DEMO_create_run_import_FEBIO_spheres_pressure

Below is a demonstration for:

Contents

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=0.5;
faceAlpha2=0.5;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;

% path names
defaultFolder = fileparts(fileparts(mfilename('fullpath')));
savePath=fullfile(defaultFolder,'data','temp');

Defining the surface models

The model will consists of two spheres one contained within the other defining two material regions. A stiff core and a soft outer later.

Control parameters for surface models

r1=2; %Outer sphere radius
numRefine1=2; %Number of refinement steps from icosahedron
faceBoundMarker1=2; %Face marker for outer sphere

r2=1.25; %Inner sphere radius
numRefine2=2; %Number of refinement steps from icosahedron
faceBoundMarker2=3; %Face marker for inner sphere

Building the spheres using geoSphere function

[F1,V1,~]=geoSphere(numRefine1,r1);
[F2,V2,~]=geoSphere(numRefine2,r2);

% Merging the model geometries into a single set
V=[V1;V2]; %Joining nodes
F=[F1;F2+size(V1,1)]; %Joining faces
faceBoundaryMarker=[faceBoundMarker1*ones(size(F1,1),1); faceBoundMarker2*ones(size(F2,1),1)]; %Create boundary markers for faces

Plotting surface models

hf=cFigure;
title('Surface models','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;

patch('Faces',F,'Vertices',V,'FaceColor','flat','CData',faceBoundaryMarker,'FaceAlpha',faceAlpha1,'lineWidth',edgeWidth,'edgeColor',edgeColor);
colormap(autumn(2));
colorbar;
camlight headlight;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;

CREATING A SOLID TETRAHEDRAL MESH USING TETGEN

First region points need to be defined. These represent a list of arbitrary coordinates for points inside the regions. 1 point per region is specified. For the example here the points are easily specified. Sometimes a raytracing algorythm or the use of the triSurf2Im function is required to find interior points.

V_regions=[0 0 (r1+r2)/2;0 0 0;]; % Define region points

Next holes are defined. These are similar to regions. However holes, as the name suggests, are regions that a not meshed and are left empty. This model does not contain holes so the list is empty

V_holes=[]; %Define hole points

For each region the mesh density parameter can be specified regionA=[0.005 0.005]; % Regional mesh parameters

[edgeLengths]=patchEdgeLengths(F1,V1);
edgeLengthsMean=mean(edgeLengths);
meanProposedVolume=edgeLengthsMean^3./(6*sqrt(2)); %For regular tetrahedron
region1_A=0.5.*meanProposedVolume;

[edgeLengths]=patchEdgeLengths(F2,V2);
edgeLengthsMean=mean(edgeLengths);
meanProposedVolume=edgeLengthsMean^3./(6*sqrt(2)); %For regular tetrahedron
region2_A=0.5.*meanProposedVolume;

regionA=[region1_A region2_A];

CREATING THE SMESH STRUCTURE. TetGen can mesh geometries from various mesh file formats. For the GIBBON toolbox .smesh files have been implemented. Below a structure is created that fully defines such as smesh file and the meshing settings for TetGen.

stringOpt='-pq1.2AaYQ';
modelName=fullfile(savePath,'tempModel');
smeshName=[modelName,'.smesh'];

smeshStruct.stringOpt=stringOpt;
smeshStruct.Faces=F;
smeshStruct.Nodes=V;
smeshStruct.holePoints=V_holes;
smeshStruct.faceBoundaryMarker=faceBoundaryMarker; %Face boundary markers
smeshStruct.regionPoints=V_regions; %region points
smeshStruct.regionA=regionA;
smeshStruct.minRegionMarker=2; %Minimum region marker
smeshStruct.smeshName=smeshName;

Mesh model using tetrahedral elements using tetGen (see: http://wias-berlin.de/software/tetgen/)

