DEMO_febio_0006_sphere_indentation

Below is a demonstration for:

Building geometry for a slab with hexahedral elements, and a triangulated sphere.
Defining the boundary conditions
Coding the febio structure
Running the model
Importing and visualizing the displacement results

Keywords
Plot settings
Control parameters
Creating model geometry and mesh
Creating triangulated sphere surface model
Joining node sets
Define contact surfaces
Define boundary conditions
Defining the FEBio input structure
Quick viewing of the FEBio input file structure
Exporting the FEBio input file
Running the FEBio analysis
Import FEBio results

Keywords

febio_spec version 4.0
febio, FEBio
indentation
contact, sliding, sticky, friction
rigid body constraints
hexahedral elements, hex8
triangular elements, tri3
slab, block, rectangular
sphere
static, solid
hyperelastic, Ogden
displacement logfile
stress logfile

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=0.8;
faceAlpha2=0.3;
markerSize=40;
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 stress
febioLogFileName_contactPressure=[febioFebFileNamePart,'_contactPressure_out.txt']; %Log file name for exporting contact pressure

%Specifying dimensions and number of elements for slab
sampleHeight=4; %Height
sampleWidth=sampleHeight*2; %Width
sampleThickness=sampleHeight*2; %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
sphereDisplacement=sphereRadius;

%Material parameter set
c1=1e-3; %Shear-modulus-like parameter
m1=2; %Material parameter setting degree of non-linearity
k_factor=100; %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
symmetric_stiffness=0;

runMode='external';% 'internal' or 'external'

%Contact parameters
contactInitialOffset=0.1;
contactPenalty=10;
laugon=0;
minaug=1;
maxaug=10;
fric_coeff=0.01;

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
minZ=min(V2(:,3));
V2(:,3)=V2(:,3)-minZ+(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);
camlight headlight;

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 primary surface of the sphere
F_contact_secondary=E2;

% The deformable secondary surface of the slab
logicContactSurf1=Cb1==6;
F_contact_primary=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_secondary,V,'g','k',1);
patchNormPlot(F_contact_secondary,V);
hl(2)=gpatch(F_contact_primary,V,'b','k',1);
patchNormPlot(F_contact_primary,V);

legend(hl,{'Secondary','Primary'});

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

Define boundary conditions

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

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='4.0';

%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.qn_method.max_ups=max_ups;
febio_spec.Control.solver.symmetric_stiffness=symmetric_stiffness;
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;

materialName2='Material2';
febio_spec.Material.material{2}.ATTR.name=materialName2;
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;

%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='hex8'; %Element type
febio_spec.Mesh.Elements{1}.elem.ATTR.id=(1:1:size(E1,1))'; %Element id's
febio_spec.Mesh.Elements{1}.elem.VAL=E1; %The element matrix

partName2='Part2';
febio_spec.Mesh.Elements{2}.ATTR.name=partName2; %Name of this part
febio_spec.Mesh.Elements{2}.ATTR.type='tri3'; %Element type
febio_spec.Mesh.Elements{2}.elem.ATTR.id=size(E1,1)+(1:1:size(E2,1))'; %Element id's
febio_spec.Mesh.Elements{2}.elem.VAL=E2; %The element matrix

% -> NodeSets
nodeSetName1='bcSupportList';
febio_spec.Mesh.NodeSet{1}.ATTR.name=nodeSetName1;
febio_spec.Mesh.NodeSet{1}.VAL=mrow(bcSupportList);

%MeshDomains section
febio_spec.MeshDomains.SolidDomain.ATTR.name=partName1;
febio_spec.MeshDomains.SolidDomain.ATTR.mat=materialName1;

febio_spec.MeshDomains.ShellDomain.ATTR.name=partName2;
febio_spec.MeshDomains.ShellDomain.ATTR.mat=materialName2;

% -> Surfaces
surfaceName1='contactSurface1';
febio_spec.Mesh.Surface{1}.ATTR.name=surfaceName1;
febio_spec.Mesh.Surface{1}.quad4.ATTR.id=(1:1:size(F_contact_primary,1))';
febio_spec.Mesh.Surface{1}.quad4.VAL=F_contact_primary;

surfaceName2='contactSurface2';
febio_spec.Mesh.Surface{2}.ATTR.name=surfaceName2;
febio_spec.Mesh.Surface{2}.tri3.ATTR.id=(1:1:size(F_contact_secondary,1))';
febio_spec.Mesh.Surface{2}.tri3.VAL=F_contact_secondary;

