DEMO_febio_0060_vertebrae_disc_01

Below is a demonstration for:

Building triangulated surface geometry for a spine segment
Defining the boundary conditions
Coding the febio structure
Running the model
Importing and visualizing results

Keywords
Control parameters
Get vertebra bone model
Mesh disc with tetrahedral elements
Joining node sets
Define boundary conditions
Defining the FEBio input structure
Running the FEBio analysis
Export input file
Run febio
Importing rigid body reaction forces from a log file
Plot animation

Keywords

febio_spec version 2.5
febio, FEBio
spine, vertebra, disc
contact, sliding, friction
tetrahedral elements, tet4
hexahedral elements, hex8
static, solid
hyperelastic, Ogden
displacement logfile

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=1;
faceAlpha2=0.3;
markerSize1=25;
markerSize2=10;
lineWidth=2;
boneColor=[1.0000    0.9500    0.8000];
discColor=[0.8500    0.5000    0.3000];

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_strainEnergy=[febioFebFileNamePart,'_energy_out.txt']; %Log file name for exporting strain energy density

%Geometric parameters
vertebraOffset=[0 0 30];
discHeight=12;
rotAngleVert2=0;
volumeFactorDisc=1;
annulusFibrosusFraction=0.5;
numLayers=3;
% Material parameters
% Disc
c1_1=1; %Shear-modulus-like parameter in MPa
m1_1=2; %Material parameter setting degree of non-linearity
k_1=c1_1*100; %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=10; %Optimum number of iterations
max_retries=8; %Maximum number of retires
dtmin=(1/numTimeSteps)/100; %Minimum time step size
dtmax=1/numTimeSteps; %Maximum time step size
symmetric_stiffness=0;
min_residual=1e-20;
runMode='external';

%Boundary condition parameters
forceApplied=1;
displacementMagnitude=-1;

Get vertebra bone model

[F1,V1]=graphicsModels('vertebra');
rotAngle=-6;
R=euler2DCM([0 (rotAngle./180)*pi 0]);
V1=V1*R;
pointSpacing=mean(patchEdgeLengths(F1,V1));

V1F=patchCentre(F1,V1);

N=patchNormal(F1,V1);
nz=[0 0 1];
a=acos(dot(N,nz(ones(size(N,1),1),:),2));

D=sqrt(sum(V1F(:,[1 2]).^2,2));
logicTop=D<24 & a<0.27;
indNotInLogic=unique(F1(~logicTop,:));
logicTop=logicTop & ~any(ismember(F1,indNotInLogic),2);
logicTop=triSurfLogicSharpFix(F1,logicTop,3);

D=minDist(V1F(:,[1 2]),V1F(logicTop,[1 2]));
logicBottom=D<3 & a>pi-0.4;
logicBottom=triSurfLogicSharpFix(F1,logicBottom,3);

indNotInLogic=unique(F1(~logicBottom,:));
logicBottom=logicBottom & ~any(ismember(F1,indNotInLogic),2);
logicBottom=triSurfLogicSharpFix(F1,logicBottom,3);

C1=zeros(size(F1,1),1);
C1(logicTop)=1;
C1(logicBottom)=2;

Eb1=patchBoundary(F1(C1==1,:),V1);
indList1=edgeListToCurve(Eb1);
indList1=indList1(1:end-1);

Eb2=patchBoundary(F1(C1==2,:),V1);
indList2=edgeListToCurve(Eb2);
indList2=indList2(1:end-1);

n=[numel(indList1) numel(indList2)];
[nMax,indMax]=max(n);
nn=abs(diff(n));
switch indMax
    case 1
        [F1,V1,Eb2,C1]=triSurfSplitBoundary(F1,V1,Eb2,size(Eb2,1)+nn,C1);
        indList2=edgeListToCurve(Eb2);
        indList2=indList2(1:end-1);
    case 2
        [F1,V1,Eb1,C1]=triSurfSplitBoundary(F1,V1,Eb1,size(Eb1,1)+nn,C1);
        indList1=edgeListToCurve(Eb1);
        indList1=indList1(1:end-1);
end

indList2=fliplr(indList2);

nc=10;
ns=50;
[V1]=smoothCurve(F1,V1,nc,ns,indList1);
[V1]=smoothCurve(F1,V1,nc,ns,indList2);

