DEMO_febio_0026_hexlattice_compression

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
Smoothen lattice
DEFINE BC's
Check porosity
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
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=[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

%Specifying dimensions and number of elements
sampleSize=10;
shrinkFactor=0.2;
nSplitPattern=1;

%Define applied displacement
appliedStrain=0.3; %Linear strain (Only used to compute applied stretch)
loadingOption='compression'; % or 'tension'
switch loadingOption
    case 'compression'
        stretchLoad=1-appliedStrain; %The applied stretch for uniaxial loading
    case 'tension'
        stretchLoad=1+appliedStrain; %The applied stretch for uniaxial loading
end
displacementMagnitude=(stretchLoad*sampleSize)-sampleSize; %The displacement magnitude

%Material parameter set
E_youngs1=0.1; %Material Young's modulus
nu1=0.4; %Material Poisson's ratio

% 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 example geometry.

X=[-1;  1; 1; -1; -1;  1; 1; -1;];
Y=[-1; -1; 1;  1; -1; -1; 1;  1;];
Z=[-1; -1;-1; -1;  1;  1; 1;  1;];
V=sampleSize*[X(:) Y(:) Z(:)]/2;
E=1:8; %Element description of the 8-node cube (hexahedral element)

[E,V,C]=subHex(E,V,nSplitPattern); %Subdevide into 8 sub-cubes
[E,V,C]=hex2tet(E,V,C,1); %Convert to tetrahedral elements

[F,~]=element2patch(E,C); %Patch data for plotting
[indBoundary]=tesBoundary(F);

Create lattice structure

testCase=1;

controlParameter.meshType='hex'; %desired output mesh type
controlParameter.indBoundary=indBoundary; %indices of the boundary faces
switch testCase
    case 1
        controlParameter.shrinkFactor=shrinkFactor; %Strut sides are formed by shrinking the input mesh faces by this factor
        controlParameter.hexSplit=1; %Number of beam hex split steps
        controlParameter.latticeSide=2; %1=side 1 the edge lattice, 2=side 2 the dual lattice to the edge lattice
        [Es,Vs,Cs]=element2lattice(E,V,controlParameter);

    case 2

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

% Fs0=Fs(CsF==0,:);
% CsF0=CsF(CsF==0);

indB=tesBoundary(Fs);
Fb=Fs(indB,:);
CsFb=CsF(indB,:);
CFsb=CFs(indB,:);

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(F,V,'none','k',0,2);
gpatch(Fb,Vs,'bw','k',0.5);
axisGeom(gca,fontSize);
camlight headlight; lighting flat;

drawnow;

faceBoundaryMarker=zeros(size(Fb,1),1);

%Find top and bottom face sets
[Nb]=patchNormal(Fb,Vs);
zVec=[0 0 1];
d=dot(Nb,zVec(ones(size(Nb,1),1),:),2);
Z=Vs(:,3);
ZF=mean(Z(Fb),2);
logicTop_Fb=(d>0.9) & ZF>=(max(Vs(:,3))-eps(sampleSize));
logicBottom_Fb=(d<-0.9) & ZF<=(min(Vs(:,3))+eps(sampleSize));

xVec=[1 0 0];
d=dot(Nb,xVec(ones(size(Nb,1),1),:),2);
X=Vs(:,1);
XF=mean(X(Fb),2);
logicSides_Fb1=(d>0.9) & XF>=(max(Vs(:,1))-eps(sampleSize));
logicSides_Fb2=(d<-0.9) & XF<=(min(Vs(:,1))+eps(sampleSize));

yVec=[0 1 0];
d=dot(Nb,yVec(ones(size(Nb,1),1),:),2);
Y=Vs(:,2);
YF=mean(Y(Fb),2);
logicSides_Fb3=(d>0.9) & YF>=(max(Vs(:,2))-eps(sampleSize));
logicSides_Fb4=(d<-0.9) & YF<=(min(Vs(:,2))+eps(sampleSize));

faceBoundaryMarker(logicBottom_Fb)=1;
faceBoundaryMarker(logicTop_Fb)=2;
faceBoundaryMarker(logicSides_Fb1)=3;
faceBoundaryMarker(logicSides_Fb2)=4;
faceBoundaryMarker(logicSides_Fb3)=5;
faceBoundaryMarker(logicSides_Fb4)=6;

Smoothen lattice

%Get "clean" surface mesh for only the boundary
[Fb_clean,Vb_clean,indFix]=patchCleanUnused(Fb,Vs);

%Find indices of points to hold on to during smoothing
indKeep=Fb_clean(faceBoundaryMarker>0,:);
indKeep=unique(indKeep(:));

