DEMO_febio_0007_sphere_sliding

Below is a demonstration for:

Contents

Keywords

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=0.8;
faceAlpha2=0.3;
markerSize=40;
lineWidth=3;

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

%Specifying dimensions and number of elements for slab
sampleHeight=5; %Height
sampleWidth=sampleHeight*4; %Width
sampleThickness=sampleHeight*1; %Thickness
pointSpacings=0.5*ones(1,3); %Desired point spacing between nodes
numElementsWidth=round(sampleWidth/pointSpacings(1)); %Number of elemens in dir 1
numElementsThickness=round(sampleThickness/pointSpacings(2)); %Number of elemens in dir 2
numElementsHeight=round(sampleHeight/pointSpacings(3)); %Number of elemens in dir 3

%Sphere parameters
numRefineStepsSphere=3;
sphereRadius=sampleHeight/2;

%Define applied displacement
sphereIndentationDisplacement=sphereRadius/2;
sphereSlideDisplacement=sampleWidth-(sphereRadius*2);

%Material parameter set
c1=1e-3; %Shear-modulus-like parameter
m1=8; %Material parameter setting degree of non-linearity
k_factor=1e2; %Bulk modulus factor
k=c1*k_factor; %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=5; %Maximum number of retires
dtmin=(1/numTimeSteps)/100; %Minimum time step size
dtmax=1/numTimeSteps; %Maximum time step size

%Contact parameters
contactInitialOffset=0.1;
contactAlg=2;
switch contactAlg
    case 1
        contactType='sticky';
    case 2
        contactType='facet-to-facet sliding';
    case 3
        contactType='sliding_with_gaps';
    case 4
        contactType='sliding2';
end

Creating model geometry and mesh

A box is created with tri-linear hexahedral (hex8) elements using the hexMeshBox function. The function offers the boundary faces with seperate labels for the top, bottom, left, right, front, and back sides. As such these can be used to define boundary conditions on the exterior.

% Create a box with hexahedral elements
beamDimensions=[sampleWidth sampleThickness sampleHeight]; %Dimensions
beamElementNumbers=[numElementsWidth numElementsThickness numElementsHeight]; %Number of elements
outputStructType=2; %A structure compatible with mesh view
[meshStruct]=hexMeshBox(beamDimensions,beamElementNumbers,outputStructType);

%Access elements, nodes, and faces from the structure
E1=meshStruct.elements; %The elements
V1=meshStruct.nodes; %The nodes (vertices)
Fb1=meshStruct.facesBoundary; %The boundary faces
Cb1=meshStruct.boundaryMarker; %The "colors" or labels for the boundary faces
elementMaterialIndices=ones(size(E1,1),1); %Element material indices

Creating triangulated sphere surface model

[E2,V2,~]=geoSphere(numRefineStepsSphere,sphereRadius);

%Offset indentor
minV2=min(V2,[],1);
minV1=min(V1,[],1);

V2(:,1)=V2(:,1)-minV2(1)+minV1(1);

V2(:,3)=V2(:,3)-minV2(3)+(sampleHeight/2)+contactInitialOffset;

center_of_mass=mean(V2,1);

Plotting model boundary surfaces and a cut view

hFig=cFigure;

subplot(1,2,1); hold on;
title('Model boundary surfaces and labels','FontSize',fontSize);
gpatch(Fb1,V1,Cb1,'k',faceAlpha1);
gpatch(E2,V2,'kw','k',faceAlpha1);
colormap(gjet(6)); icolorbar;
axisGeom(gca,fontSize);

hs=subplot(1,2,2); hold on;
title('Cut view of solid mesh','FontSize',fontSize);
optionStruct.hFig=[hFig hs];
gpatch(E2,V2,'kw','k',1);
meshView(meshStruct,optionStruct);
axisGeom(gca,fontSize);

drawnow;

Joining node sets

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

Plotting joined geometry

cFigure;
title('Joined node sets','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;
gpatch(Fb1,V,Cb1,'k',faceAlpha1);
gpatch(E2,V,'kw','k',faceAlpha1);
colormap(gjet(6)); icolorbar;
axisGeom(gca,fontSize);
camlight headlight;
drawnow;

