DEMO_febio_0013_disc_pressure_varying
Below is a demonstration for:
- Building geometry for a thin disc with tetrahedral elements
- Defining the boundary conditions
- Coding the febio structure
- Running the model
- Importing and visualizing the displacement and stress results
Contents
Keywords
- febio_spec version 3.0
- febio, FEBio
- pressure loading, spatially varying pressure, non-constant pressure
- tetrahedral elements, hex4
- tetgen
- disc
- static, solid
- hyperelastic, Ogden
- displacement logfile
- stress logfile
clear; close all; clc;
Plot settings
fontSize=20; faceAlpha1=0.8; markerSize=25; markerSize2=20; 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=[febioFebFileNamePart,'.txt']; %FEBio log file name febioLogFileName_disp=[febioFebFileNamePart,'_disp_out.txt']; %Log file name for exporting displacement febioLogFileName_stress=[febioFebFileNamePart,'_stress_out.txt']; %Log file name for exporting force %Load pressureValueMin=0.1e-4; pressureValueMax=2.0e-4; loadCase=1; switch loadCase case 1 loadType='pressure'; case 2 loadType='traction'; end %Specifying dimensions and number of elements pointSpacing=1; inputStruct.cylRadius=30; inputStruct.numRadial=round((inputStruct.cylRadius*pi)/pointSpacing); inputStruct.cylHeight=3; inputStruct.numHeight=round(inputStruct.cylHeight/pointSpacing); inputStruct.meshType='tri'; inputStruct.closeOpt=1; % Derive patch data for a cylinder [Fs,Vs,Cs]=patchcylinder(inputStruct); %Material parameter set c1=1e-3; %Shear-modulus-like parameter m1=2; %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=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
Creating model geometry and mesh
The disc is meshed using tetrahedral elements using tetgen
inputStruct.stringOpt='-pq1.2AaY'; inputStruct.Faces=Fs; inputStruct.Nodes=Vs; inputStruct.holePoints=[]; inputStruct.faceBoundaryMarker=Cs; %Face boundary markers inputStruct.regionPoints=getInnerPoint(Fs,Vs); %region points inputStruct.regionA=tetVolMeanEst(Fs,Vs); %Volume for regular tets inputStruct.minRegionMarker=2; %Minimum region marker [meshStruct]=runTetGen(inputStruct); % Mesh model using tetrahedral elements using tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 17-Dec-2020 09:18:23 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 17-Dec-2020 09:18:23 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 17-Dec-2020 09:18:24 --- Running TetGen to mesh input boundary--- 17-Dec-2020 09:18:24 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.036107 Creating surface mesh ... Surface mesh seconds: 0.005518 Recovering boundaries... Boundary recovery seconds: 0.006707 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.000927 Recovering Delaunayness... Delaunay recovery seconds: 0.015794 Refining mesh... Refinement seconds: 0.030617 Optimizing mesh... Optimization seconds: 0.002009 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: 0.034257 Total running seconds: 0.132102 Statistics: Input points: 1830 Input facets: 3656 Input segments: 5484 Input holes: 0 Input regions: 1 Mesh points: 2880 Mesh tetrahedra: 11774 Mesh faces: 25376 Mesh faces on exterior boundary: 3656 Mesh faces on input facets: 3656 Mesh edges on input segments: 5484 Steiner points inside domain: 1050 --- Done --- 17-Dec-2020 09:18:24 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 17-Dec-2020 09:18:24 --- Done --- 17-Dec-2020 09:18:24
Access model element and patch data
Fb=meshStruct.facesBoundary; Cb=meshStruct.boundaryMarker; V=meshStruct.nodes; CE=meshStruct.elementMaterialID; E=meshStruct.elements;
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(Fb,V,Cb,'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]; meshView(meshStruct,optionStruct); axisGeom(gca,fontSize); drawnow;
Defining the boundary conditions
The visualization of the model boundary shows colors for each side of the disc. These labels can be used to define boundary conditions.
