DEMO_febio_0054_lattice_hydrostatic_01

Below is a demonstration for:

Building geometry for a cube with hexahedral 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
Create lattice
DEFINE BC's
Smoothing lattice
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 2.5
febio, FEBio
uniaxial loading
compression, tension, compressive, tensile
displacement control, displacement boundary condition
hexahedral elements, hex8
cube, box, rectangular
static, solid
hyperelastic, Ogden
displacement logfile
stress logfile

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=0.8;
faceAlpha2=1;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize=25;
cMap=gjet(4);

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=fullfile(savePath,[febioFebFileNamePart,'.txt']); %FEBio log file name
febioLogFileName_disp=[febioFebFileNamePart,'_disp_out.txt']; %Log file name for exporting displacement
febioLogFileName_force=[febioFebFileNamePart,'_force_out.txt']; %Log file name for exporting force
febioLogFileName_stress=[febioFebFileNamePart,'_stress_out.txt']; %Log file name for exporting stress
febioLogFileName_stiffness=[febioFebFileNamePart,'_stiffness_out.txt']; %Log file name for exporting stiffness

%Specifying dimensions and number of elements
sampleSize=10;
latticeType=1;

%Define applied displacement
J_final=0.7; %Final Jacobian or volume ration
lambdaFinal=J_final^(1/3); %Stretch values in all directions
displacementMagnitude=((lambdaFinal*sampleSize)-sampleSize)/2; %The displacement magnitude

%Material parameter set
c1=1; %Shear-modulus-like parameter
m1=2;
k=50*c1;

% FEA control settings
numTimeSteps=50; %Number of time steps desired
max_refs=50; %Max reforms
max_ups=0; %Set to zero to use full-Newton iterations
opt_iter=25; %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
min_residual=1e-20;
symmetric_stiffness=0;

%Specifying dimensions and number of elements
r=0.5; %Radii, results in a width of 1
n=4;
nCopies=n*ones(1,3); %Number of offset copies
d=2*r; %Diameter
w=(n-1)*d; %sampleSize

Create lattice

switch latticeType
    case 1 %Octet truss
        [E,V,C,F,CF]=rhombicDodecahedronMesh(r,nCopies);
        V=V./(n-1);
        V=V*sampleSize;

        [indBoundary]=tesBoundary(F,V);
        cPar.shrinkFactor=0.15; %Strut sides are formed by shrinking the input mesh faces by this factor
        cPar.meshType='hex'; %desired output mesh type
        cPar.indBoundary=indBoundary; %indices of the boundary faces
        cPar.hexSplit=2;
        cPar.latticeSide=2; %1=side 1 the edge lattice, 2=side 2 the dual lattice to the edge lattice
        [Es,Vs,Cs]=element2lattice(E,V,cPar); %Get lattice structure

        logicKeep1=~(Vs(:,1)<=-1e-3);
        logicKeep2=~(Vs(:,2)<=-1e-3);
        logicKeep3=~(Vs(:,3)<=-1e-3);
        logicKeep4=~(Vs(:,1)>=sampleSize+1e-3);
        logicKeep5=~(Vs(:,2)>=sampleSize+1e-3);
        logicKeep6=~(Vs(:,3)>=sampleSize+1e-3);

        logicKeepEs=sum(logicKeep1(Es),2)>=4 &...
            sum(logicKeep2(Es),2)>=4 &...
            sum(logicKeep3(Es),2)>=4 &...
            sum(logicKeep4(Es),2)>=4 &...
            sum(logicKeep5(Es),2)>=4 &...
            sum(logicKeep6(Es),2)>=4;

        Es=Es(logicKeepEs,:);
        Cs=Cs(logicKeepEs,:);
        [Es,Vs,indFix]=patchCleanUnused(Es,Vs);

        % [Es,Vs,~,~]=subHex(Es,Vs,1,1);
        % Cs=repmat(Cs,8,1);

        % Create patch Data for visualization
        [Fs,CsF]=element2patch(Es,Cs); %Patch data for plotting