Define contact surfaces

% The rigid master surface of the sphere
F_contact_master=E2;

% The deformable slave surface of the slab
logicContactSurf1=Cb1==6;
F_contact_slave=Fb1(logicContactSurf1,:);

% Plotting surface models
cFigure; hold on;
title('Contact sets and normal directions','FontSize',fontSize);

gpatch(Fb1,V,'kw','none',faceAlpha2);
hl(1)=gpatch(F_contact_master,V,'g','k',1);
patchNormPlot(F_contact_master,V);
hl(2)=gpatch(F_contact_slave,V,'b','k',1);
patchNormPlot(F_contact_slave,V);

legend(hl,{'Master','Slave'});

axisGeom(gca,fontSize);
camlight headlight;
drawnow;

Define boundary conditions

%Supported nodes
logicRigid=Cb1==5;
Fr=Fb1(logicRigid,:);
bcSupportList=unique(Fr(:));

%Prescribed displacement nodes
bcPrescribeList=unique(E2(:));
bcPrescribeMagnitudes=[sphereSlideDisplacement 0 -(sphereIndentationDisplacement+contactInitialOffset)];

%Visualize BC's
hf=cFigure;
title('Boundary conditions model','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;

gpatch(Fb1,V,'kw','none',faceAlpha2);
hl2(1)=gpatch(E2,V,'kw','k',1);

hl2(2)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize);

legend(hl2,{'Rigid body sphere','BC support'});

axisGeom(gca,fontSize);
camlight headlight;
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';

%Create control structure for use by all steps
stepStruct.Control.analysis.ATTR.type='static';
stepStruct.Control.time_steps=numTimeSteps;
stepStruct.Control.step_size=1/numTimeSteps;
stepStruct.Control.time_stepper.dtmin=dtmin;
stepStruct.Control.time_stepper.dtmax=dtmax;
stepStruct.Control.time_stepper.max_retries=max_retries;
stepStruct.Control.time_stepper.opt_iter=opt_iter;
stepStruct.Control.max_refs=max_refs;
stepStruct.Control.max_ups=max_ups;

%Add template based default settings to proposed control section
[stepStruct.Control]=structComplete(stepStruct.Control,febio_spec.Control,1); %Complement provided with default if missing

%Remove control field (part of template) since step specific control sections are used
febio_spec=rmfield(febio_spec,'Control');

%Step specific control section
febio_spec.Step{1}.Control=stepStruct.Control;
febio_spec.Step{1}.ATTR.id=1;
febio_spec.Step{2}.Control=stepStruct.Control;
febio_spec.Step{2}.ATTR.id=2;

%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;
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;

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=center_of_mass;

%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='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='Slab'; %Name of the element set
febio_spec.Geometry.Elements{1}.elem.ATTR.id=(1:1:size(E1,1))'; %Element id's
febio_spec.Geometry.Elements{1}.elem.VAL=E1;

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='Sphere'; %Name of the element set
febio_spec.Geometry.Elements{2}.elem.ATTR.id=size(E1,1)+(1:1:size(E2,1))'; %Element id's
febio_spec.Geometry.Elements{2}.elem.VAL=E2;

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

% -> Surfaces
febio_spec.Geometry.Surface{1}.ATTR.name='contact_master';
febio_spec.Geometry.Surface{1}.tri3.ATTR.lid=(1:1:size(F_contact_master,1))';
febio_spec.Geometry.Surface{1}.tri3.VAL=F_contact_master;

febio_spec.Geometry.Surface{2}.ATTR.name='contact_slave';
febio_spec.Geometry.Surface{2}.quad4.ATTR.lid=(1:1:size(F_contact_slave,1))';
febio_spec.Geometry.Surface{2}.quad4.VAL=F_contact_slave;

% -> Surface pairs
febio_spec.Geometry.SurfacePair{1}.ATTR.name='Contact1';
febio_spec.Geometry.SurfacePair{1}.master.ATTR.surface=febio_spec.Geometry.Surface{1}.ATTR.name;
febio_spec.Geometry.SurfacePair{1}.slave.ATTR.surface=febio_spec.Geometry.Surface{2}.ATTR.name;