%Define supported node sets bcSupportList=unique(Fb(Cb==1,:)); %Node set part of selected face %Define pressure surface F_pressure=fliplr(Fb(Cb==2,:)); %The top face set %Create spatially varying pressure X=V(:,1); C_pressure=mean(X(F_pressure),2); %Initialize as X-coordinate C_pressure=C_pressure-min(C_pressure(:)); %Subtract minimum so range is 0-.. C_pressure=C_pressure./max(C_pressure(:)); %Devide by maximum so range is 0-1 C_pressure=C_pressure.^2; C_pressure=C_pressure.*(pressureValueMax-pressureValueMin)+pressureValueMin; %Scale/offset to pressure range
Visualizing boundary conditions. Markers plotted on the semi-transparent model denote the nodes in the various boundary condition lists.
hf=cFigure; title('Boundary conditions','FontSize',fontSize); xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on; gpatch(Fb,V,'kw','none',0.5); hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize); hl(2)=gpatch(F_pressure,V,C_pressure,'k',1); patchNormPlot(F_pressure,V); legend(hl,{'BC full support','Pressure surface'}); colormap(gjet(250)); colorbar; 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='3.0'; %Module section febio_spec.Module.ATTR.type='solid'; %Control section febio_spec.Control.analysis='STATIC'; febio_spec.Control.time_steps=numTimeSteps; febio_spec.Control.step_size=1/numTimeSteps; febio_spec.Control.solver.max_refs=max_refs; febio_spec.Control.solver.max_ups=max_ups; 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; %Material section materialName1='Material1'; febio_spec.Material.material{1}.ATTR.name=materialName1; 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; %Mesh section % -> Nodes febio_spec.Mesh.Nodes{1}.ATTR.name='nodeSet_all'; %The node set name febio_spec.Mesh.Nodes{1}.node.ATTR.id=(1:size(V,1))'; %The node id's febio_spec.Mesh.Nodes{1}.node.VAL=V; %The nodel coordinates % -> Elements partName1='Part1'; febio_spec.Mesh.Elements{1}.ATTR.name=partName1; %Name of this part febio_spec.Mesh.Elements{1}.ATTR.type='tet4'; %Element type febio_spec.Mesh.Elements{1}.elem.ATTR.id=(1:1:size(E,1))'; %Element id's febio_spec.Mesh.Elements{1}.elem.VAL=E; %The element matrix % -> Surfaces surfaceName1='LoadedSurface'; febio_spec.Mesh.Surface{1}.ATTR.name=surfaceName1; febio_spec.Mesh.Surface{1}.tri3.ATTR.id=(1:1:size(F_pressure,1))'; febio_spec.Mesh.Surface{1}.tri3.VAL=F_pressure; % -> NodeSets nodeSetName1='bcSupportList'; febio_spec.Mesh.NodeSet{1}.ATTR.name=nodeSetName1; febio_spec.Mesh.NodeSet{1}.node.ATTR.id=bcSupportList(:); %MeshDomains section febio_spec.MeshDomains.SolidDomain.ATTR.name=partName1; febio_spec.MeshDomains.SolidDomain.ATTR.mat=materialName1; %Boundary condition section % -> Fix boundary conditions febio_spec.Boundary.bc{1}.ATTR.type='fix'; febio_spec.Boundary.bc{1}.ATTR.node_set=nodeSetName1; febio_spec.Boundary.bc{1}.dofs='x,y,z'; %MeshData secion %-> Surface data loadDataName1='LoadData1'; switch loadType case 'pressure' febio_spec.MeshData.SurfaceData.ATTR.name=loadDataName1; febio_spec.MeshData.SurfaceData.ATTR.surface=surfaceName1; febio_spec.MeshData.SurfaceData.ATTR.datatype='scalar'; febio_spec.MeshData.SurfaceData.face.ATTR.lid=(1:1:numel(C_pressure))'; febio_spec.MeshData.SurfaceData.face.VAL=C_pressure; case 'traction' febio_spec.MeshData.SurfaceData.ATTR.name=loadDataName1; febio_spec.MeshData.SurfaceData.ATTR.surface=surfaceName1; febio_spec.MeshData.SurfaceData.ATTR.datatype='vec3'; febio_spec.MeshData.SurfaceData.face.ATTR.lid=(1:1:numel(C_pressure))'; febio_spec.MeshData.SurfaceData.face.VAL=[zeros(size(C_pressure)) zeros(size(C_pressure)) -C_pressure]; end %Loads section % -> Surface load switch loadType case 'pressure' febio_spec.Loads.surface_load{1}.ATTR.type='pressure'; febio_spec.Loads.surface_load{1}.ATTR.surface=surfaceName1; febio_spec.Loads.surface_load{1}.pressure.ATTR.lc=1; febio_spec.Loads.surface_load{1}.pressure.ATTR.type='map'; febio_spec.Loads.surface_load{1}.pressure.VAL=loadDataName1; febio_spec.Loads.surface_load{1}.symmetric_stiffness=1; case 'traction' febio_spec.Loads.surface_load{1}.ATTR.type='traction'; febio_spec.Loads.surface_load{1}.ATTR.surface=surfaceName1; febio_spec.Loads.surface_load{1}.traction.ATTR.lc=1; febio_spec.Loads.surface_load{1}.traction.ATTR.type='map'; febio_spec.Loads.surface_load{1}.traction.VAL=loadDataName1; end %LoadData section % -> load_controller febio_spec.LoadData.load_controller{1}.ATTR.id=1; febio_spec.LoadData.load_controller{1}.ATTR.type='loadcurve'; febio_spec.LoadData.load_controller{1}.interpolate='LINEAR'; febio_spec.LoadData.load_controller{1}.points.point.VAL=[0 0; 1 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.element_data{1}.ATTR.file=febioLogFileName_stress; febio_spec.Output.logfile.element_data{1}.ATTR.data='s1'; 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 % febView(febioFebFileName);