P11=mean(V1(indList1,:),1);
N11=mean(patchNormal(F1(C1==1,:),V1),1);

P12=mean(V1(indList2,:),1);
N12=-mean(patchNormal(F1(C1==2,:),V1),1);

cFigure; hold on;
gpatch(F1,V1,C1,'k',1);
plotV(V1(indList1,:),'r.-','MarkerSize',25,'LineWidth',3);
plotV(V1(indList2,:),'r.-','MarkerSize',25,'LineWidth',3);
% plotV(V1(indRigid,:),'c.','MarkerSize',15);
quiverVec(P11,N11,5,'r');
quiverVec(P12,N12,5,'r');

axisGeom(gca,fontSize);
colormap gjet; icolorbar;
camlight('headlight');
gdrawnow;

F2=F1;
V2=V1;
C2=C1;

R2=euler2DCM([0 (rotAngleVert2./180)*pi 0]);
V2=V2*R2;
V2=V2+vertebraOffset(ones(size(V1,1),1),:);
V2(:,3)=V2(:,3)+discHeight;

P21=mean(V2(indList1,:),1);
N21=mean(patchNormal(F2(C2==1,:),V2),1);

P22=mean(V2(indList2,:),1);
N22=-mean(patchNormal(F2(C2==2,:),V2),1);

f=discHeight/3;
p=[P11;P11+f*N11; P22-f*N22; P22];

numStepsCurve=ceil(discHeight./pointSpacing);
Vg=bezierCurve(p,numStepsCurve);

[Fds,Vds,Cds]=sweepLoft(V1(indList1,:),V2(indList2,:),N11,N12,Vg,numStepsCurve);
[~,~,Nd]=patchNormal(Fds,Vds);
CVds=faceToVertexMeasure(Fds,Vds,Cds);
CVds=CVds-min(CVds(:));
CVds=CVds./max(CVds(:));
CVds=abs(CVds-0.5);
CVds=CVds./max(CVds(:));
CVds=CVds.^2;
CVds=1-CVds;
Vds=Vds+discHeight/10*Nd.*CVds;

[Fds,Vds]=quad2tri(Fds,Vds,'a');

clear cPar;
cPar.n=5;
cPar.Method='HC';
cPar.RigidConstraints=unique(patchBoundary(Fds,Vds));
[Vds]=patchSmooth(Fds,Vds,[],cPar);

[Fd,Vd,Cd]=joinElementSets({Fds,fliplr(F2(C2==2,:)),fliplr(F1(C1==1,:))},{Vds,V2,V1});
[Fd,Vd]=patchCleanUnused(Fd,Vd);
[Fd,Vd]=mergeVertices(Fd,Vd);

Visualize imported surfaces

cFigure; hold on;
gpatch(F1,V1,'rw','none',0.5);
gpatch(F2,V2,'gw','none',0.5);
gpatch(Fd,Vd,Cd,'k',1);

% plotV(Vg,'r.-','MarkerSize',25,'LineWidth',3);

camlight('headlight');
axisGeom(gca,fontSize);
colormap gjet; icolorbar;
gdrawnow;

Mesh disc with tetrahedral elements

Tet meshing is based on tetgen. TetGen requires a interior points for regions to be meshed, as well as intertior points for holes.

