DEMO_FEBio_continuous_fibre_distribution.m

Below is a demonstration for: 1) Building an FEBio model for uniaxial compression 2) Running the model 3) Importing displacement and force results 4) Plotting Cauchy stress, displacement results

Contents

clear; close all; clc;

Plot settings

fontSize=20;
faceAlpha1=0.8;
faceAlpha2=1;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize=25;
lineWidth=3;

Control parameters

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

modelName=fullfile(savePath,'tempModel');

%Specifying dimensions and number of elements
sampleWidth=10;
sampleThickness=10;
sampleHeight=10;
pointSpacings=2*ones(1,3);
initialArea=sampleWidth*sampleThickness;

numElementsWidth=round(sampleWidth/pointSpacings(1));
numElementsThickness=round(sampleThickness/pointSpacings(2));
numElementsHeight=round(sampleHeight/pointSpacings(3));

stretchLoad=0.7;
displacementMagnitude=[0 0 (stretchLoad*sampleHeight)-sampleHeight];

%Material parameter set
c1=0.3e-3;
m1=2;
ksi=c1*0.2;
beta=3;
k_factor=1e3;
alphaFib=0.5*pi;
k=0.5.*(c1+ksi)*k_factor;

CREATING MESHED BOX

%Create box 1
boxDim=[sampleWidth sampleThickness sampleHeight]; %Dimensions
boxEl=[numElementsWidth numElementsThickness numElementsHeight]; %Number of elements
[box1]=hexMeshBox(boxDim,boxEl);
E=box1.E;
V=box1.V;
Fb=box1.Fb;
faceBoundaryMarker=box1.faceBoundaryMarker;

X=V(:,1); Y=V(:,2); Z=V(:,3);
VE=[mean(X(E),2) mean(Y(E),2) mean(Z(E),2)];

elementMaterialIndices=ones(size(E,1),1);
% Plotting boundary surfaces
hf=cFigure;
title('Model surfaces','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;
patch('Faces',Fb,'Vertices',V,'FaceColor','flat','CData',faceBoundaryMarker,'FaceAlpha',faceAlpha2,'lineWidth',edgeWidth,'edgeColor',edgeColor);

colormap(gjet(6)); colorbar;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;
drawnow;

DEFINE BC's

%Define faces
logicFace=faceBoundaryMarker==1;
Fr=Fb(logicFace,:);
bcSupportList_X=unique(Fr(:));

logicFace=faceBoundaryMarker==3;
Fr=Fb(logicFace,:);
bcSupportList_Y=unique(Fr(:));

logicFace=faceBoundaryMarker==5;
Fr=Fb(logicFace,:);
bcSupportList_Z=unique(Fr(:));

%Define line support
bcSupportList_X_axis=bcSupportList_Y(ismember(bcSupportList_Y,bcSupportList_Z));
bcSupportList_Y_axis=bcSupportList_X(ismember(bcSupportList_X,bcSupportList_Z));

%Prescribed displacement nodes
logicPrescribe=faceBoundaryMarker==6;
Fr=Fb(logicPrescribe,:);
bcPrescribeList=unique(Fr(:));
bcPrescribeMagnitudes=displacementMagnitude(ones(1,numel(bcPrescribeList)),:);

Visualize BC's

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

patch('Faces',Fb,'Vertices',V,'FaceColor','flat','CData',faceBoundaryMarker,'FaceAlpha',faceAlpha2,'lineWidth',edgeWidth,'edgeColor',edgeColor);

plotV(V(bcSupportList_Z,:),'b.','MarkerSize',markerSize);
plotV(V(bcPrescribeList,:),'k.','MarkerSize',markerSize);
plotV(V(bcSupportList_X_axis,:),'g.','MarkerSize',markerSize);
plotV(V(bcSupportList_Y_axis,:),'r.','MarkerSize',markerSize);

set(gca,'FontSize',fontSize);
colormap(gjet(6)); colorbar;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;
drawnow;

DEFINE FIBRE DIRECTIONS

[R,~]=euler2DCM([0,alphaFib,0]);
v_fib=(R*[0 0 1]')';

V_fib=v_fib(ones(size(E,1),1),:);

Visualize fibre direction vectors

[Ff,Vf,Cf]=quiver3Dpatch(VE(:,1),VE(:,2),VE(:,3),V_fib(:,1),V_fib(:,2),V_fib(:,3),ones(size(V_fib,1),1),min(pointSpacings).*ones(1,2));

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

patch('Faces',Fb,'Vertices',V,'FaceColor',0.5.*ones(1,3),'FaceAlpha',faceAlpha1,'edgeColor','k');
patch('Faces',Ff,'Vertices',Vf,'FaceColor','k','FaceAlpha',1,'edgeColor','none');

set(gca,'FontSize',fontSize);
colormap(gjet(6)); colorbar;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;
drawnow;

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

%Geometry section
FEB_struct.Geometry.Nodes=V;
FEB_struct.Geometry.Elements={E}; %The element sets
FEB_struct.Geometry.ElementType={'hex8'}; %The element types
FEB_struct.Geometry.ElementMat={elementMaterialIndices};
FEB_struct.Geometry.ElementsPartName={'Block'};