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.runMode='internal';%'internal'; [runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--------> RUNNING/MONITORING FEBIO JOB <-------- 17-Dec-2020 09:18:29
FEBio path: /home/kevin/FEBioStudio/bin/febio3
# Attempt removal of existing log files 17-Dec-2020 09:18:29
* Removal succesful 17-Dec-2020 09:18:29
# Attempt removal of existing .xplt files 17-Dec-2020 09:18:29
* Removal succesful 17-Dec-2020 09:18:29
# Starting FEBio... 17-Dec-2020 09:18:29
Max. total analysis time is: Inf s
===========================================================================
________ _________ _______ __ _________
| |\ | |\ | \\ | |\ / \\
| ____|| | ____|| | __ || |__|| | ___ ||
| |\___\| | |\___\| | |\_| || \_\| | // \ ||
| ||__ | ||__ | ||_| || | |\ | || | ||
| |\ | |\ | \\ | || | || | ||
| ___|| | ___|| | ___ || | || | || | ||
| |\__\| | |\__\| | |\__| || | || | || | ||
| || | ||___ | ||__| || | || | \\__/ ||
| || | |\ | || | || | ||
|___|| |________|| |_________// |__|| \_________//
F I N I T E E L E M E N T S F O R B I O M E C H A N I C S
version 3.1.0
FEBio is a registered trademark.
copyright (c) 2006-2020 - All rights reserved
===========================================================================
Default linear solver: pardiso
Reading file /mnt/data/MATLAB/GIBBON/data/temp/tempModel.feb ...SUCCESS!
Setting parameter "pressure" to : 0
]0;(0%) tempModel.feb - FEBio 3.1.0
===== beginning time step 1 : 0.1 =====
Setting parameter "pressure" to : 0.1
Reforming stiffness matrix: reformation #1
===== reforming stiffness matrix:
Nr of equations ........................... : 7794
Nr of nonzeroes in stiffness matrix ....... : 148887
1
Nonlinear solution status: time= 0.1
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 1
step from line search = 0.545521
convergence norms : INITIAL CURRENT REQUIRED
residual 6.560848e-07 2.105243e-04 0.000000e+00
energy 1.230880e-02 1.400077e-03 1.230880e-04
displacement 1.631704e+03 4.855837e+02 4.855837e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.1
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.560848e-07 1.351961e-05 0.000000e+00
energy 1.230880e-02 5.335784e-04 1.230880e-04
displacement 1.631704e+03 1.641225e+02 1.212671e-03
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.1
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.560848e-07 1.825677e-06 0.000000e+00
energy 1.230880e-02 3.934498e-05 1.230880e-04
displacement 1.631704e+03 2.591010e+01 1.586617e-03
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.1
stiffness updates = 0
right hand side evaluations = 6
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.560848e-07 1.016072e-09 0.000000e+00
energy 1.230880e-02 5.200896e-07 1.230880e-04
displacement 1.631704e+03 6.309398e-01 1.649589e-03
Reforming stiffness matrix: reformation #5
5
Nonlinear solution status: time= 0.1
stiffness updates = 0
right hand side evaluations = 7
stiffness matrix reformations = 5
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.560848e-07 2.643798e-14 0.000000e+00
energy 1.230880e-02 6.100024e-11 1.230880e-04
displacement 1.631704e+03 2.785961e-03 1.653770e-03
Reforming stiffness matrix: reformation #6
6
Nonlinear solution status: time= 0.1
stiffness updates = 0
right hand side evaluations = 8
stiffness matrix reformations = 6
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.560848e-07 3.884655e-21 0.000000e+00
energy 1.230880e-02 1.387350e-19 1.230880e-04
displacement 1.631704e+03 3.192749e-08 1.653770e-03
convergence summary
number of iterations : 6
number of reformations : 6
------- converged at time : 0.1
Data Record #1
===========================================================================
Step = 1
Time = 0.1
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 1
Time = 0.1
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(10%) tempModel.feb - FEBio 3.1.0
===== beginning time step 2 : 0.2 =====
Setting parameter "pressure" to : 0.2
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.2
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 1
step from line search = 0.559934
convergence norms : INITIAL CURRENT REQUIRED
residual 6.626444e-07 2.087672e-04 0.000000e+00
energy 1.206043e-02 1.300559e-03 1.206043e-04