Define region points

[V_region]=getInnerPoint(Fd,Vd);

Visualize interior points

cFigure; hold on;
hp1=gpatch(Fd,Vd,'kw','none',0.5);
patchNormPlot(Fd,Vd);
hp2=plotV(V_region,'r.','markerSize',markerSize1);
legend([hp1 hp2],{'Disc mesh','Region point'});
axisGeom(gca,fontSize);
camlight('headlight');
gdrawnow;

Mesh using tetgen

inputStruct.stringOpt='-pq1.2AaY'; %TetGen option string
inputStruct.Faces=Fd; %The faces
inputStruct.Nodes=Vd; %The vertices
inputStruct.holePoints=[]; %The hole interior points
inputStruct.faceBoundaryMarker=Cd; %Face boundary markers
inputStruct.regionPoints=V_region; %The region interior points
inputStruct.regionA=tetVolMeanEst(Fd,Vd)*volumeFactorDisc; %Volume for regular tets

Mesh model using tetrahedral elements using tetGen

[meshOutput]=runTetGen(inputStruct); %Run tetGen

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- TETGEN Tetrahedral meshing --- 07-Jul-2020 10:03:14
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Writing SMESH file --- 07-Jul-2020 10:03:14
----> Adding node field
----> Adding facet field
----> Adding holes specification
----> Adding region specification
--- Done --- 07-Jul-2020 10:03:14
--- Running TetGen to mesh input boundary--- 07-Jul-2020 10:03:14
Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh.
Delaunizing vertices...
Delaunay seconds:  0.018735
Creating surface mesh ...
Surface mesh seconds:  0.002958
Recovering boundaries...
Boundary recovery seconds:  0.004153
Removing exterior tetrahedra ...
Spreading region attributes.
Exterior tets removal seconds:  0.002478
Recovering Delaunayness...
Delaunay recovery seconds:  0.002329
Refining mesh...
Refinement seconds:  0.169956
Optimizing mesh...
Optimization seconds:  0.013369

Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node.
Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele.
Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face.
Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge.

Output seconds:  0.156609
Total running seconds:  0.370885

Statistics:

  Input points: 2066
  Input facets: 4128
  Input segments: 6192
  Input holes: 0
  Input regions: 1

  Mesh points: 12558
  Mesh tetrahedra: 73607
  Mesh faces: 149278
  Mesh faces on exterior boundary: 4128
  Mesh faces on input facets: 4128
  Mesh edges on input segments: 6192
  Steiner points inside domain: 10492

--- Done --- 07-Jul-2020 10:03:14
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Importing TetGen files --- 07-Jul-2020 10:03:14
--- Done --- 07-Jul-2020 10:03:15

Access model element and patch data

Fb_disc=meshOutput.facesBoundary; %Boundary faces of the disc
Cb_disc=meshOutput.boundaryMarker; %Boundary marker/color data for the disc
V_disc=meshOutput.nodes; %The vertices/nodes
E_disc=meshOutput.elements; %The tet4 elements

Visualizing mesh using meshView, see also anim8

meshView(meshOutput);

VE_disc=patchCentre(E_disc,V_disc);
Eb=patchBoundary(Fb_disc(ismember(Cb_disc,[2,3]),:),V_disc);
indB=unique(Fb_disc(ismember(Cb_disc,1),:));
[D,~]=minDist(VE_disc(:,[1 2]),V_disc(indB,[1 2]));
D=D./max(D(:));
D=1-D;
logicAnnulusFibrosus=D<=annulusFibrosusFraction;
D(logicAnnulusFibrosus)=annulusFibrosusFraction;
D=D-min(D(:));
D=D./max(D(:));


[FE,CF]=element2patch(E_disc,logicAnnulusFibrosus);

cFigure;  hold on;
gpatch(FE,V_disc,CF,'k',1);

axisGeom;
camlight headlight;
view(2);
colormap gjet; colorbar;
gdrawnow;

VEb=patchCentre(Eb,V_disc);
t = atan2(VEb(:,2),VEb(:,1));
T = atan2(VE_disc(:,2),VE_disc(:,1));