%Material section
FEB_struct.Materials{1}.Type='solid mixture';
% FEB_struct.Materials{1}.AnisoType='mat_axis';

FEB_struct.Materials{1}.Solid{1}.Type='Ogden unconstrained';
FEB_struct.Materials{1}.Solid{1}.Properties={'c1','m1','c2','m2','cp'};
FEB_struct.Materials{1}.Solid{1}.Values={c1,m1,c1,-m1,k};

FEB_struct.Materials{1}.Solid{2}.Type='fiber-exp-pow'; FEB_struct.Materials{1}.Solid{2}.Properties={'ksi','alpha','beta','theta','phi'}; FEB_struct.Materials{1}.Solid{2}.Values={ksi,1e-20,beta,0,0}; FEB_struct.Materials{1}.Solid{2}.AnisoType='mat_axis';

FEB_struct.Materials{1}.Solid{2}.Type='ellipsoidal fiber distribution';
FEB_struct.Materials{1}.Solid{2}.Properties={'ksi','beta'};
FEB_struct.Materials{1}.Solid{2}.Values={[ksi ksi 175*ksi],[beta beta beta]};
FEB_struct.Materials{1}.Solid{2}.AnisoType='mat_axis';

FEB_struct.Materials{1}.Solid{2}.Type='continuous fiber distribution'; FEB_struct.Materials{1}.Solid{2}.Properties={'fibers','distribution','scheme'}; FEB_struct.Materials{1}.Solid{2}.Values={[],[],[]}; FEB_struct.Materials{1}.Solid{2}.PropAttrName=cell(1,numel(FEB_struct.Materials{1}.Solid{2}.Properties)); FEB_struct.Materials{1}.Solid{2}.PropParName=cell(1,numel(FEB_struct.Materials{1}.Solid{2}.Properties));

FEB_struct.Materials{1}.Solid{2}.PropAttrName{1}='type'; FEB_struct.Materials{1}.Solid{2}.PropAttrVal{1}='fiber-exponential-power-law'; FEB_struct.Materials{1}.Solid{2}.PropParName{1}={'alpha','beta','ksi'}; FEB_struct.Materials{1}.Solid{2}.PropParVal{1}={0,beta,ksi*beta};

FEB_struct.Materials{1}.Solid{2}.PropAttrName{2}='type'; FEB_struct.Materials{1}.Solid{2}.PropAttrVal{2}='von-Mises-3d'; FEB_struct.Materials{1}.Solid{2}.PropParName{2}={'b'}; FEB_struct.Materials{1}.Solid{2}.PropParVal{2}={0.25};

% FEB_struct.Materials{1}.Solid{2}.PropAttrName{2}='type'; % FEB_struct.Materials{1}.Solid{2}.PropAttrVal{2}='ellipsoidal'; % FEB_struct.Materials{1}.Solid{2}.PropParName{2}={'spa'}; % FEB_struct.Materials{1}.Solid{2}.PropParVal{2}={[1 1 175]}; % FEB_struct.Materials{1}.Solid{2}.PropAttrName{3}='type'; FEB_struct.Materials{1}.Solid{2}.PropAttrVal{3}='fibers-3d-gkt'; FEB_struct.Materials{1}.Solid{2}.PropParName{3}={'nph','nth'}; FEB_struct.Materials{1}.Solid{2}.PropParVal{3}={11,31};

% FEB_struct.Materials{1}.Solid{2}.PropAttrName{3}='type'; % FEB_struct.Materials{1}.Solid{2}.PropAttrVal{3}='fibers-3d-fei'; % FEB_struct.Materials{1}.Solid{2}.PropParName{3}={'resolution'}; % FEB_struct.Materials{1}.Solid{2}.PropParVal{3}={1796};

FEB_struct.Materials{1}.Solid{2}.AnisoType='mat_axis';

%Adding fibre direction, construct local orthonormal basis vectors
[a,d]=vectorOrthogonalPair(V_fib);

VF_E=zeros(size(V_fib,1),size(V_fib,2),2);
VF_E(:,:,1)=a; %a1 ~ e1 ~ X or first direction
VF_E(:,:,2)=d; %a2 ~ e2 ~ Y or second direction
%Vf_E %a3 ~ e3 ~ Z, third direction, or fibre direction

FEB_struct.Geometry.ElementData.MatAxis.ElementIndices=1:1:size(E,1);
FEB_struct.Geometry.ElementData.MatAxis.Basis=VF_E;

%Control section
FEB_struct.Control.AnalysisType='static';
FEB_struct.Control.Properties={'time_steps','step_size',...
    'max_refs','max_ups',...
    'dtol','etol','rtol','lstol'};
n=25;
FEB_struct.Control.Values={n,1/n,...
    25,0,...
    0.001,0.01,0,0.9};
FEB_struct.Control.TimeStepperProperties={'dtmin','dtmax','max_retries','opt_iter','aggressiveness'};
FEB_struct.Control.TimeStepperValues={1/(100*n),1/n,10,10,1};