        %Get new boundary set
        indB=tesBoundary(Fs,Vs);
        Fb=Fs(indB,:);
    case 2 %Rhombic dodecahedron mesh ("dual" of octet truss lattice)
        [E,V,C,F,CF]=rhombicDodecahedronMesh(r,nCopies);
        V=V./(n-1);
        V=V*sampleSize;

        [indBoundary]=tesBoundary(F,V);
        cPar.shrinkFactor=0.15; %Strut sides are formed by shrinking the input mesh faces by this factor
        cPar.meshType='hex'; %desired output mesh type
        cPar.indBoundary=indBoundary; %indices of the boundary faces
        cPar.hexSplit=2;
        cPar.latticeSide=1; %1=side 1 the edge lattice, 2=side 2 the dual lattice to the edge lattice
        [Es,Vs,Cs]=element2lattice(E,V,cPar); %Get lattice structure

        logicKeep1=~(Vs(:,1)<=-1e-3);
        logicKeep2=~(Vs(:,2)<=-1e-3);
        logicKeep3=~(Vs(:,3)<=-1e-3);
        logicKeep4=~(Vs(:,1)>=sampleSize+1e-3);
        logicKeep5=~(Vs(:,2)>=sampleSize+1e-3);
        logicKeep6=~(Vs(:,3)>=sampleSize+1e-3);

        logicKeepEs=sum(logicKeep1(Es),2)>=4 &...
            sum(logicKeep2(Es),2)>=4 &...
            sum(logicKeep3(Es),2)>=4 &...
            sum(logicKeep4(Es),2)>=4 &...
            sum(logicKeep5(Es),2)>=4 &...
            sum(logicKeep6(Es),2)>=4;

        Es=Es(logicKeepEs,:);
        Cs=Cs(logicKeepEs,:);
        [Es,Vs,indFix]=patchCleanUnused(Es,Vs);

        % [Es,Vs,~,~]=subHex(Es,Vs,1,1);
        % Cs=repmat(Cs,8,1);

        % Create patch Data for visualization
        [Fs,CsF]=element2patch(Es,Cs); %Patch data for plotting

        %Get new boundary set
        indB=tesBoundary(Fs,Vs);
        Fb=Fs(indB,:);
    case 3
        boxDim=sampleSize*[1 1 1];
        boxEl=[2 2 2];
        [meshStruct]=hexMeshBox(boxDim,boxEl);
        E=meshStruct.E;
        V=meshStruct.V;
        minV=min(V,[],1); %Get lower left front corner
        V=V-minV(ones(size(V,1),1),:); %Set corner as origin
        [E,V,~]=hex2tet(E,V,[],1); %Convert to tetrahedral elements
        [F,C]=element2patch(E,[]); %Patch data for plotting
        [indBoundary]=tesBoundary(F,V);

        % Create lattice structure
        controlParameter.latticeSide=1;
        controlParameter.numDigitKeep=5; %used for merging nodes
        controlParameter.indBoundary=indBoundary; %indices of the boundary faces
        controlParameter.shrinkFactor=0.15;
        controlParameter.meshType='hex';
        controlParameter.hexSplit=2;

        [Es,Vs,Cs]=element2lattice(E,V,controlParameter); %Get lattice structure

        % Create patch Data for visualization
        [Fs,CsF]=element2patch(Es,Cs); %Patch data for plotting

        indB=tesBoundary(Fs,Vs);
        Fb=Fs(indB,:);
end

Visualizing input mesh and lattic structures

cFigure;
hs=subplot(1,2,1);
title('The input mesh','fontSize',fontSize)
hold on;
gpatch(F,V,0.5*ones(1,3),'k',0.5);
axisGeom(gca,fontSize);
camlight headlight; lighting flat;

subplot(1,2,2);
title('Lattice side 1','fontSize',fontSize)
hold on;
gpatch(Fb,Vs,'bw','k',1);
% patchNormPlot(Fs,Vs);
axisGeom(gca,fontSize);
camlight headlight; lighting flat;

drawnow;