%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;

% -> Prescribed boundary conditions on the rigid body
febio_spec.Step{1}.Boundary.rigid_body{1}.ATTR.mat=2;
febio_spec.Step{1}.Boundary.rigid_body{1}.fixed{1}.ATTR.bc='x';
febio_spec.Step{1}.Boundary.rigid_body{1}.fixed{2}.ATTR.bc='y';
febio_spec.Step{1}.Boundary.rigid_body{1}.fixed{3}.ATTR.bc='Rx';
febio_spec.Step{1}.Boundary.rigid_body{1}.fixed{4}.ATTR.bc='Ry';
febio_spec.Step{1}.Boundary.rigid_body{1}.fixed{5}.ATTR.bc='Rz';
febio_spec.Step{1}.Boundary.rigid_body{1}.prescribed.ATTR.bc='z';
febio_spec.Step{1}.Boundary.rigid_body{1}.prescribed.ATTR.lc=1;
febio_spec.Step{1}.Boundary.rigid_body{1}.prescribed.VAL=bcPrescribeMagnitudes(3);

febio_spec.Step{2}.Boundary.rigid_body{1}.ATTR.mat=2;
febio_spec.Step{2}.Boundary.rigid_body{1}.fixed{1}.ATTR.bc='z';
febio_spec.Step{2}.Boundary.rigid_body{1}.fixed{2}.ATTR.bc='y';
febio_spec.Step{2}.Boundary.rigid_body{1}.fixed{3}.ATTR.bc='Rx';
febio_spec.Step{2}.Boundary.rigid_body{1}.fixed{4}.ATTR.bc='Ry';
febio_spec.Step{2}.Boundary.rigid_body{1}.fixed{5}.ATTR.bc='Rz';
febio_spec.Step{2}.Boundary.rigid_body{1}.prescribed.ATTR.bc='x';
febio_spec.Step{2}.Boundary.rigid_body{1}.prescribed.ATTR.lc=2;
febio_spec.Step{2}.Boundary.rigid_body{1}.prescribed.VAL=bcPrescribeMagnitudes(1);

%Contact section
switch contactType
    case 'sticky'
        febio_spec.Contact.contact{1}.ATTR.surface_pair=febio_spec.Geometry.SurfacePair{1}.ATTR.name;
        febio_spec.Contact.contact{1}.ATTR.type='sticky';
        febio_spec.Contact.contact{1}.penalty=100;
        febio_spec.Contact.contact{1}.laugon=0;
        febio_spec.Contact.contact{1}.tolerance=0.1;
        febio_spec.Contact.contact{1}.minaug=0;
        febio_spec.Contact.contact{1}.maxaug=10;
        febio_spec.Contact.contact{1}.snap_tol=0;
        febio_spec.Contact.contact{1}.max_traction=0;
        febio_spec.Contact.contact{1}.search_tolerance=0.1;
    case 'facet-to-facet sliding'
        febio_spec.Contact.contact{1}.ATTR.surface_pair=febio_spec.Geometry.SurfacePair{1}.ATTR.name;
        febio_spec.Contact.contact{1}.ATTR.type='facet-to-facet sliding';
        febio_spec.Contact.contact{1}.penalty=100;
        febio_spec.Contact.contact{1}.auto_penalty=1;
        febio_spec.Contact.contact{1}.two_pass=0;
        febio_spec.Contact.contact{1}.laugon=0;
        febio_spec.Contact.contact{1}.tolerance=0.1;
        febio_spec.Contact.contact{1}.gaptol=0;
        febio_spec.Contact.contact{1}.minaug=0;
        febio_spec.Contact.contact{1}.maxaug=10;
        febio_spec.Contact.contact{1}.search_tol=0.01;
        febio_spec.Contact.contact{1}.search_radius=mean(pointSpacings)/2;
    case 'sliding_with_gaps'
        febio_spec.Contact.contact{1}.ATTR.surface_pair=febio_spec.Geometry.SurfacePair{1}.ATTR.name;
        febio_spec.Contact.contact{1}.ATTR.type='sliding_with_gaps';
        febio_spec.Contact.contact{1}.penalty=100;
        febio_spec.Contact.contact{1}.auto_penalty=1;
        febio_spec.Contact.contact{1}.two_pass=0;
        febio_spec.Contact.contact{1}.laugon=0;
        febio_spec.Contact.contact{1}.tolerance=0.1;
        febio_spec.Contact.contact{1}.gaptol=0;
        febio_spec.Contact.contact{1}.minaug=0;
        febio_spec.Contact.contact{1}.maxaug=10;
        febio_spec.Contact.contact{1}.fric_coeff=0;
        febio_spec.Contact.contact{1}.fric_penalty=0;
        febio_spec.Contact.contact{1}.ktmult=1;
        febio_spec.Contact.contact{1}.seg_up=0;
        febio_spec.Contact.contact{1}.search_tol=0.01;
    case 'sliding2'
        febio_spec.Contact.contact{1}.ATTR.surface_pair=febio_spec.Geometry.SurfacePair{1}.ATTR.name;
        febio_spec.Contact.contact{1}.ATTR.type='sliding2';
        febio_spec.Contact.contact{1}.penalty=30;
        febio_spec.Contact.contact{1}.auto_penalty=1;
        febio_spec.Contact.contact{1}.two_pass=0;
        febio_spec.Contact.contact{1}.laugon=0;
        febio_spec.Contact.contact{1}.tolerance=0.1;
        febio_spec.Contact.contact{1}.gaptol=0;
        febio_spec.Contact.contact{1}.symmetric_stiffness=0;
        febio_spec.Contact.contact{1}.search_tol=0.01;
        febio_spec.Contact.contact{1}.search_radius=mean(pointSpacings)/2;
end