%Smoothing
cPar.Method='HC';
cPar.n=15;
cPar.RigidConstraints=indKeep;
[Vb_clean]=tesSmooth(Fb_clean,Vb_clean,[],cPar);

%Override coordinates in full mesh with smoothed coordinates
ind=Fb(:);
ind=unique(ind(:));
Vs(ind,:)=Vb_clean;

Visualize smoothed mesh

cFigure; hold on;
title('Smoothed mesh','FontSize',fontSize);
gpatch(F,V,'kw','none',0.1);
gpatch(Fb,Vs,faceBoundaryMarker,'k',1);
% plotV(Vb_clean(indKeep,:),'r.','markerSize',15)
axisGeom;
camlight headlight;
set(gca,'FontSize',fontSize);
% axis off
drawnow;

DEFINE BC's

%Supported nodes
bcSupportList=unique(Fb(faceBoundaryMarker==1,:));

%Prescribed force nodes
bcPrescribeList=unique(Fb(faceBoundaryMarker==2,:));

Visualize BC's

cFigure; hold on;
title('Boundary conditions','FontSize',fontSize);
gpatch(Fb,Vs,'kw','none',0.4);
hl(1)=plotV(Vs(bcSupportList,:),'k.','MarkerSize',markerSize);
hl(2)=plotV(Vs(bcPrescribeList,:),'r.','MarkerSize',markerSize);
legend(hl,{'BC full support','BC prescribed Z displacement'})
axisGeom;
camlight headlight;
set(gca,'FontSize',fontSize);
drawnow;

logicNotBeam=CsF==1;
Fss=Fs(logicNotBeam,:);

controlParGroup.outputType='label';
g=tesgroup(Fss,controlParGroup);

R=nan(max(g),1);

for q=1:1:max(g)
    logicNow= (g==q);
    F_now=Fss(logicNow,:);
    indNow=unique(F_now(:));
    indNow=indNow(ismember(indNow,Fb));
    V_now=Vs(indNow,:);
    V_now=V_now-mean(V_now);
    R(q)=mean(sqrt(sum(V_now.^2,2)));
end
strutThicknessMean=2*mean(R);

cFigure; hold on; gpatch(F,V,'none','k',0,2); gpatch(Fb,Vs,'none','k',1,1); gpatch(Fss,Vs,g,'k',0.5); axisGeom(gca,fontSize); camlight headlight; lighting flat; % colormap spectral; icolorbar drawnow;

Check porosity

vol_lattice=sum(hexVol(Es,Vs)); %Volume of hexahedra
porosity_lattice=vol_lattice./sampleSize.^3; %Porosity

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='neo-Hookean';
febio_spec.Material.material{1}.ATTR.id=1;
febio_spec.Material.material{1}.E=E_youngs1;
febio_spec.Material.material{1}.v=nu1;

%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(Vs,1))'; %The node id's
febio_spec.Mesh.Nodes{1}.node.VAL=Vs; %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(Es,1))'; %Element id's
febio_spec.Mesh.Elements{1}.elem.VAL=Es; %The element matrix

% -> NodeSets
nodeSetName1='bcSupportList';
febio_spec.Mesh.NodeSet{1}.ATTR.name=nodeSetName1;
febio_spec.Mesh.NodeSet{1}.VAL=mrow(bcSupportList);

nodeSetName2='bcPrescribeList';
febio_spec.Mesh.NodeSet{2}.ATTR.name=nodeSetName2;
febio_spec.Mesh.NodeSet{2}.VAL=mrow(bcPrescribeList);

%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='zero_displacement_xyz';
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;

febio_spec.Boundary.bc{2}.ATTR.name='zero_displacement_xy';
febio_spec.Boundary.bc{2}.ATTR.type='zero displacement';
febio_spec.Boundary.bc{2}.ATTR.node_set=nodeSetName2;
febio_spec.Boundary.bc{2}.x_dof=1;
febio_spec.Boundary.bc{2}.y_dof=1;
febio_spec.Boundary.bc{2}.z_dof=0;

febio_spec.Boundary.bc{3}.ATTR.name='prescibed_displacement_z';
febio_spec.Boundary.bc{3}.ATTR.type='prescribed displacement';
febio_spec.Boundary.bc{3}.ATTR.node_set=nodeSetName2;
febio_spec.Boundary.bc{3}.dof='z';
febio_spec.Boundary.bc{3}.value.ATTR.lc=1;
febio_spec.Boundary.bc{3}.value.VAL=displacementMagnitude;
febio_spec.Boundary.bc{3}.relative=0;

%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.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.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=',';