DEFINE BC's

% Define node set logics
indAll=(1:1:size(Vs,1))';
logicBoundary=ismember(indAll,Fb);

Z=Vs(:,3);
logicTop=Z>=(sampleSize-eps(sampleSize))& logicBoundary;
logicBottom=Z<=eps(sampleSize) & logicBoundary;

X=Vs(:,1);
logicSide1=X>=(sampleSize-eps(sampleSize))& logicBoundary;
logicSide2=X<=eps(sampleSize)& logicBoundary;

Y=Vs(:,2);
logicSide3=Y>=(sampleSize-eps(sampleSize))& logicBoundary;
logicSide4=Y<=eps(sampleSize)& logicBoundary;

%Prescribed force nodes
bcPrescribeListCell{1}=find(logicSide1)';
bcPrescribeListCell{2}=find(logicSide2)';
bcPrescribeListCell{3}=find(logicSide3)';
bcPrescribeListCell{4}=find(logicSide4)';
bcPrescribeListCell{5}=find(logicTop)';
bcPrescribeListCell{6}=find(logicBottom)';

Smoothing lattice

% indKeep=unique([bcPrescribeListCell{:}]);
% [Fb_clean,Vb_clean,indFix]=patchCleanUnused(Fb,Vs);
%
% cPar.Method='HC';
% cPar.n=6;
%
% cPar.RigidConstraints=indFix(indKeep);
% % cPar.RigidConstraints=cPar.RigidConstraints(cPar.RigidConstraints>0);
%
% [Vb_clean]=tesSmooth(Fb_clean,Vb_clean,[],cPar);
% ind=Fb(:);
% ind=unique(ind(:));
% Vs(ind,:)=Vb_clean;

% cFigure; hold on;
% gpatch(Fb,Vs,'bw','k',1);
% % patchNormPlot(Fs,Vs);
% % plotV(Vs(indKeep,:),'k.','MarkerSize',25)
% axisGeom(gca,fontSize);
% camlight headlight; lighting flat;
% drawnow;

Visualizing input mesh and lattic structures

cFigure;
hs=subplot(1,2,1);
title('The input mesh','fontSize',fontSize)
hold on;
gpatch(F,V,0.5*ones(1,3),'k',0.5);
axisGeom(gca,fontSize);
camlight headlight; lighting flat;

subplot(1,2,2);
title('Lattice side 1','fontSize',fontSize)
hold on;
gpatch(Fb,Vs,'bw');
% patchNormPlot(Fs,Vs);
axisGeom(gca,fontSize);
camlight headlight; lighting flat;

drawnow;

Visualize BC's

cFigure; hold on;
title('Boundary conditions','FontSize',fontSize);
gpatch(Fb,Vs,'kw','none',0.4);
hl=gobjects(1,6);
plotColors=gjet(6);
for q=1:1:numel(bcPrescribeListCell)
    hl(q)=plotV(Vs(bcPrescribeListCell{q},:),'k.','MarkerSize',markerSize);
    hl(q).Color=plotColors(q,:);
end

legend(hl,{'BC 1','BC 2','BC 3','BC 4','BC 5','BC 6'});
axisGeom;
camlight headlight;
set(gca,'FontSize',fontSize);
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='2.5';

%Module section
febio_spec.Module.ATTR.type='solid';

%Control section
febio_spec.Control.analysis.ATTR.type='static';
febio_spec.Control.title='Lattice analysis';
febio_spec.Control.time_steps=numTimeSteps;
febio_spec.Control.step_size=1/numTimeSteps;
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;
febio_spec.Control.max_refs=max_refs;
febio_spec.Control.max_ups=max_ups;
febio_spec.Control.symmetric_stiffness=symmetric_stiffness;
febio_spec.Control.min_residual=min_residual;

%Material section
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;
% 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=c2;
% febio_spec.Material.material{1}.m2=m2;
% febio_spec.Material.material{1}.c3=c3;
% febio_spec.Material.material{1}.m3=m3;
% febio_spec.Material.material{1}.k=k;