% LoadData section
febio_spec.LoadData.loadcurve{1}.ATTR.id=1;
febio_spec.LoadData.loadcurve{1}.ATTR.type='linear';
febio_spec.LoadData.loadcurve{1}.point.VAL=[0 0; 1 1; 2 1];

febio_spec.LoadData.loadcurve{2}.ATTR.id=2;
febio_spec.LoadData.loadcurve{2}.ATTR.type='linear';
febio_spec.LoadData.loadcurve{2}.point.VAL=[0 0; 1 0; 2 1];

%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);

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 12:43:38
Waiting for log file...
Proceeding to check log file...04-Jun-2019 12:43:40
------- 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
------- converged at time : 1.05
------- converged at time : 1.09241
------- converged at time : 1.12973
------- converged at time : 1.17045
------- converged at time : 1.20931
------- converged at time : 1.24487
------- converged at time : 1.28392
------- converged at time : 1.32627
------- converged at time : 1.36669
------- converged at time : 1.40712
------- converged at time : 1.4441
------- converged at time : 1.47942
------- converged at time : 1.50884
------- converged at time : 1.5358
------- converged at time : 1.55873
------- converged at time : 1.58583
------- converged at time : 1.62154
------- converged at time : 1.64648
------- converged at time : 1.67549
------- converged at time : 1.70106
------- converged at time : 1.72148
------- converged at time : 1.75744
------- converged at time : 1.79177
------- converged at time : 1.82455
------- converged at time : 1.85585
------- converged at time : 1.89525
------- converged at time : 1.92872
------- converged at time : 1.96218
------- converged at time : 1.99281
------- converged at time : 2
--- Done --- 04-Jun-2019 12:45:08

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;
    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,:);
    [CF]=vertexToFaceMeasure(Fb1,DN_magnitude);

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']);
    hp1=gpatch(Fb1,V_def,CF,'k',1); %Add graphics object to animate
    hp2=gpatch(E2,V_def,'kw','none',faceAlpha2); %Add graphics object to animate
    gpatch(Fb1,V,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(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
        DN_magnitude=sqrt(sum(DN.^2,2)); %Current displacement magnitude
        V_def=V+DN; %Current nodal coordinates
        [CF]=vertexToFaceMeasure(Fb1,DN_magnitude); %Current color data to use

        %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,CF,V_def}; %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.

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