% Plotfile section
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

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    <-------- 20-Apr-2023 10:45:51
FEBio path: /home/kevin/FEBioStudio2/bin/febio4
# Attempt removal of existing log files                20-Apr-2023 10:45:51
 * Removal succesful                                   20-Apr-2023 10:45:51
# Attempt removal of existing .xplt files              20-Apr-2023 10:45:51
 * Removal succesful                                   20-Apr-2023 10:45:51
# Starting FEBio...                                    20-Apr-2023 10:45:51
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       20-Apr-2023 10:45:51
   Max. wait time: 30 s
 * Log file found.                                     20-Apr-2023 10:45:52
# Parsing log file...                                  20-Apr-2023 10:45:52
    number of iterations   : 3                         20-Apr-2023 10:45:53
    number of reformations : 3                         20-Apr-2023 10:45:53
------- converged at time : 0.1                        20-Apr-2023 10:45:53
    number of iterations   : 3                         20-Apr-2023 10:45:54
    number of reformations : 3                         20-Apr-2023 10:45:54
------- converged at time : 0.2                        20-Apr-2023 10:45:54
    number of iterations   : 4                         20-Apr-2023 10:45:55
    number of reformations : 4                         20-Apr-2023 10:45:55
------- converged at time : 0.3                        20-Apr-2023 10:45:55
    number of iterations   : 4                         20-Apr-2023 10:45:57
    number of reformations : 4                         20-Apr-2023 10:45:57
------- converged at time : 0.4                        20-Apr-2023 10:45:57
    number of iterations   : 4                         20-Apr-2023 10:45:58
    number of reformations : 4                         20-Apr-2023 10:45:58
------- converged at time : 0.5                        20-Apr-2023 10:45:58
    number of iterations   : 4                         20-Apr-2023 10:45:59
    number of reformations : 4                         20-Apr-2023 10:45:59
------- converged at time : 0.6                        20-Apr-2023 10:45:59
    number of iterations   : 4                         20-Apr-2023 10:46:01
    number of reformations : 4                         20-Apr-2023 10:46:01
------- converged at time : 0.7                        20-Apr-2023 10:46:01
    number of iterations   : 4                         20-Apr-2023 10:46:02
    number of reformations : 4                         20-Apr-2023 10:46:02
------- converged at time : 0.8                        20-Apr-2023 10:46:02
    number of iterations   : 4                         20-Apr-2023 10:46:03
    number of reformations : 4                         20-Apr-2023 10:46:03
------- converged at time : 0.9                        20-Apr-2023 10:46:03
    number of iterations   : 3                         20-Apr-2023 10:46:04
    number of reformations : 3                         20-Apr-2023 10:46:04
------- converged at time : 1                          20-Apr-2023 10:46:04
 Elapsed time : 0:00:12                                20-Apr-2023 10:46:04
 N O R M A L   T E R M I N A T I O N
# Done                                                 20-Apr-2023 10:46:04
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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
    Vs_DEF=N_disp_mat+repmat(Vs,[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,Vs_DEF(:,:,end),DN_magnitude,'k',1); %Add graphics object to animate

    hp.FaceColor='interp';

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([0 max(DN_magnitude)]);
    axis(axisLim(Vs_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}={Vs_DEF(:,:,qt),DN_magnitude}; %Property values for to set in order to animate
    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(Es,Vs,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('$\sigma_{zz}$ [MPa]','Interpreter','Latex')
    hp=gpatch(Fb,Vs_DEF(:,:,end),CV,'k',1); %Add graphics object to animate

    hp.FaceColor='interp';

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([min(E_stress_mat(:)) max(E_stress_mat(:))]/3);
    axis(axisLim(Vs_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(Es,Vs,E_stress_mat(:,:,qt));

        %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(:,:,qt),CV}; %Property values for to set in order to animate
    end
    anim8(hf,animStruct); %Initiate animation feature
    drawnow;

Importing nodal forces from a log file

    [dataStruct]=importFEBio_logfile(fullfile(savePath,febioLogFileName_force),0,1); %Nodal forces

    %Access data
    timeVec=dataStruct.time;
    f_sum_x=squeeze(sum(dataStruct.data(bcPrescribeList,1,:),1));
    f_sum_y=squeeze(sum(dataStruct.data(bcPrescribeList,2,:),1));
    f_sum_z=squeeze(sum(dataStruct.data(bcPrescribeList,3,:),1));

Visualize force data

    displacementApplied=timeVec.*displacementMagnitude;

    cFigure; hold on;
    xlabel('$u$ [mm]','Interpreter','Latex');
    ylabel('$F_z$ [N]','Interpreter','Latex');
    hp=plot(displacementApplied(:),f_sum_z(:),'b-','LineWidth',3);
    grid on; box on; axis square; axis tight;
    set(gca,'FontSize',fontSize);
    drawnow;

end

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

GIBBON footer text

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/.