displacement 1.549428e+03 4.857859e+02 4.857859e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.2
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.626444e-07 9.456362e-06 0.000000e+00
energy 1.206043e-02 4.488306e-04 1.206043e-04
displacement 1.549428e+03 1.402653e+02 1.146245e-03
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.2
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.626444e-07 9.360270e-07 0.000000e+00
energy 1.206043e-02 2.374715e-05 1.206043e-04
displacement 1.549428e+03 1.811182e+01 1.447273e-03
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.2
stiffness updates = 0
right hand side evaluations = 6
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.626444e-07 1.522817e-10 0.000000e+00
energy 1.206043e-02 1.429079e-07 1.206043e-04
displacement 1.549428e+03 2.371102e-01 1.483970e-03
Reforming stiffness matrix: reformation #5
5
Nonlinear solution status: time= 0.2
stiffness updates = 0
right hand side evaluations = 7
stiffness matrix reformations = 5
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.626444e-07 7.017868e-16 0.000000e+00
energy 1.206043e-02 3.307750e-12 1.206043e-04
displacement 1.549428e+03 3.714045e-04 1.485393e-03
convergence summary
number of iterations : 5
number of reformations : 5
------- converged at time : 0.2
Data Record #1
===========================================================================
Step = 2
Time = 0.2
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 2
Time = 0.2
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(20%) tempModel.feb - FEBio 3.1.0
===== beginning time step 3 : 0.3 =====
Setting parameter "pressure" to : 0.3
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.3
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 1
step from line search = 0.606455
convergence norms : INITIAL CURRENT REQUIRED
residual 6.756341e-07 2.069292e-04 0.000000e+00
energy 1.140565e-02 1.049744e-03 1.140565e-04
displacement 1.342761e+03 4.938511e+02 4.938511e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.3
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.756341e-07 4.316413e-06 0.000000e+00
energy 1.140565e-02 3.113704e-04 1.140565e-04
displacement 1.342761e+03 9.784634e+01 1.029522e-03
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.3
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.756341e-07 2.833858e-07 0.000000e+00
energy 1.140565e-02 8.874961e-06 1.140565e-04
displacement 1.342761e+03 9.561960e+00 1.233896e-03
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.3
stiffness updates = 0
right hand side evaluations = 6
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.756341e-07 4.826462e-12 0.000000e+00
energy 1.140565e-02 1.359626e-08 1.140565e-04
displacement 1.342761e+03 3.871479e-02 1.247315e-03
Reforming stiffness matrix: reformation #5
5
Nonlinear solution status: time= 0.3
stiffness updates = 0
right hand side evaluations = 7
stiffness matrix reformations = 5
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.756341e-07 8.716456e-18 0.000000e+00
energy 1.140565e-02 1.106687e-14 1.140565e-04
displacement 1.342761e+03 7.367364e-06 1.247405e-03
convergence summary
number of iterations : 5
number of reformations : 5
------- converged at time : 0.3
Data Record #1
===========================================================================
Step = 3
Time = 0.3
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 3
Time = 0.3
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(30%) tempModel.feb - FEBio 3.1.0
===== beginning time step 4 : 0.4 =====
Setting parameter "pressure" to : 0.4
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.4
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.935111e-07 9.826278e-04 0.000000e+00
energy 1.062778e-02 7.942441e-03 1.062778e-04
displacement 1.117155e+03 1.117155e+03 1.117155e-03
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.4
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.935111e-07 8.255817e-09 0.000000e+00
energy 1.062778e-02 5.772412e-06 1.062778e-04
displacement 1.117155e+03 9.890901e-01 1.069474e-03
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.4
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.935111e-07 6.622765e-10 0.000000e+00
energy 1.062778e-02 1.184349e-08 1.062778e-04
displacement 1.117155e+03 4.656540e-01 1.027459e-03
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.4
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 6.935111e-07 1.757025e-16 0.000000e+00
energy 1.062778e-02 5.516322e-14 1.062778e-04
displacement 1.117155e+03 9.497625e-05 1.027588e-03
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 0.4