[meshOutput]=runTetGen(smeshStruct); %Run tetGen
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- TETGEN Tetrahedral meshing --- 13-Mar-2017 16:30:10
Warning: smeshStruct.smeshName input will be replaced by smeshStruct.modelName
in future releases! 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Writing SMESH file --- 13-Mar-2017 16:30:10
Warning: smeshStruct.smeshName input will be replaced by smeshStruct.modelName
in future releases! 
----> Adding node field
----> Adding facet field
----> Adding holes specification
----> Adding region specification
--- Done --- 13-Mar-2017 16:30:10
--- Running TetGen to mesh input boundary--- 13-Mar-2017 16:30:10
Opening /mnt/data/MATLAB/GIT/GIBBON/lib_ext/tetGen/tempFiles/tempModel.smesh.
--- Done --- 13-Mar-2017 16:30:11
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Importing TetGen files --- 13-Mar-2017 16:30:11
--- Done --- 13-Mar-2017 16:30:11

Accessing the model element and patch data

FT=meshOutput.faces;
Fb=meshOutput.facesBoundary;
Cb=meshOutput.boundaryMarker;
VT=meshOutput.nodes;
C=meshOutput.faceMaterialID;
E=meshOutput.elements;
elementMaterialIndices=meshOutput.elementMaterialID;

Plotting the meshed geometry

hf1=cFigure;
subplot(1,3,1);
title('Solid tetrahedral mesh model','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;
hps=patch('Faces',FT,'Vertices',VT,'FaceColor','flat','CData',C,'lineWidth',edgeWidth,'edgeColor',edgeColor);
view(3); axis tight;  axis equal;  grid on;
colormap(autumn);
camlight headlight;
set(gca,'FontSize',fontSize);

subplot(1,3,2);
title('Model boundaries','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;
hps=patch('Faces',Fb,'Vertices',VT,'FaceColor','flat','CData',Cb,'lineWidth',edgeWidth,'edgeColor',edgeColor,'FaceAlpha',faceAlpha1);
view(3); axis tight;  axis equal;  grid on;
colormap(autumn);
set(gca,'FontSize',fontSize);
drawnow;

subplot(1,3,3);
%Selecting half of the model to see interior
Y=VT(:,2); YE=mean(Y(E),2);
L=YE>mean(Y);
[Fs,Cs]=element2patch(E(L,:),C(L),'tet4');

title('Cut view of solid tetrahedral mesh model','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;
hps=patch('Faces',Fs,'Vertices',VT,'FaceColor','flat','CData',Cs,'lineWidth',edgeWidth,'edgeColor',edgeColor);
view(3); axis tight;  axis equal;  grid on;
colormap(autumn);
camlight headlight;
set(gca,'FontSize',fontSize);
drawnow;

DEFINE FACES FOR PRESSURE

For this example the outer sphere nodes are subjected to a pressure

%Get outer surface (numbering may have altered due to tetgen behaviour so
%redefined here)
F1=Fb(Cb==2,:);
F1=fliplr(F1);
hf=cFigure;
title('The outer surface','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;

patch('Faces',F1,'Vertices',VT,'FaceColor','flat','CData',Cb(Cb==2),'FaceAlpha',0.5);
[hp]=patchNormPlot(F1,VT,0.5);
colormap jet; colorbar;
camlight headlight;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;

Define node numbers for rigid support

[minVal,minInd]=min(sum((VT-(ones(size(VT,1),1)*mean(VT,1))).^2,2)); %Find node closest to centre
boundaryConditionNodeList=minInd; %Node closest to centre is constrained from moving

CONSTRUCTING FEB MODEL

FEB_struct.febio_spec.version='2.0';
FEB_struct.Module.Type='solid';

% Defining file names
FEB_struct.run_filename=[modelName,'.feb']; %FEB file name
FEB_struct.run_logname=[modelName,'.txt']; %FEBio log file name

febMatID=elementMaterialIndices;
febMatID(elementMaterialIndices==-2)=1;
febMatID(elementMaterialIndices==-3)=2;

%Creating FEB_struct
FEB_struct.Geometry.Nodes=VT;
FEB_struct.Geometry.Elements={E}; %The element sets
FEB_struct.Geometry.ElementType={'tet4'}; %The element types
FEB_struct.Geometry.ElementMat={febMatID};
FEB_struct.Geometry.ElementsPartName={'Sphere'};