%Defining node sets
FEB_struct.Geometry.NodeSet{1}.Set=bcSupportList_Y_axis;
FEB_struct.Geometry.NodeSet{1}.Name='bcSupportList_Y_axis';
FEB_struct.Geometry.NodeSet{2}.Set=bcSupportList_X_axis;
FEB_struct.Geometry.NodeSet{2}.Name='bcSupportList_X_axis';
FEB_struct.Geometry.NodeSet{3}.Set=bcSupportList_Z;
FEB_struct.Geometry.NodeSet{3}.Name='bcSupportList_Z';
% FEB_struct.Geometry.NodeSet{4}.Set=bcPrescribeList;
% FEB_struct.Geometry.NodeSet{4}.Name='bcPrescribeList';

%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{2}.Name;
FEB_struct.Boundary.Fix{3}.bc='z';
FEB_struct.Boundary.Fix{3}.SetName=FEB_struct.Geometry.NodeSet{3}.Name;

FEB_struct.Boundary.Prescribe{1}.Set=bcPrescribeList;
FEB_struct.Boundary.Prescribe{1}.bc='z';
FEB_struct.Boundary.Prescribe{1}.lc=1;
FEB_struct.Boundary.Prescribe{1}.nodeScale=displacementMagnitude(ones(numel(bcPrescribeList),1),3);
FEB_struct.Boundary.Prescribe{1}.Type='relative';

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

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

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

SAVING .FEB FILE

FEB_struct.disp_opt=0; %Display waitbars
febStruct2febFile(FEB_struct);
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Writing FEBio XML object --- 18-Aug-2017 14:37:07
Adding Module level
Adding Control level
Adding Globals level
Adding Material level
Adding Geometry level
----> Adding node field
----> Adding element field
----> Adding hex8 element entries....
----> Adding element data field
----> MatAxis data entries found
----> Adding NodeSet field
Adding Boundary level
----> Defining fix type boundary conditions
----> Defining prescribe type boundary conditions
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 
Warning: Provided path of logfile is replaced by .feb file path. Only provide
filename to avoid this warning 
Writing .feb file
--- Done --- 18-Aug-2017 14:37:07

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 --- 18-Aug-2017 14:37:07
Waiting for log file...
Proceeding to check log file...18-Aug-2017 14:37:08
------- converged at time : 0.04
------- converged at time : 0.08
------- converged at time : 0.12
------- converged at time : 0.16
------- converged at time : 0.2
------- converged at time : 0.24
------- converged at time : 0.28
------- converged at time : 0.32
------- converged at time : 0.36
------- converged at time : 0.4
------- converged at time : 0.44
------- converged at time : 0.48
------- converged at time : 0.52
------- converged at time : 0.56
------- converged at time : 0.6
------- converged at time : 0.64
------- converged at time : 0.68
------- converged at time : 0.72
------- converged at time : 0.76
------- converged at time : 0.8
------- converged at time : 0.84
------- converged at time : 0.88
------- converged at time : 0.92
------- converged at time : 0.96
------- converged at time : 1
--- Done --- 18-Aug-2017 14:37:09
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

    V_def=V+DN;
    DN_magnitude=sqrt(sum(DN.^2,2));

Plotting the deformed model

    [CF]=vertexToFaceMeasure(Fb,DN_magnitude);

    hf1=cFigure;
    title('The deformed model','FontSize',fontSize);
    xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;

    hps=patch('Faces',Fb,'Vertices',V_def,'FaceColor','flat','CData',CF);

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

IMPORTING NODAL FORCES

Importing nodal forces from a log file

    [time_mat, N_force_mat,~]=importFEBio_logfile(FEB_struct.run_output_names{2}); %Nodal displacements

    FZ_set=N_force_mat(bcPrescribeList,end,:); %Final nodal displacements

DERIVING STRESS METRICS

    %Get Z forces
    FZ=sum(N_force_mat(bcPrescribeList,end,:),1);
    FZ=[0; FZ(:)]; %Mean top surface nodal forces

    %Derive applied stretch
    DZ_set=N_disp_mat(bcPrescribeList,end,:); %Final nodal displacements
    DZ_set=mean(DZ_set,1);
    stretch_sim=(DZ_set+sampleHeight)./sampleHeight;
    stretch_sim=[1; stretch_sim(:)];

    %Derive simulated Cauchy stress (alternatively import stress and take the mean)
    currentArea=initialArea./stretch_sim;
    stress_cauchy_sim=FZ./currentArea; %Cauchy stress
    stress_cauchy_sim=stress_cauchy_sim.*1e3; %Scale to kPa
    hf1=cFigure;
    title('Stretch stress curves','FontSize',fontSize);
    xlabel('\lambda Stretch [.]','FontSize',fontSize); ylabel('\sigma Cauchy stress [kPa]','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;

    plot(stretch_sim,stress_cauchy_sim,'r.-','lineWidth',lineWidth,'markerSize',markerSize);

    view(2); axis tight;  grid on;
    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.

Copyright (C) 2017 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/.