Data Record #1
===========================================================================
Step = 4
Time = 0.4
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 4
Time = 0.4
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(40%) tempModel.feb - FEBio 3.1.0
===== beginning time step 5 : 0.5 =====
Setting parameter "pressure" to : 0.5
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.5
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.150052e-07 6.424882e-04 0.000000e+00
energy 9.909670e-03 5.130960e-03 9.909670e-05
displacement 9.277275e+02 9.277275e+02 9.277275e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.5
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.150052e-07 3.638928e-09 0.000000e+00
energy 9.909670e-03 9.497994e-07 9.909670e-05
displacement 9.277275e+02 1.117559e+00 8.830079e-04
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.5
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.150052e-07 2.000106e-10 0.000000e+00
energy 9.909670e-03 1.395723e-10 9.909670e-05
displacement 9.277275e+02 2.594857e-01 8.545748e-04
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.5
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.150052e-07 2.560380e-16 0.000000e+00
energy 9.909670e-03 4.427032e-14 9.909670e-05
displacement 9.277275e+02 9.087444e-05 8.547185e-04
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 0.5
Data Record #1
===========================================================================
Step = 5
Time = 0.5
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 5
Time = 0.5
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(50%) tempModel.feb - FEBio 3.1.0
===== beginning time step 6 : 0.6 =====
Setting parameter "pressure" to : 0.6
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.6
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.391810e-07 4.380335e-04 0.000000e+00
energy 9.309286e-03 3.445254e-03 9.309286e-05
displacement 7.829883e+02 7.829883e+02 7.829883e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.6
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.391810e-07 2.180063e-09 0.000000e+00
energy 9.309286e-03 8.955842e-08 9.309286e-05
displacement 7.829883e+02 1.150408e+00 7.441095e-04
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.6
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.391810e-07 5.011097e-11 0.000000e+00
energy 9.309286e-03 1.234230e-09 9.309286e-05
displacement 7.829883e+02 1.343752e-01 7.253724e-04
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.6
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.391810e-07 3.115929e-16 0.000000e+00
energy 9.309286e-03 4.391844e-14 9.309286e-05
displacement 7.829883e+02 7.795754e-05 7.255449e-04
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 0.6
Data Record #1
===========================================================================
Step = 6
Time = 0.6
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 6
Time = 0.6
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(60%) tempModel.feb - FEBio 3.1.0
===== beginning time step 7 : 0.7 =====
Setting parameter "pressure" to : 0.7
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.7
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.655205e-07 3.156210e-04 0.000000e+00
energy 8.825418e-03 2.437041e-03 8.825418e-05
displacement 6.749907e+02 6.749907e+02 6.749907e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.7
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.655205e-07 1.534264e-09 0.000000e+00
energy 8.825418e-03 3.707826e-07 8.825418e-05
displacement 6.749907e+02 1.154418e+00 6.422386e-04
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.7
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.655205e-07 1.393533e-11 0.000000e+00
energy 8.825418e-03 7.466577e-10 8.825418e-05
displacement 6.749907e+02 7.462477e-02 6.293017e-04
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.7
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.655205e-07 3.752631e-16 0.000000e+00
energy 8.825418e-03 3.649248e-14 8.825418e-05
displacement 6.749907e+02 6.853441e-05 6.294902e-04
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 0.7
Data Record #1
===========================================================================
Step = 7
Time = 0.7
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 7
Time = 0.7
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(70%) tempModel.feb - FEBio 3.1.0
===== beginning time step 8 : 0.8 =====
Setting parameter "pressure" to : 0.8
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.8