% DEFINING MATERIALS
k_factor=1000;

%Material 1
c1=1e-3;
k=c1*k_factor;
FEB_struct.Materials{1}.Type='Mooney-Rivlin';
FEB_struct.Materials{1}.Properties={'c1','c2','k'};
FEB_struct.Materials{1}.Values={c1,0,k};

%Material 2
c1=2e-3;
k=c1*k_factor;
FEB_struct.Materials{2}.Type='Mooney-Rivlin';
FEB_struct.Materials{2}.Properties={'c1','c2','k'};
FEB_struct.Materials{2}.Values={c1,0,k};

%Defining surfaces
FEB_struct.Geometry.Surface{1}.Set=F1;
FEB_struct.Geometry.Surface{1}.Type='tri3';
FEB_struct.Geometry.Surface{1}.Name='Pressure_surface';

%Defining node sets
FEB_struct.Geometry.NodeSet{1}.Set=boundaryConditionNodeList;
FEB_struct.Geometry.NodeSet{1}.Name='boundaryConditionNodeList';

%Adding BC information
FEB_struct.Boundary.Fix{1}.bc='x';
FEB_struct.Boundary.Fix{1}.SetName=FEB_struct.Geometry.NodeSet{1}.Name;
FEB_struct.Boundary.Fix{2}.bc='y';
FEB_struct.Boundary.Fix{2}.SetName=FEB_struct.Geometry.NodeSet{1}.Name;
FEB_struct.Boundary.Fix{3}.bc='z';
FEB_struct.Boundary.Fix{3}.SetName=FEB_struct.Geometry.NodeSet{1}.Name;

%Adding load information
% FEB_struct.Loads.Surface_load{1}.Type='pressure';
% % FEB_struct.Loads.Surface_load{1}.Set=F1;
% FEB_struct.Loads.Surface_load{1}.SetName=FEB_struct.Geometry.Surface{1}.Name;
% FEB_struct.Loads.Surface_load{1}.lcPar='pressure';
% FEB_struct.Loads.Surface_load{1}.lcParValue=0.5;
% FEB_struct.Loads.Surface_load{1}.lc=1;

FEB_struct.Loads.Surface_load{1}.Type='pressure';
% FEB_struct.Loads.Surface_load{1}.Set=F1;
FEB_struct.Loads.Surface_load{1}.SetName=FEB_struct.Geometry.Surface{1}.Name;
FEB_struct.Loads.Surface_load{1}.lcPar='pressure';
FEB_struct.Loads.Surface_load{1}.lcParValue=0.5;
FEB_struct.Loads.Surface_load{1}.lc=1;


%Adding output requests
FEB_struct.Output.VarTypes={'displacement','stress','relative volume','shell thickness'};

%Specify log file output
run_node_output_name=[FEB_struct.run_filename(1:end-4),'_node_out.txt'];
FEB_struct.run_output_names={run_node_output_name};
FEB_struct.output_types={'node_data'};
FEB_struct.data_types={'ux;uy;uz'};

%Control section
FEB_struct.Control.AnalysisType='static';
FEB_struct.Control.Properties={'time_steps','step_size',...
    'max_refs','max_ups',...
    'dtol','etol','rtol','lstol'};
FEB_struct.Control.Values={10,0.1,...
    25,0,...
    0.001,0.01,0,0.9};
FEB_struct.Control.TimeStepperProperties={'dtmin','dtmax','max_retries','opt_iter','aggressiveness'};
FEB_struct.Control.TimeStepperValues={1e-5, 0.1, 5, 5, 1};

%Load curves
FEB_struct.LoadData.LoadCurves.id=1;
FEB_struct.LoadData.LoadCurves.type={'linear'};
FEB_struct.LoadData.LoadCurves.loadPoints={[0 0;1 1]};

