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
- 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 febioLogFileName_stress_prin=[febioFebFileNamePart,'_stress_prin_out.txt']; %Log file name for exporting principal stress %Specifying geometry parameters pointSpacing=1; radiusInner1=9; radiusInner2=10; radiusOuter1=10; radiusOuter2=12; vesselLength=50; %Load appliedPressure=0.1; %MPa %Material parameter set c1=1; %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 min_residual=1e-20;
Creating model boundary polygons
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
Creating model boundary surfaces
% controlStructLoft.numSteps=17; controlStructLoft.closeLoopOpt=1; controlStructLoft.patchType='quad'; %Meshing outer surface [F1,V1]=polyLoftLinear(v1_Inner,v2_Inner,controlStructLoft); F1=fliplr(F1); %Invert orientation
outerRadii=V1(:,1); %x outerRadii=outerRadii-min(outerRadii(:)); %[0 - ...] outerRadii=outerRadii./max(outerRadii(:)); %[0 - 1] outerRadii=radiusOuter1+(outerRadii.*(radiusOuter2-radiusOuter1)); %[0 - 1] innerRadii=V1(:,1); %x innerRadii=innerRadii-min(innerRadii(:)); %[0 - ...] innerRadii=innerRadii./max(innerRadii(:)); %[0 - 1] innerRadii=radiusInner1+(innerRadii.*(radiusInner2-radiusInner1)); %[0 - 1] wallThickness=outerRadii-innerRadii;
Plotting model boundary polygons
cFigure; hold on; title('Inner surface and polygons','FontSize',fontSize); gpatch(F1,V1,outerRadii); plotV(v1_Inner,'g.-','LineWidth',3); plotV(v2_Inner,'g.-','LineWidth',3); axisGeom(gca,fontSize); camlight headlight; colormap gjet; colorbar; gdrawnow;

numSteps=ceil(max(wallThickness)./pointSpacing);
[E,V,Fp1,Fp2]=patchThick(F1,V1,1,wallThickness,numSteps);
[F,~,C_type]=element2patch(E,[],'hex8');
indBoundary=tesBoundary(F);
Fb=F(indBoundary,:);
Cb=C_type(indBoundary,:);
Plotting model boundary surfaces
cFigure; hold on; title('Model boundary surfaces','FontSize',fontSize); gpatch(Fb,V,Cb); axisGeom(gca,fontSize); camlight headlight; colormap gjet; icolorbar; drawnow;

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=Fb(Cb==1,:);
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','none',0.5); hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize); hl(2)=gpatch(F_pressure,V,'rw','r',1); patchNormPlot(F_pressure,V); 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.solver.min_residual=min_residual; 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='hex8'; %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); febio_spec.Output.logfile.element_data{1}.ATTR.file=febioLogFileName_stress_prin; febio_spec.Output.logfile.element_data{1}.ATTR.data='s1;s2;s3'; febio_spec.Output.logfile.element_data{1}.ATTR.delim=',';
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 <-------- 30-Mar-2022 11:28:57 FEBio path: /home/kevin/FEBioStudio/bin/febio3 # Attempt removal of existing log files 30-Mar-2022 11:28:57 * Removal succesful 30-Mar-2022 11:28:57 # Attempt removal of existing .xplt files 30-Mar-2022 11:28:57 * Removal succesful 30-Mar-2022 11:28:57 # Starting FEBio... 30-Mar-2022 11:28:57 Max. total analysis time is: 1e+99 s * Waiting for log file creation 30-Mar-2022 11:28:57 Max. wait time: 10 s * Log file found. 30-Mar-2022 11:28:57 # Parsing log file... 30-Mar-2022 11:28:57 number of iterations : 3 30-Mar-2022 11:28:59 number of reformations : 3 30-Mar-2022 11:28:59 ------- converged at time : 0.1 30-Mar-2022 11:28:59 number of iterations : 3 30-Mar-2022 11:29:00 number of reformations : 3 30-Mar-2022 11:29:00 ------- converged at time : 0.2 30-Mar-2022 11:29:00 number of iterations : 3 30-Mar-2022 11:29:02 number of reformations : 3 30-Mar-2022 11:29:02 ------- converged at time : 0.3 30-Mar-2022 11:29:02 number of iterations : 3 30-Mar-2022 11:29:03 ------- converged at time : 0.4 30-Mar-2022 11:29:03 number of iterations : 3 30-Mar-2022 11:29:05 number of reformations : 3 30-Mar-2022 11:29:05 ------- converged at time : 0.5 30-Mar-2022 11:29:05 number of iterations : 3 30-Mar-2022 11:29:06 number of reformations : 3 30-Mar-2022 11:29:06 ------- converged at time : 0.6 30-Mar-2022 11:29:06 number of iterations : 3 30-Mar-2022 11:29:08 number of reformations : 3 30-Mar-2022 11:29:08 ------- converged at time : 0.7 30-Mar-2022 11:29:08 number of iterations : 3 30-Mar-2022 11:29:09 number of reformations : 3 30-Mar-2022 11:29:09 ------- converged at time : 0.8 30-Mar-2022 11:29:09 number of iterations : 3 30-Mar-2022 11:29:11 number of reformations : 3 30-Mar-2022 11:29:11 ------- converged at time : 0.9 30-Mar-2022 11:29:11 number of iterations : 3 30-Mar-2022 11:29:12 number of reformations : 3 30-Mar-2022 11:29:12 ------- converged at time : 1 30-Mar-2022 11:29:12 Elapsed time : 0:00:15 30-Mar-2022 11:29:12 N O R M A L T E R M I N A T I O N # Done 30-Mar-2022 11:29:13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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)]);
Importing element principal stresses from a log file
dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_stress_prin),1,1);
%Access data
E_stress_prin_mat=dataStruct.data;
S1_mat=E_stress_prin_mat(:,1,:);
S2_mat=E_stress_prin_mat(:,2,:);
S3_mat=E_stress_prin_mat(:,3,:);
S_vm = sqrt(((S1_mat-S2_mat).^2+(S2_mat-S3_mat).^2+(S3_mat-S1_mat).^2)./2);
Plotting the simulated results using anim8 to visualize and animate deformations
[~,CF_S_vm,~]=element2patch(E,S_vm(:,:,end),'hex8'); Cb_S_vm=CF_S_vm(indBoundary,:); % Create basic view and store graphics handle to initiate animation hf=cFigure; %Open figure gtitle([febioFebFileNamePart,': Press play to animate']); title('Von Mises stres [MPa]','Interpreter','Latex') hp=gpatch(Fb,V_DEF(:,:,end),Cb_S_vm,'k',1); %Add graphics object to animate axisGeom(gca,fontSize); colormap(gjet(250)); colorbar; caxis([0 max(S_vm(:))]); 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 [~,CF_S_vm,~]=element2patch(E,S_vm(:,:,qt),'hex8'); Cb_S_vm=CF_S_vm(indBoundary,:); %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),Cb_S_vm}; %Property values for to set in order to animate end anim8(hf,animStruct); %Initiate animation feature drawnow;

Importing element principal stresses from a log file
dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_stress_prin),1,1);
%Access data
E_stress_prin_mat=dataStruct.data;
time_vec=dataStruct.time;
end
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Kevin Mattheus Moerman, [email protected]
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GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.
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