DEMO_febio_0026_hexlattice_compression

Below is a demonstration for:

Contents

Keywords

clear; close all; clc;

Plot settings

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;

%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
c1=1e-3; %Shear-modulus-like parameter
m1=6; %Material parameter setting degree of non-linearity
k_factor=500; %Bulk modulus factor
k=c1*k_factor; %Bulk modulus
formulationType='uncoupled'; %coupled

% 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

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); %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

% Create lattice structure
controlParameter.growSteps=1; %0 is normal, positive or negative integers increase or decrease the edge lattice thickness respectively
controlParameter.latticeSide=2; %Empty outputs both, 1=side 1 the edge lattice, 2=side 2 the dual lattice to the edge lattice
[Es,Vs,Cs]=element2HexLattice(E,V,controlParameter); %Get lattice structure
elementMaterialIndices=ones(size(Es,1),1);

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

indB=tesBoundary(Fs,Vs);
Fb=Fs(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(Fb,Vs,'bw');
% patchNormPlot(Fs,Vs);
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));

logicSides_Fb=logicSides_Fb1 | logicSides_Fb2 | logicSides_Fb3 | logicSides_Fb4;

faceBoundaryMarker(logicBottom_Fb)=1;
faceBoundaryMarker(logicTop_Fb)=2;
faceBoundaryMarker(logicSides_Fb)=3;

cFigure;
hold on;
gpatch(Fs,Vs,'kw','none',0.2);
gpatch(Fb(faceBoundaryMarker==1,:),Vs,'r','k',1);
gpatch(Fb(faceBoundaryMarker==2,:),Vs,'b','k',1);
% gpatch(Fb(faceBoundaryMarker==3,:),Vs,'g','k',1);
axisGeom(gca,fontSize);
colormap(cMap);
camlight headlight; lighting flat;
drawnow;

DEFINE BC's

%Supported nodes
logicRigid=faceBoundaryMarker==1;
Fr=Fb(logicRigid,:);
bcRigidList=unique(Fr(:));

%Prescribed force nodes
logicPrescribe=faceBoundaryMarker==2;
Fr=Fb(logicPrescribe,:);
bcPrescribeList=unique(Fr(:));
bcPrescribeMagnitudes=displacementMagnitude(ones(1,numel(bcPrescribeList)),:);

Visualize BC's

cFigure; hold on;
title('Boundary conditions','FontSize',fontSize);
gpatch(Fb,Vs,0.5*ones(1,3),'none',0.4);
hl(1)=plotV(Vs(bcRigidList,:),'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;
[Fb_clean,Vb_clean,indFix]=patchCleanUnused(Fb,Vs);

cPar.Method='HC';
cPar.n=15;
indKeep=Fb_clean(faceBoundaryMarker>0,:);
indKeep=unique(indKeep(:));
cPar.RigidConstraints=indKeep;

[Vb_clean]=tesSmooth(Fb_clean,Vb_clean,[],cPar);
ind=Fb(:);
ind=unique(ind(:));
Vs(ind,:)=Vb_clean;
cFigure; hold on;
title('Smoothed mesh','FontSize',fontSize);
gpatch(Fs,Vs,'kw','k',1);
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;

%Material section
switch formulationType
    case 'coupled'
        febio_spec.Material.material{1}.ATTR.type='Ogden unconstrained';
        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}.cp=k;
    case 'uncoupled'
        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;
end

%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
febio_spec.Geometry.NodeSet{1}.ATTR.name='bcRigidList';
febio_spec.Geometry.NodeSet{1}.node.ATTR.id=bcRigidList(:);

febio_spec.Geometry.NodeSet{2}.ATTR.name='bcPrescribeList';
febio_spec.Geometry.NodeSet{2}.node.ATTR.id=bcPrescribeList(:);

%Boundary condition section
% -> Fix boundary conditions
febio_spec.Boundary.fix{1}.ATTR.bc='x';
febio_spec.Boundary.fix{1}.ATTR.node_set=febio_spec.Geometry.NodeSet{1}.ATTR.name;
febio_spec.Boundary.fix{2}.ATTR.bc='y';
febio_spec.Boundary.fix{2}.ATTR.node_set=febio_spec.Geometry.NodeSet{1}.ATTR.name;
febio_spec.Boundary.fix{3}.ATTR.bc='z';
febio_spec.Boundary.fix{3}.ATTR.node_set=febio_spec.Geometry.NodeSet{1}.ATTR.name;
febio_spec.Boundary.fix{4}.ATTR.bc='x';
febio_spec.Boundary.fix{4}.ATTR.node_set=febio_spec.Geometry.NodeSet{2}.ATTR.name;
febio_spec.Boundary.fix{5}.ATTR.bc='y';
febio_spec.Boundary.fix{5}.ATTR.node_set=febio_spec.Geometry.NodeSet{2}.ATTR.name;

% -> Prescribe boundary conditions
febio_spec.Boundary.prescribe{1}.ATTR.bc='z';
febio_spec.Boundary.prescribe{1}.ATTR.node_set=febio_spec.Geometry.NodeSet{2}.ATTR.name;
febio_spec.Boundary.prescribe{1}.scale.ATTR.lc=1;
febio_spec.Boundary.prescribe{1}.scale.VAL=1;
febio_spec.Boundary.prescribe{1}.relative=1;
febio_spec.Boundary.prescribe{1}.value=displacementMagnitude;

%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=3; %Max log file checking time

[runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- STARTING FEBIO JOB --- 04-Jun-2019 12:53:39
Waiting for log file...
Proceeding to check log file...04-Jun-2019 12:53:41
------- converged at time : 0.1
------- converged at time : 0.181833
------- converged at time : 0.25767
------- converged at time : 0.33834
------- converged at time : 0.419009
------- converged at time : 0.503545
------- converged at time : 0.591173
------- converged at time : 0.681276
------- converged at time : 0.773359
------- converged at time : 0.867024
------- converged at time : 0.961957
------- converged at time : 1
--- Done --- 04-Jun-2019 12:54:08

Import FEBio results

if runFlag==1 %i.e. a succesful run
    % Importing nodal displacements from a log file
    [~, N_disp_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_disp)); %Nodal displacements

    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;
    [CF]=vertexToFaceMeasure(Fb,DN_magnitude);

    % 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)'];

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,CF,'k',1); %Add graphics object to animate
    gpatch(Fb,Vs,0.5*ones(1,3),'none',0.25); %A static graphics object

    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
        [CF]=vertexToFaceMeasure(Fb,DN_magnitude); %Current color data to use

        %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,CF}; %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) 2019 Kevin Mattheus Moerman

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.

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