001  704 
cylinder_flow_mech.ippara      12-Nov-2002  5.9k
cylinder_flow_mech.ipregi      02-Oct-2001  136 
cylinder_mech.ipbase           02-Oct-2001  6.8k
cylinder_mech.ipcoor           02-Oct-2001  681 
cylinder_mech.ipelem           02-Oct-2001  1.0k
cylinder_mech.ipelfb           02-Oct-2001  393 
cylinder_mech.ipequa           02-May-2004  2.1k
cylinder_mech.ipfibr           02-Oct-2001  1.4k
cylinder_mech.ipinit           12-Dec-2002  8.6k
cylinder_mech.ipmate           12-Dec-2002  2.3k
cylinder_mech.ipnode           02-Oct-2001  2.2k
cylinder_mech.ipsolv           16-Aug-2010  2.4k
cylinder_mech.ipsolv.old       13-Apr-2007  2.2k
fluid.exelem                   02-Oct-2001   30k
fluid0.0005.exnode             02-Oct-2001   22k
fluid0.001.exnode              02-Oct-2001   22k
fluid0.0015.exnode             02-Oct-2001   22k
fluid0.002.exnode              02-Oct-2001   22k
fluid0.0025.exnode             02-Oct-2001   22k
fluid0.003.exnode              02-Oct-2001   22k
fluid0.0035.exnode             02-Oct-2001   22k
fluid0.004.exnode              02-Oct-2001   22k
fluid0.0045.exnode             02-Oct-2001   22k
fluid0.005.exnode              02-Oct-2001   22k
fluid0.exnode                  02-Oct-2001   22k
solid.exelem                   02-Oct-2001  6.9k
solid0.0005.exnode             02-Oct-2001  1.6k
solid0.001.exnode              02-Oct-2001  1.6k
solid0.0015.exnode             02-Oct-2001  1.6k
solid0.002.exnode              02-Oct-2001  1.6k
solid0.0025.exnode             02-Oct-2001  1.6k
solid0.003.exnode              02-Oct-2001  1.6k
solid0.0035.exnode             02-Oct-2001  1.6k
solid0.004.exnode              02-Oct-2001  1.6k
solid0.0045.exnode             02-Oct-2001  1.6k
solid0.005.exnode              02-Oct-2001  1.6k
solid0.exnode                  02-Oct-2001  1.6k
test_output.com                02-Oct-2001   41

Download the entire example:

Name                      Modified     Size


examples_8_84_844.tar.gz  17-Aug-2010  503k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:02:17 20162
cm-debugSuccessSat Mar 5 00:14:29 20166
mips-irix
cmSuccessSun Aug 19 01:52:08 200723
cm-debugSuccessWed Aug 15 01:56:13 200773
cm-debug-clear-mallocSuccessSat Aug 18 02:17:53 2007131
cm-debug-clear-malloc7SuccessMon Aug 20 02:15:25 200791
cm64SuccessSun Aug 19 01:52:59 200724
cm64-debugSuccessTue Aug 21 01:56:30 200776
cm64-debug-clear-mallocSuccessThu Apr 1 10:50:40 200434
rs6000-aix
cmSuccessWed Mar 4 01:09:38 20093
cm-debugSuccessMon Mar 2 01:14:31 200923
cm64SuccessWed Mar 4 01:09:40 20094
cm64-debugSuccessTue Mar 3 01:19:18 200923
x86_64-linux
cmSuccessSun Mar 6 00:01:10 20162
cm-debugSuccessSat Mar 5 00:01:53 20164

Testing status by file:

Html last generated: Sun Mar 6 05:50:33 2016

Input last modified: Mon Aug 16 11:22:35 2010

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