DEMO_febio_0013_disc_pressure_varying

Below is a demonstration for:

Building geometry for a thin disc with tetrahedral elements
Defining the boundary conditions
Coding the febio structure
Running the model
Importing and visualizing the displacement and stress results

Keywords
Plot settings
Control parameters
Creating model geometry and mesh
Defining the boundary conditions
Defining the boundary conditions
Create spatially varying pressure
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 4.0
febio, FEBio
pressure loading, spatially varying pressure, non-constant pressure
tetrahedral elements, hex4
tetgen
disc
static, solid
hyperelastic, Ogden
displacement logfile
stress logfile

clear; close all; clc;

Plot settings

fontSize=20;
faceAlpha1=0.8;
markerSize=25;
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=[febioFebFileNamePart,'_stress_out.txt']; %Log file name for exporting force

%Load
pressureValueMin=0.1e-4;
pressureValueMax=2.0e-4;
loadCase=1;
switch loadCase
    case 1
        loadType='pressure';
    case 2
        loadType='traction';
end

elementType='penta6'; % 'penta6' or 'tet4'

%Specifying dimensions and number of elements
pointSpacing=1.5;
discRadius=30;
discHeight=2;

%Material parameter set
c1=1e-3; %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=6; %Optimum number of iterations
max_retries=5; %Maximum number of retires
dtmin=(1/numTimeSteps)/100; %Minimum time step size
dtmax=1/numTimeSteps; %Maximum time step size

runMode='external';% 'internal' or 'external'

Creating model geometry and mesh

switch elementType
    case 'tet4'

        % Derive patch data for a disc
        inputStruct.cylRadius=discRadius;
        inputStruct.numRadial=ceil((discRadius*2*pi)/pointSpacing);
        inputStruct.cylHeight=discHeight;
        inputStruct.numHeight=ceil(discHeight/pointSpacing);
        inputStruct.meshType='tri';
        inputStruct.closeOpt=1;

        [Fs,Vs,Cs]=patchcylinder(inputStruct);

        % The disc is meshed with tetrahedral elements using tetgen
        inputStruct.stringOpt='-pq1.2AaY';
        inputStruct.Faces=Fs;
        inputStruct.Nodes=Vs;
        inputStruct.holePoints=[];
        inputStruct.faceBoundaryMarker=Cs; %Face boundary markers
        inputStruct.regionPoints=getInnerPoint(Fs,Vs); %region points
        inputStruct.regionA=tetVolMeanEst(Fs,Vs); %Volume for regular tets
        inputStruct.minRegionMarker=2; %Minimum region marker
        [meshStruct]=runTetGen(inputStruct); % Mesh model using tetrahedral elements using tetGen

        % Access model element and patch data
        Fb=meshStruct.facesBoundary;
        Cb=meshStruct.boundaryMarker;
        V=meshStruct.nodes;
        CE=meshStruct.elementMaterialID;
        E=meshStruct.elements;

Visualize mesh

        hFig=cFigure;
        subplot(1,2,1); hold on;
        title('Model boundary surfaces and labels','FontSize',fontSize);
        gpatch(Fb,V,Cb,'k',faceAlpha1);
        colormap(gjet(6)); icolorbar;
        axisGeom(gca,fontSize);

        hs=subplot(1,2,2); hold on;
        title('Cut view of solid mesh','FontSize',fontSize);
        optionStruct.hFig=[hFig hs];
        meshView(meshStruct,optionStruct);
        axisGeom(gca,fontSize);
        drawnow;

Defining the boundary conditions

The visualization of the model boundary shows colors for each side of the disc. These labels can be used to define boundary conditions.

        %Define supported node sets
        bcSupportList=unique(Fb(Cb==1,:)); %Node set part of selected face

        %Define pressure surface
        F_pressure=fliplr(Fb(Cb==2,:)); %The top face set

    case 'penta6'

        nc=ceil((2*pi*discRadius)./pointSpacing); %Number of points in circumference
        t=linspace(0,2*pi,nc+1)';
        t=t(1:end-1);
        regionTriMeshinputStructure.regionCell={discRadius.*[cos(t) sin(t)]};
        regionTriMeshinputStructure.pointSpacing=pointSpacing;
        regionTriMeshinputStructure.resampleCurveOpt=0;
        [Fc,Vc]=regionTriMesh2D(regionTriMeshinputStructure);

        numHeight=ceil(discHeight/pointSpacing);
        [E,V,F1,F2]=patchThick(Fc,Vc,1,discHeight,numHeight);

        F=element2patch(E,[],elementType);
        indB=tesBoundary(F);

        Fb= {F{1}(indB{1},:), F{2}(indB{2},:)};

Visualize mesh

        cFigure;
        gpatch(F,V,'o','k',0.5);
        patchNormPlot(F,V);
        axisGeom(gca,fontSize); camlight headlight;
        gdrawnow;

Defining the boundary conditions

The visualization of the model boundary shows colors for each side of the disc. These labels can be used to define boundary conditions.