SAVING .FEB FILE

FEB_struct.disp_opt=0; %Display waitbars
febStruct2febFile(FEB_struct);
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Writing FEBio XML object --- 13-Mar-2017 16:30:12
Adding Module level
Adding Control level
Adding Globals level
Adding Material level
Adding Geometry level
----> Adding node field
----> Adding element field
----> Adding tet4 element entries....
----> Adding surface field
----> Adding NodeSet field
Adding Boundary level
----> Defining fix type boundary conditions
Adding Loads level
----> Defining surface loads
Adding LoadData level
----> Defining load curves
Adding Output level
----> Adding plotfile field
----> Adding logfile field
Warning: Provided path of logfile is replaced by .feb file path. Only provide
filename to avoid this warning 
Writing .feb file
--- Done --- 13-Mar-2017 16:30:13

RUNNING FEBIO JOB

FEBioRunStruct.run_filename=FEB_struct.run_filename;
FEBioRunStruct.run_logname=FEB_struct.run_logname;
FEBioRunStruct.disp_on=1;
FEBioRunStruct.disp_log_on=1;
FEBioRunStruct.runMode='external';%'internal';
FEBioRunStruct.t_check=0.25; %Time for checking log file (dont set too small)
FEBioRunStruct.maxtpi=1e99; %Max analysis time
FEBioRunStruct.maxLogCheckTime=3; %Max log file checking time

[runFlag]=runMonitorFEBio(FEBioRunStruct);%START FEBio NOW!!!!!!!!
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- STARTING FEBIO JOB --- 13-Mar-2017 16:30:13
Waiting for log file...
Proceeding to check log file...13-Mar-2017 16:30:13
------- 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 --- 13-Mar-2017 16:30:15
if runFlag==1 %i.e. a succesful run

IMPORTING NODAL DISPLACEMENT RESULTS

Importing nodal displacements from a log file

    [~, N_disp_mat,~]=importFEBio_logfile(FEB_struct.run_output_names{1}); %Nodal displacements

    DN=N_disp_mat(:,2:end,end); %Final nodal displacements

CREATING NODE SET IN DEFORMED STATE

    VT_def=VT+DN;

Plotting the meshed geometry

    %Selecting half of the model to see interior
    Z=VT(:,3); ZE=mean(Z(E),2);
    L=ZE<mean(Z);
    [Fs,~]=element2patch(E(L,:),[],'tet4');

    Cs=sqrt(sum(DN.^2,2)); %Color towards displacement magnitude

    hf1=cFigure;
    title('Cut view of deformed model showing internal results','FontSize',fontSize);
    xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;

    hps=patch('Faces',Fs,'Vertices',VT_def,'FaceColor','flat','FaceVertexCData',Cs);

    view(3); axis tight;  axis equal;  grid on;
    colormap jet; colorbar; shading interp;
    camlight headlight;
    set(gca,'FontSize',fontSize);
    drawnow;

EXAMPLE FOR VISUALIZATION OF MODEL OUTER SURFACE ONLY

Visualizing the outer surface only is less memory intensive for large models

    %Get free faces
    TR = triangulation(E,VT_def); %"Triangulation" representation
    F_free = freeBoundary(TR); %Free boundary triangles i.e. outer surface
    ind_V_free =unique(F_free(:)); %Indices of nodes at free boundary

    %Compute an example distance metric for visualization
    D=minDist(VT_def(ind_V_free,:),VT(ind_V_free,:));

    %Disance metric is known for a list of points not suitable yet for colouring
    %faces
    C=zeros(size(VT,1),1); %Initialse vertex color list
    C(ind_V_free)=D; %Set color for point selection
    [CF]=vertexToFaceMeasure(F_free,C); %Convert vertex to face color measure

    hf1=cFigure;
    title('Outer surface only with distance metric','FontSize',fontSize);
    xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;

    hps=patch('Faces',F_free,'Vertices',VT_def,'FaceColor','flat','CData',CF);
    hps=patch('Faces',F_free,'Vertices',VT,'FaceColor',0.5.*ones(1,3),'FaceAlpha',0.5,'EdgeColor','none');

    view(3); axis tight;  axis equal;  grid on;
    colormap jet; colorbar; caxis([0 max(CF(:))]);
    camlight headlight;
    set(gca,'FontSize',fontSize);
    drawnow;
end

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]