DEMO_febio_0019_vessel_pressure_inflate
Below is a demonstration for:
- Building geometry for a cylindrical vessel with tetrahedral elements
- Defining the boundary conditions
- Coding the febio structure
- Running the model
- Importing and visualizing the displacement results
Contents
- Keywords
- Plot settings
- Control parameters
- Creating model boundary polygons
- Creating model boundary surfaces
- Tetrahedral meshing of vessel
- Defining the boundary conditions
- Defining the FEBio input structure
- Quick viewing of the FEBio input file structure
- Exporting the FEBio input file
- Running the FEBio analysis
- Import FEBio results
Keywords
- febio_spec version 3.0
- febio, FEBio
- vessel, cylinder
- prescribed pressure
- tetrahedral elements, tet4
- tube, cylindrical
- static, solid
- hyperelastic, Ogden
- displacement logfile
- stress logfile
clear; close all; clc;
Plot settings
fontSize=20; faceAlpha1=0.8; markerSize=40; markerSize2=20; lineWidth=3;
Control parameters
% Path names defaultFolder = fileparts(fileparts(mfilename('fullpath'))); savePath=fullfile(defaultFolder,'data','temp'); % Defining file names febioFebFileNamePart='tempModel'; febioFebFileName=fullfile(savePath,[febioFebFileNamePart,'.feb']); %FEB file name febioLogFileName=[febioFebFileNamePart,'.txt']; %FEBio log file name febioLogFileName_disp=[febioFebFileNamePart,'_disp_out.txt']; %Log file name for exporting displacement %Specifying geometry parameters pointSpacing=1; radiusOuter1=10; radiusInner1=9; radiusOuter2=9; radiusInner2=7; vesselLength=60; %Load appliedPressure=5e-3; %Material parameter set c1=0.03; %Shear-modulus-like parameter m1=2; %Material parameter setting degree of non-linearity k_factor=1e2; %Bulk modulus factor k=c1*k_factor; %Bulk modulus % FEA control settings numTimeSteps=10; %Number of time steps desired max_refs=25; %Max reforms max_ups=0; %Set to zero to use full-Newton iterations opt_iter=12; %Optimum number of iterations max_retries=10; %Maximum number of retires dtmin=(1/numTimeSteps)/100; %Minimum time step size dtmax=1/numTimeSteps; %Maximum time step size
Creating model boundary polygons
nRad=round((2*pi*mean([radiusOuter1 radiusOuter2]))/pointSpacing); %Number of radial steps t=linspace(0,2*pi,nRad)'; %Angles t=t(1:end-1); %take away last which equals start v1_Outer=[-(vesselLength/2)*ones(size(t)) radiusOuter1*sin(t) radiusOuter1*cos(t)]; %Circular coordinates t=linspace(0,2*pi,nRad)'; %Angles t=t(1:end-1); %take away last which equals start v2_Outer=[(vesselLength/2)*ones(size(t)) radiusOuter2*sin(t) radiusOuter2*cos(t)]; %Circular coordinates nRad=round((2*pi*mean([radiusInner1 radiusInner2]))/pointSpacing); %Number of radial steps t=linspace(0,2*pi,nRad)'; %Angles t=t(1:end-1); %take away last which equals start v1_Inner=[-(vesselLength/2)*ones(size(t)) radiusInner1*sin(t) radiusInner1*cos(t)]; %Circular coordinates t=linspace(0,2*pi,nRad)'; %Angles t=t(1:end-1); %take away last which equals start v2_Inner=[(vesselLength/2)*ones(size(t)) radiusInner2*sin(t) radiusInner2*cos(t)]; %Circular coordinates
Plotting model boundary polygons
cFigure; hold on; title('Model boundary polygons','FontSize',fontSize); plotV(v1_Outer,'r.-') plotV(v1_Inner,'g.-') plotV(v2_Outer,'b.-') plotV(v2_Inner,'y.-') axisGeom(gca,fontSize); drawnow;

Creating model boundary surfaces
