DEMO_febio_0027_layer_spatially_varying_material

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;
markerSize1=10;
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_sed=[febioFebFileNamePart,'_sed_out.txt']; %Log file name for exporting strain energy density

% 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

DEFINING AND VISUALIZING THE PARAMETER MAP

numElemIncLayer=3;
numElemTopLayer=3;
numElemLayers=numElemTopLayer+numElemIncLayer;
displacementMagnitude=-0.3.*numElemLayers;

[G]=textImage('GIBBON','Arial',25,5);
G=flipud(G);
G=G-min(G(:));
G=G./max(G(:));

S=zeros(size(G,1),size(G,2),numElemLayers);
S(:,:,1:numElemIncLayer)=repmat(G,[1 1 numElemIncLayer]);

Control parameters

nBins=50;
minC=1e-3; %minimum value
maxC=minC*100; %Maximum value
c1_range_ini=linspace(minC,maxC,nBins); %Value range
k_factor=50;

VISUALIZING THE MAPPING

[F,V,C]=ind2patch(true(size(S)),S,'vb');
[C_rgb]=gray2RGBColorMap(C,jet(250),[min(S(:)) max(S(:))]);

[Fs1,Vs1,Cs1]=ind2patch(S>0,S,'vb');
[Fs2,Vs2,Cs2]=ind2patch(S==0,S,'vb');

cFigure;

subplot(1,2,1);
title('Stiff inclusion','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;
patch('Faces',Fs1,'Vertices',Vs1,'FaceColor','flat','CData',Cs1,'EdgeColor','k','FaceAlpha',1);
axis equal; view(3); axis tight; axis vis3d; grid on; view([-20,22]);
colormap(cMap); caxis([min(S(:)) max(S(:))]); colorbar;
set(gca,'FontSize',fontSize);

subplot(1,2,2);
title('Soft matrix','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;
patch('Faces',Fs2,'Vertices',Vs2,'FaceColor','flat','CData',Cs2,'EdgeColor','k','FaceAlpha',1);
axis equal; view(3); axis tight; axis vis3d; grid on; view([-20,22]);
colormap(cMap); caxis([min(S(:)) max(S(:))]); colorbar;
set(gca,'FontSize',fontSize);

drawnow;

BUILD MODEL

%Create hexahedral elements with function based colors
[E,V,C]=ind2patch(true(size(S)),S,'hu');

%Define element parameter mapping
elementMaterialID=C;
elementMaterialID=elementMaterialID-min(elementMaterialID(:));
elementMaterialID=elementMaterialID./max(elementMaterialID(:)); %Normalized
elementMaterialID=round(elementMaterialID.*(nBins-1))+1; %1-nPar

indUni=unique(elementMaterialID(:)); %Unique indices of used materials
c1=c1_range_ini(indUni); %Select relevant points
numMaterials=numel(c1);

%Fix indices
indFix1=1:numel(indUni);
indFix2=zeros(nBins,1);
indFix2(indUni)=indFix1;
elementMaterialID=indFix2(elementMaterialID);

%Reorder elementMaterialIndices and element matrix
[elementMaterialID,indSort]=sort(elementMaterialID);
E=E(indSort,:);

[F,PF]=element2patch(E,elementMaterialID);

%Get boundary faces for light plotting
[indBoundary]=tesBoundary(F,V);
Fb=F(indBoundary,:);

SET UP BOUNDARY CONDITIONS

%List of nodes for applying displacement
logicTopNodes=abs(V(:,3)-max(V(:,3)))<=max(eps(V(:,3)));
bcPrescribeList=find(logicTopNodes);

%List of nodes to fix
logicBottomNodes=abs(V(:,3)-min(V(:,3)))<=max(eps(V(:,3)));
bcRigidList=find(logicBottomNodes);