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.937196e-07 2.398308e-04 0.000000e+00
energy 8.438632e-03 1.812885e-03 8.438632e-05
displacement 5.938915e+02 5.938915e+02 5.938915e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.8
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.937196e-07 1.184228e-09 0.000000e+00
energy 8.438632e-03 7.850879e-07 8.438632e-05
displacement 5.938915e+02 1.171198e+00 5.665382e-04
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.8
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.937196e-07 5.048997e-12 0.000000e+00
energy 8.438632e-03 4.122479e-10 8.438632e-05
displacement 5.938915e+02 4.778884e-02 5.568358e-04
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.8
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 7.937196e-07 4.750112e-16 0.000000e+00
energy 8.438632e-03 3.039492e-14 8.438632e-05
displacement 5.938915e+02 6.514542e-05 5.570299e-04
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 0.8
Data Record #1
===========================================================================
Step = 8
Time = 0.8
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 8
Time = 0.8
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(80%) tempModel.feb - FEBio 3.1.0
===== beginning time step 9 : 0.9 =====
Setting parameter "pressure" to : 0.9
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 0.9
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.235964e-07 1.907834e-04 0.000000e+00
energy 8.128412e-03 1.408807e-03 8.128412e-05
displacement 5.319135e+02 5.319135e+02 5.319135e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 0.9
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.235964e-07 1.006502e-09 0.000000e+00
energy 8.128412e-03 1.096311e-06 8.128412e-05
displacement 5.319135e+02 1.218196e+00 5.090126e-04
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 0.9
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.235964e-07 2.530315e-12 0.000000e+00
energy 8.128412e-03 2.564876e-10 8.128412e-05
displacement 5.319135e+02 3.597247e-02 5.010345e-04
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 0.9
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.235964e-07 6.379387e-16 0.000000e+00
energy 8.128412e-03 2.839361e-14 8.128412e-05
displacement 5.319135e+02 6.763128e-05 5.012287e-04
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 0.9
Data Record #1
===========================================================================
Step = 9
Time = 0.9
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 9
Time = 0.9
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(90%) tempModel.feb - FEBio 3.1.0
===== beginning time step 10 : 1 =====
Setting parameter "pressure" to : 1
Reforming stiffness matrix: reformation #1
1
Nonlinear solution status: time= 1
stiffness updates = 0
right hand side evaluations = 2
stiffness matrix reformations = 1
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.550345e-07 1.576339e-04 0.000000e+00
energy 7.877729e-03 1.135505e-03 7.877729e-05
displacement 4.835651e+02 4.835651e+02 4.835651e-04
Reforming stiffness matrix: reformation #2
2
Nonlinear solution status: time= 1
stiffness updates = 0
right hand side evaluations = 3
stiffness matrix reformations = 2
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.550345e-07 9.416239e-10 0.000000e+00
energy 7.877729e-03 1.294410e-06 7.877729e-05
displacement 4.835651e+02 1.300404e+00 4.642561e-04
Reforming stiffness matrix: reformation #3
3
Nonlinear solution status: time= 1
stiffness updates = 0
right hand side evaluations = 4
stiffness matrix reformations = 3
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.550345e-07 1.723653e-12 0.000000e+00
energy 7.877729e-03 1.872886e-10 7.877729e-05
displacement 4.835651e+02 3.131571e-02 4.571281e-04
Reforming stiffness matrix: reformation #4
4
Nonlinear solution status: time= 1
stiffness updates = 0
right hand side evaluations = 5
stiffness matrix reformations = 4
step from line search = 1.000000
convergence norms : INITIAL CURRENT REQUIRED
residual 8.550345e-07 9.053577e-16 0.000000e+00
energy 7.877729e-03 3.070357e-14 7.877729e-05
displacement 4.835651e+02 7.618258e-05 4.573198e-04
convergence summary
number of iterations : 4
number of reformations : 4
------- converged at time : 1
Data Record #1
===========================================================================
Step = 10
Time = 1
Data = ux;uy;uz
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_disp_out.txt
Data Record #2
===========================================================================
Step = 10