VEb=patchCentre(Eb,V_disc);
NE=vecnormalize(V_disc(Eb(:,1),:)-V_disc(Eb(:,2),:));
NE(:,3)=0;
NE=vecnormalize(NE);
[~,indMin]=minDist(T,t);
% z=[0 0 1];
% NFC=cross(NF,z(ones(size(NF,1),1),:),2);
NE_disc=NE(indMin,:);

% NE_disc(:,[1 2])=NE_disc(:,[1 2]).*sin(numLayers.*D(:,ones(1,2)).*2*pi);
% NE_disc(:,3)=cos(numLayers.*D.*2*pi);
% NE_disc(logicAnnulusFibrosus,:)=NaN;

logicEven=iseven(round(D.*numLayers));
NE_disc(logicEven,3)=1;
NE_disc(~logicEven,3)=-1;
NE_disc=vecnormalize(NE_disc);
NE_disc(logicAnnulusFibrosus,:)=NaN;

cFigure;  hold on;
gpatch(Fb_disc,V_disc,'w','none',0.1);
gpatch(Eb,V_disc,'none','k',1,3);
% plotV(VE_disc,'k.','MarkerSize',1);
plotV(mean(V_disc,1),'r.','MarkerSize',25);
quiverVec(VE_disc(1:10:end,:),NE_disc(1:10:end,:),1,D(1:10:end,:));
axisGeom;
camlight headlight;
view(2);
colormap gjet;
gdrawnow;

Joining node sets

V=[V_disc;V1;V2]; %Combined node sets
E1=F1+size(V_disc,1); %Fixed element indices
E2=F2+size(V_disc,1)+size(V1,1); %Fixed element indices

numDigitsMerge=6-numOrder(pointSpacing);
[~,indKeep,indFix]=unique(pround(V,numDigitsMerge),'rows');
V=V(indKeep,:);
E_disc=indFix(E_disc);
E1=indFix(E1);
E2=indFix(E2);
Fb_disc=indFix(Fb_disc);

Define boundary conditions

Visualize BC's

cFigure; hold on;
title('Boundary conditions');
hp(1)=gpatch(Fb_disc,V,'w','none',0.5);
hp(2)=gpatch(E1,V,'rw','none',1);
hp(3)=gpatch(E2,V,'bw','none',1);
legend(hp,{'Disc','Constrained vertebra','BC vertebra'});

axisGeom;
camlight headlight;
gdrawnow;

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.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_1;
febio_spec.Material.material{1}.m1=m1_1;
febio_spec.Material.material{1}.c2=c1_1;
febio_spec.Material.material{1}.m2=-m1_1;
febio_spec.Material.material{1}.k=k_1;

febio_spec.Material.material{2}.ATTR.type='rigid body';
febio_spec.Material.material{2}.ATTR.id=2;
febio_spec.Material.material{2}.density=1;
febio_spec.Material.material{2}.center_of_mass=mean(V1);

febio_spec.Material.material{3}.ATTR.type='rigid body';
febio_spec.Material.material{3}.ATTR.id=3;
febio_spec.Material.material{3}.density=1;
febio_spec.Material.material{3}.center_of_mass=mean(V2);

%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(V,1))'; %The node id's
febio_spec.Geometry.Nodes{1}.node.VAL=V; %The nodel coordinates

% -> Elements
febio_spec.Geometry.Elements{1}.ATTR.type='tet4'; %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='disc'; %Name of the element set
febio_spec.Geometry.Elements{1}.elem.ATTR.id=(1:1:size(E_disc,1))'; %Element id's
febio_spec.Geometry.Elements{1}.elem.VAL=E_disc;

febio_spec.Geometry.Elements{2}.ATTR.type='tri3'; %Element type of this set
febio_spec.Geometry.Elements{2}.ATTR.mat=2; %material index for this set
febio_spec.Geometry.Elements{2}.ATTR.name='Bone1'; %Name of the element set
febio_spec.Geometry.Elements{2}.elem.ATTR.id=size(E_disc,1)+(1:1:size(E1,1))'; %Element id's
febio_spec.Geometry.Elements{2}.elem.VAL=E1;

febio_spec.Geometry.Elements{3}.ATTR.type='tri3'; %Element type of this set
febio_spec.Geometry.Elements{3}.ATTR.mat=3; %material index for this set
febio_spec.Geometry.Elements{3}.ATTR.name='Bone2'; %Name of the element set
febio_spec.Geometry.Elements{3}.elem.ATTR.id=size(E_disc,1)+size(E1,1)+(1:1:size(E2,1))'; %Element id's
febio_spec.Geometry.Elements{3}.elem.VAL=E2;