        %Define supported node sets
        bcSupportList=unique(Fb{2}); %Node set part of selected face

        %Define pressure surface
        F_pressure=F2; %The top face set

end

Create spatially varying pressure

X=V(:,1);
C_pressure=mean(X(F_pressure),2); %Initialize as X-coordinate
C_pressure=C_pressure-min(C_pressure(:)); %Subtract minimum so range is 0-..
C_pressure=C_pressure./max(C_pressure(:)); %Devide by maximum so range is 0-1
C_pressure=C_pressure.^2;
C_pressure=C_pressure.*(pressureValueMax-pressureValueMin)+pressureValueMin; %Scale/offset to pressure range

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,C_pressure,'k',1);
patchNormPlot(F_pressure,V);
legend(hl,{'BC full support','Pressure surface'});
colormap(gjet(250)); colorbar;
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='4.0';

%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.qn_method.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=elementType; %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}.VAL=mrow(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.name='FixedDisplacement01';
febio_spec.Boundary.bc{1}.ATTR.type='zero displacement';
febio_spec.Boundary.bc{1}.ATTR.node_set=nodeSetName1;
febio_spec.Boundary.bc{1}.x_dof=1;
febio_spec.Boundary.bc{1}.y_dof=1;
febio_spec.Boundary.bc{1}.z_dof=1;

%MeshData secion
%-> Surface data
loadDataName1='LoadData1';
switch loadType
    case 'pressure'
        febio_spec.MeshData.SurfaceData.ATTR.name=loadDataName1;
        febio_spec.MeshData.SurfaceData.ATTR.surface=surfaceName1;
        febio_spec.MeshData.SurfaceData.ATTR.data_type='scalar';
        febio_spec.MeshData.SurfaceData.face.ATTR.lid=(1:1:numel(C_pressure))';
        febio_spec.MeshData.SurfaceData.face.VAL=C_pressure;
    case 'traction'
        febio_spec.MeshData.SurfaceData.ATTR.name=loadDataName1;
        febio_spec.MeshData.SurfaceData.ATTR.surface=surfaceName1;
        febio_spec.MeshData.SurfaceData.ATTR.data_type='vec3';
        febio_spec.MeshData.SurfaceData.face.ATTR.lid=(1:1:numel(C_pressure))';
        febio_spec.MeshData.SurfaceData.face.VAL=[zeros(size(C_pressure)) zeros(size(C_pressure)) -C_pressure];
end

%Loads section
% -> Surface load
switch loadType
    case 'pressure'
        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.ATTR.type='map';
        febio_spec.Loads.surface_load{1}.pressure.VAL=loadDataName1;
        febio_spec.Loads.surface_load{1}.symmetric_stiffness=1;
    case 'traction'
        febio_spec.Loads.surface_load{1}.ATTR.type='traction';
        febio_spec.Loads.surface_load{1}.ATTR.surface=surfaceName1;
        febio_spec.Loads.surface_load{1}.traction.ATTR.lc=1;
        febio_spec.Loads.surface_load{1}.traction.ATTR.type='map';
        febio_spec.Loads.surface_load{1}.traction.VAL=loadDataName1;
end

%LoadData section
% -> load_controller
febio_spec.LoadData.load_controller{1}.ATTR.name='LC_1';
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}.extend='CONSTANT';
febio_spec.LoadData.load_controller{1}.points.pt.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.element_data{1}.ATTR.file=febioLogFileName_stress;
febio_spec.Output.logfile.element_data{1}.ATTR.data='s1';
febio_spec.Output.logfile.element_data{1}.ATTR.delim=',';

febio_spec.Output.plotfile.compression=0;

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

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
% febView(febioFebFileName);

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.runMode=runMode;

[runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-------->    RUNNING/MONITORING FEBIO JOB    <-------- 29-May-2023 10:10:22
FEBio path: /home/kevin/FEBioStudio/bin/febio4
# Attempt removal of existing log files                29-May-2023 10:10:22
 * Removal succesful                                   29-May-2023 10:10:22
# Attempt removal of existing .xplt files              29-May-2023 10:10:22
 * Removal succesful                                   29-May-2023 10:10:22
# Starting FEBio...                                    29-May-2023 10:10:22
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       29-May-2023 10:10:22
   Max. wait time: 30 s
 * Log file found.                                     29-May-2023 10:10:22
# Parsing log file...                                  29-May-2023 10:10:22
    number of iterations   : 11                        29-May-2023 10:10:24
    number of reformations : 11                        29-May-2023 10:10:24
------- converged at time : 0.1                        29-May-2023 10:10:24
    number of iterations   : 6                         29-May-2023 10:10:24
    number of reformations : 6                         29-May-2023 10:10:24
------- converged at time : 0.174116                   29-May-2023 10:10:24
    number of iterations   : 5                         29-May-2023 10:10:24
    number of reformations : 5                         29-May-2023 10:10:24
------- converged at time : 0.248233                   29-May-2023 10:10:24
    number of iterations   : 5                         29-May-2023 10:10:24
    number of reformations : 5                         29-May-2023 10:10:24
------- converged at time : 0.32482                    29-May-2023 10:10:24
    number of iterations   : 4                         29-May-2023 10:10:25
    number of reformations : 4                         29-May-2023 10:10:25
------- converged at time : 0.403641                   29-May-2023 10:10:25
    number of iterations   : 4                         29-May-2023 10:10:25
    number of reformations : 4                         29-May-2023 10:10:25
------- converged at time : 0.486698                   29-May-2023 10:10:25
    number of iterations   : 4                         29-May-2023 10:10:25
    number of reformations : 4                         29-May-2023 10:10:25
------- converged at time : 0.573144                   29-May-2023 10:10:25
    number of iterations   : 4                         29-May-2023 10:10:26
    number of reformations : 4                         29-May-2023 10:10:26
------- converged at time : 0.662301                   29-May-2023 10:10:26
    number of iterations   : 4                         29-May-2023 10:10:26
    number of reformations : 4                         29-May-2023 10:10:26
------- converged at time : 0.753626                   29-May-2023 10:10:26
    number of iterations   : 5                         29-May-2023 10:10:26
    number of reformations : 5                         29-May-2023 10:10:26
------- converged at time : 0.846686                   29-May-2023 10:10:26
    number of iterations   : 5                         29-May-2023 10:10:27
    number of reformations : 5                         29-May-2023 10:10:27
------- converged at time : 0.940409                   29-May-2023 10:10:27
    number of iterations   : 5                         29-May-2023 10:10:27
    number of reformations : 5                         29-May-2023 10:10:27
------- converged at time : 1                          29-May-2023 10:10:27
 Elapsed time : 0:00:04                                29-May-2023 10:10:27
 N O R M A L   T E R M I N A T I O N
# Done                                                 29-May-2023 10:10:27
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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),0,1);

    %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

    switch elementType
        case 'tet4'
            hp.Marker='.';
            hp.MarkerSize=markerSize2;
            hp.FaceColor='interp';
        case 'penta6'
            hp(1).Marker='.';
            hp(1).MarkerSize=markerSize2;
            hp(1).FaceColor='interp';
            hp(2).Marker='.';
            hp(2).MarkerSize=markerSize2;
            hp(2).FaceColor='interp';
    end

    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
        switch elementType
            case 'tet4'
                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
            case 'penta6'
                animStruct.Handles{qt}=[hp(1) hp(1) hp(2) hp(2)]; %Handles of objects to animate
                animStruct.Props{qt}={'Vertices','CData','Vertices','CData'}; %Properties of objects to animate
                animStruct.Set{qt}={V_DEF(:,:,qt),DN_magnitude,V_DEF(:,:,qt),DN_magnitude}; %Property values for to set in order to animate
        end
    end
    anim8(hf,animStruct); %Initiate animation feature
    drawnow;

Importing element stress from a log file

    dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_stress),0,1);

    %Access data
    E_stress_mat=dataStruct.data;

    E_stress_mat(isnan(E_stress_mat))=0;

Plotting the simulated results using anim8 to visualize and animate deformations

    [CV]=faceToVertexMeasure(E,V,E_stress_mat(:,:,end));

    % Create basic view and store graphics handle to initiate animation
    hf=cFigure; %Open figure
    gtitle([febioFebFileNamePart,': Press play to animate']);
    title('$\sigma_{1}$ [MPa]','Interpreter','Latex')
    hp=gpatch(Fb,V_DEF(:,:,end),CV,'k',1); %Add graphics object to animate

    switch elementType
        case 'tet4'
            hp.Marker='.';
            hp.MarkerSize=markerSize2;
            hp.FaceColor='interp';
        case 'penta6'
            hp(1).Marker='.';
            hp(1).MarkerSize=markerSize2;
            hp(1).FaceColor='interp';
            hp(2).Marker='.';
            hp(2).MarkerSize=markerSize2;
            hp(2).FaceColor='interp';
    end

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([min(E_stress_mat(:)) max(E_stress_mat(:))]/3);
    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

        [CV]=faceToVertexMeasure(E,V,E_stress_mat(:,:,qt));


        %Set entries in animation structure
        switch elementType
            case 'tet4'
                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),CV}; %Property values for to set in order to animate
            case 'penta6'
                animStruct.Handles{qt}=[hp(1) hp(1) hp(2) hp(2)]; %Handles of objects to animate
                animStruct.Props{qt}={'Vertices','CData','Vertices','CData'}; %Properties of objects to animate
                animStruct.Set{qt}={V_DEF(:,:,qt),CV,V_DEF(:,:,qt),CV}; %Property values for to set in order to animate
        end
    end
    anim8(hf,animStruct); %Initiate animation feature
    drawnow;

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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DEMO_febio_0013_disc_pressure_varying

Contents

Keywords

Plot settings

Control parameters

Creating model geometry and mesh

Defining the boundary conditions

Defining the boundary conditions

Create spatially varying pressure

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