Visualize BC's

cFigure; hold on;
title('Boundary conditions','FontSize',fontSize);
gpatch(Fb,V,'kw','none',0.4);
hl(1)=plotV(V(bcRigidList,:),'k.','MarkerSize',markerSize1);
hl(2)=plotV(V(bcPrescribeList,:),'r.','MarkerSize',markerSize1);
legend(hl,{'BC full support','BC prescribed pressure'})
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
for q=1:1:numMaterials
    febio_spec.Material.material{q}.ATTR.type='Ogden';
    febio_spec.Material.material{q}.ATTR.id=q;
    febio_spec.Material.material{q}.c1=c1(q);
    febio_spec.Material.material{q}.m1=2;
    febio_spec.Material.material{q}.c2=c1(q);
    febio_spec.Material.material{q}.m2=-2;
    febio_spec.Material.material{q}.k=k_factor.*c1(q);
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(V,1))'; %The node id's
febio_spec.Geometry.Nodes{1}.node.VAL=V; %The nodel coordinates

% -> Elements
n=1;
for q=1:1:numMaterials
    logicMaterialNow=(elementMaterialID==q);
    febio_spec.Geometry.Elements{q}.ATTR.type='hex8'; %Element type of this set
    febio_spec.Geometry.Elements{q}.ATTR.mat=q; %material index for this set
    febio_spec.Geometry.Elements{q}.ATTR.name=['Layer_mat',num2str(q)]; %Name of the element set
    febio_spec.Geometry.Elements{q}.elem.ATTR.id=(n:1:(n-1+nnz(logicMaterialNow)))'; %Element id's
    febio_spec.Geometry.Elements{q}.elem.VAL=E(logicMaterialNow,:);
    n=n+nnz(logicMaterialNow);
end

% -> 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(V,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(V,1);

febio_spec.Output.logfile.element_data{1}.ATTR.file=febioLogFileName_sed;
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,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 12:54:26
Waiting for log file...
Proceeding to check log file...04-Jun-2019 12:54:28
------- 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 --- 04-Jun-2019 12:55:07

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));
    V_def=V+DN;
    [CF]=vertexToFaceMeasure(Fb,DN_magnitude);

Axis limits for plotting

    minD=min(V+min(N_disp_mat,[],3),[],1);
    maxD=max(V+max(N_disp_mat,[],3),[],1);
    axisLim=[minD(1) maxD(1) minD(2) maxD(2) minD(3) maxD(3)];
    [~, N_sed_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_sed)); %Element strain energy density
    N_sed_mat=N_sed_mat(:,2:end,:);
    sizImport=size(N_sed_mat);
    sizImport(3)=sizImport(3)+1;
    N_sed_mat_n=zeros(sizImport);
    N_sed_mat_n(:,:,2:end)=N_sed_mat;
    N_sed_mat=N_sed_mat_n;

Plotting the simulated results using anim8 to visualize and animate deformations

    [F,CF]=element2patch(E,N_sed_mat(:,:,1));

    %Get boundary faces for light plotting
    [indBoundary]=tesBoundary(F,V);
    Fb=F(indBoundary,:);
    Cb=CF(indBoundary,:);

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

    hp=gpatch(Fb,V_def,Cb,'k',1);
%     gpatch(Fb,V,0.5*ones(1,3),'none',0.25);

    view(3); axis tight;  axis equal;  grid on; box on;
    colormap(gjet(250)); colorbar;
    caxis([min(N_sed_mat(:)) max(N_sed_mat(:))/7]);
    view(130,25);
    camlight headlight;
    set(gca,'FontSize',fontSize);
    axis(axisLim);
    drawnow;

    animStruct.Time=time_mat;

    for qt=1:1:size(N_disp_mat,3)

        DN=N_disp_mat(:,:,qt);
        DN_magnitude=sqrt(sum(DN(:,3).^2,2));
        V_def=V+DN;

        [~,CF]=element2patch(E,N_sed_mat(:,:,qt));
        Cb=CF(indBoundary,:);

        %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}={V_def,Cb}; %Property values for to set in order to animate
    end

    anim8(hf,animStruct);
    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.

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