% -> NodeSets
febio_spec.Geometry.NodeSet{1}.ATTR.name='All';
febio_spec.Geometry.NodeSet{1}.node.ATTR.id=(1:1:size(V,1))';

%Boundary condition section
% -> Prescribed boundary conditions on the rigid body
febio_spec.Boundary.rigid_body{1}.ATTR.mat=2;
febio_spec.Boundary.rigid_body{1}.fixed{1}.ATTR.bc='x';
febio_spec.Boundary.rigid_body{1}.fixed{2}.ATTR.bc='y';
febio_spec.Boundary.rigid_body{1}.fixed{3}.ATTR.bc='z';
febio_spec.Boundary.rigid_body{1}.fixed{4}.ATTR.bc='Rx';
febio_spec.Boundary.rigid_body{1}.fixed{5}.ATTR.bc='Ry';
febio_spec.Boundary.rigid_body{1}.fixed{6}.ATTR.bc='Rz';

febio_spec.Boundary.rigid_body{2}.ATTR.mat=3;
febio_spec.Boundary.rigid_body{2}.fixed{1}.ATTR.bc='x';
febio_spec.Boundary.rigid_body{2}.fixed{2}.ATTR.bc='y';
febio_spec.Boundary.rigid_body{2}.fixed{3}.ATTR.bc='Rx';
febio_spec.Boundary.rigid_body{2}.fixed{4}.ATTR.bc='Ry';
febio_spec.Boundary.rigid_body{2}.fixed{5}.ATTR.bc='Rz';

febio_spec.Boundary.rigid_body{2}.prescribed.ATTR.bc='z';
febio_spec.Boundary.rigid_body{2}.prescribed.ATTR.lc=1;
febio_spec.Boundary.rigid_body{2}.prescribed.VAL=displacementMagnitude;

% febio_spec.Boundary.rigid_body{2}.force.ATTR.bc='z';
% febio_spec.Boundary.rigid_body{2}.force.ATTR.lc=1;
% febio_spec.Boundary.rigid_body{2}.force.VAL=forceBody;

%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.rigid_body_data{1}.ATTR.file=febioLogFileName_force;
febio_spec.Output.logfile.rigid_body_data{1}.ATTR.data='Fx;Fy;Fz';
febio_spec.Output.logfile.rigid_body_data{1}.ATTR.delim=',';
febio_spec.Output.logfile.rigid_body_data{1}.VAL=2; %Rigid body material id

febio_spec.Output.logfile.element_data{1}.ATTR.file=febioLogFileName_strainEnergy;
febio_spec.Output.logfile.element_data{1}.ATTR.data='sed';
febio_spec.Output.logfile.element_data{1}.ATTR.delim=',';
febio_spec.Output.logfile.element_data{1}.VAL=1:size(E_disc,1);

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=runMode;%'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

Export 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

Run febio

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

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- STARTING FEBIO JOB --- 07-Jul-2020 10:03:26
Waiting for log file...
Proceeding to check log file...07-Jul-2020 10:03:27
------- converged at time : 0.1
------- converged at time : 0.2
------- converged at time : 0.3
------- converged at time : 0.4
------- converged at time : 0.5
------- converged at time : 0.6
------- converged at time : 0.7
------- converged at time : 0.8
------- converged at time : 0.9
------- converged at time : 1
--- Done --- 07-Jul-2020 10:04:16