% controlStructLoft.numSteps=17; controlStructLoft.closeLoopOpt=1; controlStructLoft.patchType='tri'; %Meshing outer surface [F1,V1]=polyLoftLinear(v1_Outer,v2_Outer,controlStructLoft); F1=fliplr(F1); %Invert orientation %Meshing inner surface [F2,V2]=polyLoftLinear(v1_Inner,v2_Inner,controlStructLoft); %Meshing left [F3,V3]=regionTriMesh3D({v1_Outer,v1_Inner},pointSpacing,0,'linear'); F3=fliplr(F3); %Invert orientation %Meshing right [F4,V4]=regionTriMesh3D({v2_Outer,v2_Inner},pointSpacing,0,'linear'); %Merging surface sets [Fv,Vv,Cv]=joinElementSets({F1,F2,F3,F4},{V1,V2,V3,V4}); [Fv,Vv]=mergeVertices(Fv,Vv); Fv=fliplr(Fv);
Plotting model boundary surfaces
cFigure; hold on; title('Model boundary surfaces','FontSize',fontSize); gpatch(Fv,Vv,Cv); % patchNormPlot(Fv,Vv); icolorbar; colormap(gjet(4)); axisGeom(gca,fontSize); camlight headlight; drawnow;

Tetrahedral meshing of vessel
faceBoundaryMarker=Cv; [V_regions]=getInnerPoint(Fv,Vv); [regionA]=tetVolMeanEst(Fv,Vv); %Volume for regular tets stringOpt='-pq1.2AaY'; inputStruct.stringOpt=stringOpt; inputStruct.Faces=Fv; inputStruct.Nodes=Vv; inputStruct.holePoints=[]; inputStruct.faceBoundaryMarker=faceBoundaryMarker; %Face boundary markers inputStruct.regionPoints=V_regions; %region points inputStruct.regionA=regionA; inputStruct.minRegionMarker=2; %Minimum region marker % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 11-Dec-2020 12:22:35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 11-Dec-2020 12:22:35 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 11-Dec-2020 12:22:35 --- Running TetGen to mesh input boundary--- 11-Dec-2020 12:22:35 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.474423 Creating surface mesh ... Surface mesh seconds: 0.013527 Recovering boundaries... Boundary recovery seconds: 0.039334 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.01613 Recovering Delaunayness... Delaunay recovery seconds: 0.012089 Refining mesh... Refinement seconds: 0.111095 Optimizing mesh... Optimization seconds: 0.00742 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.125806 Total running seconds: 0.800328 Statistics: Input points: 6565 Input facets: 13130 Input segments: 19695 Input holes: 0 Input regions: 1 Mesh points: 9848 Mesh tetrahedra: 40525 Mesh faces: 87615 Mesh faces on exterior boundary: 13130 Mesh faces on input facets: 13130 Mesh edges on input segments: 19695 Steiner points inside domain: 3283 --- Done --- 11-Dec-2020 12:22:36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 11-Dec-2020 12:22:36 --- Done --- 11-Dec-2020 12:22:36
Access model element and patch data
Fb=meshOutput.facesBoundary; Cb=meshOutput.boundaryMarker; V=meshOutput.nodes; CE=meshOutput.elementMaterialID; E=meshOutput.elements;
Visualizing mesh using meshView, see also anim8
meshView(meshOutput,[]);

Defining the boundary conditions
The visualization of the model boundary shows colors for each side of the cube. These labels can be used to define boundary conditions.
%Define supported node set bcSupportList=unique(Fb(ismember(Cb,[3 4]),:)); %Node set part of selected face F_pressure=fliplr(Fb(Cb==2,:));
Visualizing boundary conditions. Markers plotted on the semi-transparent model denote the nodes in the various boundary condition lists.
hf=cFigure; title('Boundary conditions','FontSize',fontSize); xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on; gpatch(Fb,V,'kw','k',0.5); hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize); hl(2)=gpatch(F_pressure,V,'rw','r',0.5); legend(hl,{'BC support','Pressure surface'}); axisGeom(gca,fontSize); camlight headlight; drawnow;

Defining the FEBio input structure
See also febioStructTemplate and febioStruct2xml and the FEBio user manual.