%Geometry section
% -> Nodes
febio_spec.Geometry.Nodes{1}.ATTR.name='nodeSet_all'; %The node set name
febio_spec.Geometry.Nodes{1}.node.ATTR.id=(1:size(Vs,1))'; %The node id's
febio_spec.Geometry.Nodes{1}.node.VAL=Vs; %The nodel coordinates

% -> Elements
febio_spec.Geometry.Elements{1}.ATTR.type='hex8'; %Element type of this set
febio_spec.Geometry.Elements{1}.ATTR.mat=1; %material index for this set
febio_spec.Geometry.Elements{1}.ATTR.name='Cube'; %Name of the element set
febio_spec.Geometry.Elements{1}.elem.ATTR.id=(1:1:size(Es,1))'; %Element id's
febio_spec.Geometry.Elements{1}.elem.VAL=Es;

% -> NodeSets
for q=1:1:numel(bcPrescribeListCell)
    febio_spec.Geometry.NodeSet{q}.ATTR.name=['bcPrescribeList_',num2str(q)];
    febio_spec.Geometry.NodeSet{q}.node.ATTR.id=bcPrescribeListCell{q}';
end

%Boundary condition section

% -> Prescribe boundary conditions
directionStringSet={'x','x','y','y','z','z'};
displacementMagnitudeDir=[1 -1 1 -1 1 -1];
for q=1:1:numel(bcPrescribeListCell)
    febio_spec.Boundary.prescribe{q}.ATTR.bc=directionStringSet{q};
    febio_spec.Boundary.prescribe{q}.ATTR.node_set=febio_spec.Geometry.NodeSet{q}.ATTR.name;
    febio_spec.Boundary.prescribe{q}.scale.ATTR.lc=1;
    febio_spec.Boundary.prescribe{q}.scale.VAL=1;
    febio_spec.Boundary.prescribe{q}.relative=1;
    febio_spec.Boundary.prescribe{q}.value=displacementMagnitudeDir(q).*displacementMagnitude;
end

%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(Vs,1);

febio_spec.Output.logfile.node_data{2}.ATTR.file=febioLogFileName_force;
febio_spec.Output.logfile.node_data{2}.ATTR.data='Rx;Ry;Rz';
febio_spec.Output.logfile.node_data{2}.ATTR.delim=',';
febio_spec.Output.logfile.node_data{2}.VAL=1:size(Vs,1);

% febio_spec.Output.logfile.element_data{1}.ATTR.file=febioLogFileName_stress;
% febio_spec.Output.logfile.element_data{1}.ATTR.data='sz';
% febio_spec.Output.logfile.element_data{1}.ATTR.delim=',';
% febio_spec.Output.logfile.element_data{1}.VAL=1:size(Es,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

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!!!!!!!!

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- STARTING FEBIO JOB --- 13-Mar-2020 12:41:46
Waiting for log file...
Proceeding to check log file...13-Mar-2020 12:41:47
------- converged at time : 0.02
------- converged at time : 0.04
------- converged at time : 0.06
------- converged at time : 0.08
------- converged at time : 0.0949841
------- converged at time : 0.110971
------- converged at time : 0.127761
------- converged at time : 0.145193
------- converged at time : 0.163139
------- converged at time : 0.181495
------- converged at time : 0.20018
------- converged at time : 0.219128
------- converged at time : 0.238287
------- converged at time : 0.257613
------- converged at time : 0.277075
------- converged at time : 0.296644
------- converged at time : 0.316299
------- converged at time : 0.336024
------- converged at time : 0.355803
------- converged at time : 0.375626
------- converged at time : 0.395485
------- converged at time : 0.415372
------- converged at time : 0.435282
------- converged at time : 0.45521
------- converged at time : 0.475152
------- converged at time : 0.495106
------- converged at time : 0.515069
------- converged at time : 0.535039
------- converged at time : 0.555015
------- converged at time : 0.574996
------- converged at time : 0.594981
------- converged at time : 0.614969
------- converged at time : 0.634959
------- converged at time : 0.654952
------- converged at time : 0.674945
------- converged at time : 0.69494
------- converged at time : 0.714936
------- converged at time : 0.734933
------- converged at time : 0.754931
------- converged at time : 0.774929
------- converged at time : 0.794927
------- converged at time : 0.814926
------- converged at time : 0.834925
------- converged at time : 0.854924
------- converged at time : 0.874923
------- converged at time : 0.894923
------- converged at time : 0.914922
------- converged at time : 0.934922
------- converged at time : 0.954922
------- converged at time : 0.974921
------- converged at time : 0.994921
------- converged at time : 1
--- Done --- 13-Mar-2020 12:44:17