Time = 1
Data = s1
File = /mnt/data/MATLAB/GIBBON/data/temp/tempModel_stress_out.txt
]0;(100%) tempModel.feb - FEBio 3.1.0
N O N L I N E A R I T E R A T I O N I N F O R M A T I O N
Number of time steps completed .................... : 10
Total number of equilibrium iterations ............ : 44
Average number of equilibrium iterations .......... : 4.4
Total number of right hand evaluations ............ : 57
Total number of stiffness reformations ............ : 44
L I N E A R S O L V E R S T A T S
Total calls to linear solver ........ : 44
Avg iterations per solve ............ : 1
Time in linear solver: 0:00:02
]0;(0%) tempModel.feb - FEBio 3.1.0
Elapsed time : 0:00:04
N O R M A L T E R M I N A T I O N
* Log file found. 17-Dec-2020 09:18:33
# Parsing log file... 17-Dec-2020 09:18:33
number of iterations : 6 17-Dec-2020 09:18:34
number of reformations : 6 17-Dec-2020 09:18:34
------- converged at time : 0.1 17-Dec-2020 09:18:34
number of iterations : 5 17-Dec-2020 09:18:34
number of reformations : 5 17-Dec-2020 09:18:34
------- converged at time : 0.2 17-Dec-2020 09:18:34
number of iterations : 5 17-Dec-2020 09:18:34
number of reformations : 5 17-Dec-2020 09:18:34
------- converged at time : 0.3 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 0.4 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 0.5 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 0.6 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 0.7 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 0.8 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 0.9 17-Dec-2020 09:18:34
number of iterations : 4 17-Dec-2020 09:18:34
number of reformations : 4 17-Dec-2020 09:18:34
------- converged at time : 1 17-Dec-2020 09:18:34
Elapsed time : 0:00:04 17-Dec-2020 09:18:34
N O R M A L T E R M I N A T I O N
# Done 17-Dec-2020 09:18:34
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Import FEBio results
if runFlag==1 %i.e. a succesful run
Importing nodal displacements from a log file
dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_disp),1,1);
%Access data
N_disp_mat=dataStruct.data; %Displacement
timeVec=dataStruct.time; %Time
%Create deformed coordinate set
V_DEF=N_disp_mat+repmat(V,[1 1 size(N_disp_mat,3)]);
Plotting the simulated results using anim8 to visualize and animate deformations
DN_magnitude=sqrt(sum(N_disp_mat(:,:,end).^2,2)); %Current displacement magnitude % Create basic view and store graphics handle to initiate animation hf=cFigure; %Open figure gtitle([febioFebFileNamePart,': Press play to animate']); title('Displacement magnitude [mm]','Interpreter','Latex') hp=gpatch(Fb,V_DEF(:,:,end),DN_magnitude,'k',1); %Add graphics object to animate hp.Marker='.'; hp.MarkerSize=markerSize2; hp.FaceColor='interp'; axisGeom(gca,fontSize); colormap(gjet(250)); colorbar; caxis([0 max(DN_magnitude)]); axis(axisLim(V_DEF)); %Set axis limits statically camlight headlight; % Set up animation features animStruct.Time=timeVec; %The time vector for qt=1:1:size(N_disp_mat,3) %Loop over time increments DN_magnitude=sqrt(sum(N_disp_mat(:,:,qt).^2,2)); %Current displacement magnitude %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(:,:,qt),DN_magnitude}; %Property values for to set in order to animate end anim8(hf,animStruct); %Initiate animation feature drawnow;
Importing element stress from a log file
dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_stress),1,1);
%Access data
E_stress_mat=dataStruct.data;
E_stress_mat(isnan(E_stress_mat))=0;
Plotting the simulated results using anim8 to visualize and animate deformations
[CV]=faceToVertexMeasure(E,V,E_stress_mat(:,:,end));
% Create basic view and store graphics handle to initiate animation
hf=cFigure; %Open figure
gtitle([febioFebFileNamePart,': Press play to animate']);
title('$\sigma_{1}$ [MPa]','Interpreter','Latex')
hp=gpatch(Fb,V_DEF(:,:,end),CV,'k',1); %Add graphics object to animate
hp.Marker='.';
hp.MarkerSize=markerSize2;
hp.FaceColor='interp';
axisGeom(gca,fontSize);
colormap(gjet(250)); colorbar;
caxis([min(E_stress_mat(:)) max(E_stress_mat(:))]/3);
axis(axisLim(V_DEF)); %Set axis limits statically
camlight headlight;
% Set up animation features
animStruct.Time=timeVec; %The time vector
for qt=1:1:size(N_disp_mat,3) %Loop over time increments
[CV]=faceToVertexMeasure(E,V,E_stress_mat(:,:,qt));
%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(:,:,qt),CV}; %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]
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) 2006-2020 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/.