%Get a template with default settings [febio_spec]=febioStructTemplate; %febio_spec version febio_spec.ATTR.version='3.0'; %Module section febio_spec.Module.ATTR.type='solid'; %Control section febio_spec.Control.analysis='STATIC'; febio_spec.Control.time_steps=numTimeSteps; febio_spec.Control.step_size=1/numTimeSteps; febio_spec.Control.solver.max_refs=max_refs; febio_spec.Control.solver.max_ups=max_ups; febio_spec.Control.time_stepper.dtmin=dtmin; febio_spec.Control.time_stepper.dtmax=dtmax; febio_spec.Control.time_stepper.max_retries=max_retries; febio_spec.Control.time_stepper.opt_iter=opt_iter; %Material section materialName1='Material1'; febio_spec.Material.material{1}.ATTR.name=materialName1; febio_spec.Material.material{1}.ATTR.type='Ogden'; febio_spec.Material.material{1}.ATTR.id=1; febio_spec.Material.material{1}.c1=c1; febio_spec.Material.material{1}.m1=m1; febio_spec.Material.material{1}.c2=c1; febio_spec.Material.material{1}.m2=-m1; febio_spec.Material.material{1}.k=k; %Mesh section % -> Nodes febio_spec.Mesh.Nodes{1}.ATTR.name='nodeSet_all'; %The node set name febio_spec.Mesh.Nodes{1}.node.ATTR.id=(1:size(V,1))'; %The node id's febio_spec.Mesh.Nodes{1}.node.VAL=V; %The nodel coordinates % -> Elements partName1='Part1'; febio_spec.Mesh.Elements{1}.ATTR.name=partName1; %Name of this part febio_spec.Mesh.Elements{1}.ATTR.type='tet4'; %Element type febio_spec.Mesh.Elements{1}.elem.ATTR.id=(1:1:size(E,1))'; %Element id's febio_spec.Mesh.Elements{1}.elem.VAL=E; %The element matrix % -> Surfaces surfaceName1='LoadedSurface'; febio_spec.Mesh.Surface{1}.ATTR.name=surfaceName1; febio_spec.Mesh.Surface{1}.tri3.ATTR.id=(1:1:size(F_pressure,1))'; febio_spec.Mesh.Surface{1}.tri3.VAL=F_pressure; % -> NodeSets nodeSetName1='bcSupportList'; febio_spec.Mesh.NodeSet{1}.ATTR.name=nodeSetName1; febio_spec.Mesh.NodeSet{1}.node.ATTR.id=bcSupportList(:); %MeshDomains section febio_spec.MeshDomains.SolidDomain.ATTR.name=partName1; febio_spec.MeshDomains.SolidDomain.ATTR.mat=materialName1; %Boundary condition section % -> Fix boundary conditions febio_spec.Boundary.bc{1}.ATTR.type='fix'; febio_spec.Boundary.bc{1}.ATTR.node_set=nodeSetName1; febio_spec.Boundary.bc{1}.dofs='x,y,z'; %Loads section % -> Surface load febio_spec.Loads.surface_load{1}.ATTR.type='pressure'; febio_spec.Loads.surface_load{1}.ATTR.surface=surfaceName1; febio_spec.Loads.surface_load{1}.pressure.ATTR.lc=1; febio_spec.Loads.surface_load{1}.pressure.VAL=appliedPressure; febio_spec.Loads.surface_load{1}.symmetric_stiffness=1; %LoadData section % -> load_controller febio_spec.LoadData.load_controller{1}.ATTR.id=1; febio_spec.LoadData.load_controller{1}.ATTR.type='loadcurve'; febio_spec.LoadData.load_controller{1}.interpolate='LINEAR'; febio_spec.LoadData.load_controller{1}.points.point.VAL=[0 0; 1 1]; %Output section % -> log file febio_spec.Output.logfile.ATTR.file=febioLogFileName; febio_spec.Output.logfile.node_data{1}.ATTR.file=febioLogFileName_disp; febio_spec.Output.logfile.node_data{1}.ATTR.data='ux;uy;uz'; febio_spec.Output.logfile.node_data{1}.ATTR.delim=','; febio_spec.Output.logfile.node_data{1}.VAL=1:size(V,1);
Quick viewing of the FEBio input file structure
The febView function can be used to view the xml structure in a MATLAB figure window.
febView(febio_spec); %Viewing the febio file febView(febio_spec)
Exporting the FEBio input file
Exporting the febio_spec structure to an FEBio input file is done using the febioStruct2xml function.
febioStruct2xml(febio_spec,febioFebFileName); %Exporting to file and domNode
Running the FEBio analysis
To run the analysis defined by the created FEBio input file the runMonitorFEBio function is used. The input for this function is a structure defining job settings e.g. the FEBio input file name. The optional output runFlag informs the user if the analysis was run succesfully.