Import FEBio results

if runFlag==1 %i.e. a succesful run

    % Importing nodal displacements from a log file
    [time_mat, N_disp_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_disp)); %Nodal displacements
    time_mat=[0; time_mat(:)]; %Time

    N_disp_mat=N_disp_mat(:,2:end,:);
    sizImport=size(N_disp_mat);
    sizImport(3)=sizImport(3)+1;
    N_disp_mat_n=zeros(sizImport);
    N_disp_mat_n(:,:,2:end)=N_disp_mat;
    N_disp_mat=N_disp_mat_n;
    DN=N_disp_mat(:,:,end);
    DN_magnitude=sqrt(sum(DN(:,3).^2,2));
    Vs_def=Vs+DN;

    %     % Importing element stress from a log file
    %     [time_mat, E_stress_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_stress)); %Nodal forces
    %     time_mat=[0; time_mat(:)]; %Time
    %     stress_cauchy_sim=[0; mean(squeeze(E_stress_mat(:,end,:)),1)'];

    % Importing nodal forces
    [~, N_force_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_force)); %Nodal displacements
    N_force_mat=N_force_mat(:,2:end,:);
    sizImport=size(N_force_mat);
    sizImport(3)=sizImport(3)+1;
    N_force_mat_n=zeros(sizImport);
    N_force_mat_n(:,:,2:end)=N_force_mat;
    N_force_mat=N_force_mat_n;

    indicesSide=bcPrescribeListCell{1};
    areaSide=sampleSize.^2;

    stressVal=mean(squeeze(N_force_mat(indicesSide,1,:))./areaSide,1);
    J_Val=1-((1-J_final).*time_mat(:));

    cFigure;
    plot(J_Val(:),stressVal(:),'r.-','LineWidth',3,'MarkerSize',15);
    axis square; axis tight; grid on; box on;
    drawnow;

Plotting the simulated results using anim8 to visualize and animate deformations

    % Create basic view and store graphics handle to initiate animation
    hf=cFigure; %Open figure
    gtitle([febioFebFileNamePart,': Press play to animate']);
    hp=gpatch(Fb,Vs_def,DN_magnitude,'k',1); %Add graphics object to animate
    %     gpatch(Fb,Vs,'kw','none',0.25); %A static graphics object
    hp.FaceColor='interp';

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([0 max(DN_magnitude)]);
    axis([min([Vs_def(:,1);Vs(:,1)]) max([Vs_def(:,1);Vs(:,1)])...
        min([Vs_def(:,2);Vs(:,2)]) max([Vs_def(:,2);Vs(:,2)])...
        min([Vs_def(:,3);Vs(:,3)]) max([Vs_def(:,3);Vs(:,3)]) ]); %Set axis limits statically
    %     view(130,25); %Set view direction
    camlight headlight;

    % Set up animation features
    animStruct.Time=time_mat; %The time vector
    for qt=1:1:size(N_disp_mat,3) %Loop over time increments
        DN=N_disp_mat(:,:,qt); %Current displacement
        DN_magnitude=sqrt(sum(DN.^2,2)); %Current displacement magnitude
        Vs_def=Vs+DN; %Current nodal coordinates

        %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}={Vs_def,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.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.