Importing rigid body reaction forces from a log file

        [time_mat, R_force_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_force)); %Nodal forces
        time_mat=[0; time_mat(:)]; %Time

        F_reaction=[0 0 0; R_force_mat(:,2:end)]; %Get force, add zeros, remove rigidbody id column

        Fz_final=F_reaction(end,3);

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);

V_def=V+DN;
V_DEF=N_disp_mat+repmat(V,[1 1 size(N_disp_mat,3)]);
X_DEF=V_DEF(:,1,:);
Y_DEF=V_DEF(:,2,:);
Z_DEF=V_DEF(:,3,:);

C=sqrt(sum(DN(:,3).^2,2));
[CF]=vertexToFaceMeasure(Fb_disc,C);

Importing element strain energies from a log file

[~,E_energy,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_strainEnergy)); %Element strain energy

%Remove nodal index column
E_energy=E_energy(:,2:end,:);

%Add initial state i.e. zero energy
sizImport=size(E_energy);
sizImport(3)=sizImport(3)+1;
E_energy_mat_n=zeros(sizImport);
E_energy_mat_n(:,:,2:end)=E_energy;
E_energy=E_energy_mat_n;

[FE_disc,C_energy_disc]=element2patch(E_disc,E_energy(:,:,end));
%     [FE_disc,C_energy_disc]=element2patch(E_disc,E_energy(1:size(E_disc,1),:,1));
indBoundaryFacesdisc=tesBoundary(FE_disc,V);

Plot animation

Plotting the simulated results using anim8 to visualize and animate deformations

% Create basic view and store graphics handle to initiate animation
hf=cFigure; hold on; %Open figure
gtitle([febioFebFileNamePart,': Press play to animate']);
CV=faceToVertexMeasure(FE_disc(indBoundaryFacesdisc,:),V_def,C_energy_disc(indBoundaryFacesdisc));
hp1=gpatch(Fb_disc,V_def,CV,'none',1); %Add graphics object to animate
hp1.FaceColor='Interp';
hp2=gpatch([E1;E2],V_def,'w','none',0.5); %Add graphics object to animate

axisGeom(gca,fontSize);
colormap(gjet(250)); colorbar;
caxis([0 max(C_energy_disc)/25]);
axis([min(X_DEF(:)) max(X_DEF(:)) min(Y_DEF(:)) max(Y_DEF(:)) min(Z_DEF(:)) max(Z_DEF(:))]);
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
    V_def=V+DN; %Current nodal coordinates

    [FE_disc,C_energy_disc]=element2patch(E_disc,E_energy(:,:,qt));
    CV=faceToVertexMeasure(FE_disc(indBoundaryFacesdisc,:),V_def,C_energy_disc(indBoundaryFacesdisc));

    %Set entries in animation structure
    animStruct.Handles{qt}=[hp1 hp1 hp2]; %Handles of objects to animate
    animStruct.Props{qt}={'Vertices','CData','Vertices'}; %Properties of objects to animate
    animStruct.Set{qt}={V_def,CV,V_def}; %Property values for to set in order to animate
end
anim8(hf,animStruct); %Initiate animation feature
gdrawnow;

function [V1]=smoothCurve(F1,V1,nc,ns,indList1)
clear cPar
cPar.n=nc;
cPar.Method='HC';
e=[(1:numel(indList1))' [(2:numel(indList1))';1]];
v=V1(indList1,:);
[v]=patchSmooth(e,v,[],cPar);
V1(indList1,:)=v;

indTouch=unique(F1(any(ismember(F1,indList1),2),:));
indTouch=unique(F1(any(ismember(F1,indTouch),2),:));
logicRigid=true(size(V1,1),1);
logicRigid(indTouch)=0;
logicRigid(indList1)=1;
indRigid=find(logicRigid);

cPar.n=ns;
cPar.Method='HC';
cPar.RigidConstraints=indRigid;
[V1]=patchSmooth(F1,V1,[],cPar);
end

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

GIBBON discer 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/.