febioAnalysis.run_filename=febioFebFileName; %The input file name febioAnalysis.run_logname=febioLogFileName; %The name for the log file febioAnalysis.disp_on=1; %Display information on the command window febioAnalysis.disp_log_on=1; %Display convergence information in the command window febioAnalysis.runMode='external';%'internal'; febioAnalysis.t_check=0.25; %Time for checking log file (dont set too small) febioAnalysis.maxtpi=1e99; %Max analysis time febioAnalysis.maxLogCheckTime=10; %Max log file checking time [runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --------> RUNNING/MONITORING FEBIO JOB <-------- 11-Dec-2020 12:22:41 FEBio path: /home/kevin/FEBioStudio/bin/febio3 # Attempt removal of existing log files 11-Dec-2020 12:22:41 * Removal succesful 11-Dec-2020 12:22:41 # Attempt removal of existing .xplt files 11-Dec-2020 12:22:41 * Removal succesful 11-Dec-2020 12:22:41 # Starting FEBio... 11-Dec-2020 12:22:41 Max. total analysis time is: 1e+99 s * Waiting for log file creation 11-Dec-2020 12:22:41 Max. wait time: 10 s * Log file found. 11-Dec-2020 12:22:41 # Parsing log file... 11-Dec-2020 12:22:41 number of iterations : 4 11-Dec-2020 12:22:43 number of reformations : 4 11-Dec-2020 12:22:43 ------- converged at time : 0.1 11-Dec-2020 12:22:43 number of iterations : 4 11-Dec-2020 12:22:44 number of reformations : 4 11-Dec-2020 12:22:44 ------- converged at time : 0.2 11-Dec-2020 12:22:44 number of iterations : 4 11-Dec-2020 12:22:46 number of reformations : 4 11-Dec-2020 12:22:46 ------- converged at time : 0.3 11-Dec-2020 12:22:46 number of iterations : 4 11-Dec-2020 12:22:48 number of reformations : 4 11-Dec-2020 12:22:48 ------- converged at time : 0.4 11-Dec-2020 12:22:48 number of iterations : 4 11-Dec-2020 12:22:49 number of reformations : 4 11-Dec-2020 12:22:49 ------- converged at time : 0.5 11-Dec-2020 12:22:49 number of iterations : 5 11-Dec-2020 12:22:51 number of reformations : 5 11-Dec-2020 12:22:51 ------- converged at time : 0.6 11-Dec-2020 12:22:51 number of iterations : 5 11-Dec-2020 12:22:54 number of reformations : 5 11-Dec-2020 12:22:54 ------- converged at time : 0.7 11-Dec-2020 12:22:54 number of iterations : 7 11-Dec-2020 12:22:57 number of reformations : 7 11-Dec-2020 12:22:57 ------- converged at time : 0.8 11-Dec-2020 12:22:57 number of iterations : 8 11-Dec-2020 12:23:00 number of reformations : 8 11-Dec-2020 12:23:00 ------- converged at time : 0.9 11-Dec-2020 12:23:00 number of iterations : 6 11-Dec-2020 12:23:03 number of reformations : 6 11-Dec-2020 12:23:03 ------- converged at time : 1 11-Dec-2020 12:23:03 Elapsed time : 0:00:22 11-Dec-2020 12:23:03 N O R M A L T E R M I N A T I O N # Done 11-Dec-2020 12:23:03 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Import FEBio results
if runFlag==1 %i.e. a succesful run
Importing nodal displacements from a log file
dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_disp),1,1); %Access data N_disp_mat=dataStruct.data; %Displacement timeVec=dataStruct.time; %Time %Create deformed coordinate set V_DEF=N_disp_mat+repmat(V,[1 1 size(N_disp_mat,3)]);
Plotting the simulated results using anim8 to visualize and animate deformations
DN_magnitude=sqrt(sum(N_disp_mat(:,:,end).^2,2)); %Current displacement magnitude % Create basic view and store graphics handle to initiate animation hf=cFigure; %Open figure gtitle([febioFebFileNamePart,': Press play to animate']); title('Displacement magnitude [mm]','Interpreter','Latex') hp=gpatch(Fb,V_DEF(:,:,end),DN_magnitude,'k',1); %Add graphics object to animate hp.Marker='.'; hp.MarkerSize=markerSize2; hp.FaceColor='interp'; axisGeom(gca,fontSize); colormap(gjet(250)); colorbar; caxis([0 max(DN_magnitude)]); axis(axisLim(V_DEF)); %Set axis limits statically camlight headlight; % Set up animation features animStruct.Time=timeVec; %The time vector for qt=1:1:size(N_disp_mat,3) %Loop over time increments DN_magnitude=sqrt(sum(N_disp_mat(:,:,qt).^2,2)); %Current displacement magnitude %Set entries in animation structure animStruct.Handles{qt}=[hp hp]; %Handles of objects to animate animStruct.Props{qt}={'Vertices','CData'}; %Properties of objects to animate animStruct.Set{qt}={V_DEF(:,:,qt),DN_magnitude}; %Property values for to set in order to animate end anim8(hf,animStruct); %Initiate animation feature drawnow;

end
GIBBON www.gibboncode.org
Kevin Mattheus Moerman, [email protected]
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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE
GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.
Copyright (C) 2006-2020 Kevin Mattheus Moerman
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