% -> Surface pairs
contactPairName='Contact1';
febio_spec.Mesh.SurfacePair{1}.ATTR.name=contactPairName;
febio_spec.Mesh.SurfacePair{1}.primary=surfaceName1;
febio_spec.Mesh.SurfacePair{1}.secondary=surfaceName2;

%Boundary condition section
% -> Fix boundary conditions
febio_spec.Boundary.bc{1}.ATTR.name='zero_displacement_xyz';
febio_spec.Boundary.bc{1}.ATTR.type='zero displacement';
febio_spec.Boundary.bc{1}.ATTR.node_set=nodeSetName1;
febio_spec.Boundary.bc{1}.x_dof=1;
febio_spec.Boundary.bc{1}.y_dof=1;
febio_spec.Boundary.bc{1}.z_dof=1;

%Rigid section
% ->Rigid body fix boundary conditions
febio_spec.Rigid.rigid_bc{1}.ATTR.name='RigidFix';
febio_spec.Rigid.rigid_bc{1}.ATTR.type='rigid_fixed';
febio_spec.Rigid.rigid_bc{1}.rb=2;
febio_spec.Rigid.rigid_bc{1}.Rx_dof=1;
febio_spec.Rigid.rigid_bc{1}.Ry_dof=1;
febio_spec.Rigid.rigid_bc{1}.Rz_dof=0;
febio_spec.Rigid.rigid_bc{1}.Ru_dof=1;
febio_spec.Rigid.rigid_bc{1}.Rv_dof=1;
febio_spec.Rigid.rigid_bc{1}.Rw_dof=1;

% ->Rigid body prescribe boundary conditions
febio_spec.Rigid.rigid_bc{2}.ATTR.name='RigidPrescribe';
febio_spec.Rigid.rigid_bc{2}.ATTR.type='rigid_displacement';
febio_spec.Rigid.rigid_bc{2}.rb=2;
febio_spec.Rigid.rigid_bc{2}.dof='z';
febio_spec.Rigid.rigid_bc{2}.value.ATTR.lc=1;
febio_spec.Rigid.rigid_bc{2}.value.VAL=-(sphereDisplacement+contactInitialOffset);
febio_spec.Rigid.rigid_bc{2}.relative=0;

%Contact section
febio_spec.Contact.contact{1}.ATTR.type='sliding-elastic';
febio_spec.Contact.contact{1}.ATTR.surface_pair=contactPairName;
febio_spec.Contact.contact{1}.two_pass=0;
febio_spec.Contact.contact{1}.laugon=laugon;
febio_spec.Contact.contact{1}.tolerance=0.2;
febio_spec.Contact.contact{1}.gaptol=0;
febio_spec.Contact.contact{1}.minaug=minaug;
febio_spec.Contact.contact{1}.maxaug=maxaug;
febio_spec.Contact.contact{1}.search_tol=0.01;
febio_spec.Contact.contact{1}.search_radius=0.1*sqrt(sum((max(V,[],1)-min(V,[],1)).^2,2));
febio_spec.Contact.contact{1}.symmetric_stiffness=0;
febio_spec.Contact.contact{1}.auto_penalty=1;
febio_spec.Contact.contact{1}.update_penalty=1;
febio_spec.Contact.contact{1}.penalty=contactPenalty;
febio_spec.Contact.contact{1}.fric_coeff=fric_coeff;

%LoadData section
% -> load_controller
febio_spec.LoadData.load_controller{1}.ATTR.name='LC_1';
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}.extend='CONSTANT';
febio_spec.LoadData.load_controller{1}.points.pt.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.element_data{1}.ATTR.file=febioLogFileName_stress;
febio_spec.Output.logfile.element_data{1}.ATTR.data='s3';
febio_spec.Output.logfile.element_data{1}.ATTR.delim=',';

febio_spec.Output.logfile.face_data{1}.ATTR.file=febioLogFileName_contactPressure;
febio_spec.Output.logfile.face_data{1}.ATTR.data='contact pressure';
febio_spec.Output.logfile.face_data{1}.ATTR.surface=surfaceName1;
febio_spec.Output.logfile.face_data{1}.ATTR.delim=',';

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.runMode=runMode;

[runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-------->    RUNNING/MONITORING FEBIO JOB    <-------- 29-May-2023 09:40:17
FEBio path: /home/kevin/FEBioStudio/bin/febio4
# Attempt removal of existing log files                29-May-2023 09:40:17
 * Removal succesful                                   29-May-2023 09:40:17
# Attempt removal of existing .xplt files              29-May-2023 09:40:17
 * Removal succesful                                   29-May-2023 09:40:17
# Starting FEBio...                                    29-May-2023 09:40:17
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       29-May-2023 09:40:17
   Max. wait time: 30 s
 * Log file found.                                     29-May-2023 09:40:17
# Parsing log file...                                  29-May-2023 09:40:17
    number of iterations   : 5                         29-May-2023 09:40:18
    number of reformations : 5                         29-May-2023 09:40:18
------- converged at time : 0.1                        29-May-2023 09:40:18
    number of iterations   : 5                         29-May-2023 09:40:18
    number of reformations : 5                         29-May-2023 09:40:18
------- converged at time : 0.2                        29-May-2023 09:40:18
    number of iterations   : 5                         29-May-2023 09:40:18
    number of reformations : 5                         29-May-2023 09:40:18
------- converged at time : 0.3                        29-May-2023 09:40:18
    number of iterations   : 5                         29-May-2023 09:40:19
    number of reformations : 5                         29-May-2023 09:40:19
------- converged at time : 0.4                        29-May-2023 09:40:19
    number of iterations   : 5                         29-May-2023 09:40:19
    number of reformations : 5                         29-May-2023 09:40:19
------- converged at time : 0.5                        29-May-2023 09:40:19
    number of iterations   : 6                         29-May-2023 09:40:19
    number of reformations : 6                         29-May-2023 09:40:19
------- converged at time : 0.6                        29-May-2023 09:40:19
    number of iterations   : 6                         29-May-2023 09:40:20
    number of reformations : 6                         29-May-2023 09:40:20
------- converged at time : 0.7                        29-May-2023 09:40:20
    number of iterations   : 6                         29-May-2023 09:40:20
    number of reformations : 6                         29-May-2023 09:40:20
------- converged at time : 0.8                        29-May-2023 09:40:20
    number of iterations   : 6                         29-May-2023 09:40:20
    number of reformations : 6                         29-May-2023 09:40:20
------- converged at time : 0.9                        29-May-2023 09:40:20
    number of iterations   : 6                         29-May-2023 09:40:21
    number of reformations : 6                         29-May-2023 09:40:21
------- converged at time : 1                          29-May-2023 09:40:21
 Elapsed time : 0:00:04                                29-May-2023 09:40:21
 N O R M A L   T E R M I N A T I O N
# Done                                                 29-May-2023 09:40:21
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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),0,1);

    %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)]);

Importing element stress from a log file

    dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_stress),0,1);

    %Access data
    E_stress_mat=dataStruct.data;

Importing contact pressure from a log file

    dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_contactPressure),0,1);

    %Access data
    F_primary_contact_pressure_mat=dataStruct.data;

Plotting the simulated results using anim8 to visualize and animate deformations

    [CV]=faceToVertexMeasure(E1,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('$\sigma_{3}$ [MPa]','Interpreter','Latex')
    hp=gpatch(Fb1,V_DEF(:,:,end),CV,'k',1); %Add graphics object to animate
    hp.Marker='.';
    hp.MarkerSize=markerSize2;
    hp.FaceColor='interp';

    hp2=gpatch(E2,V_DEF(:,:,end),'w','none',0.5); %Add graphics object to animate

    axisGeom(gca,fontSize);
    colormap(flipud(gjet(250))); colorbar;
    caxis([min(E_stress_mat(:)) max(E_stress_mat(:))]);
    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(E1,V,E_stress_mat(:,:,qt));

        %Set entries in animation structure
        animStruct.Handles{qt}=[hp hp hp2]; %Handles of objects to animate
        animStruct.Props{qt}={'Vertices','CData','Vertices'}; %Properties of objects to animate
        animStruct.Set{qt}={V_DEF(:,:,qt),CV,V_DEF(:,:,qt)}; %Property values for to set in order to animate
    end
    anim8(hf,animStruct); %Initiate animation feature
    drawnow;

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']);
    title('Contact pressure [MPa]','Interpreter','Latex')
    gpatch(Fb1,V_DEF(:,:,end),'w','none',0.1);
    hp=gpatch(F_contact_primary,V_DEF(:,:,end),F_primary_contact_pressure_mat(:,:,1),'k',1); %Add graphics object to animate

    hp2=gpatch(E2,V_DEF(:,:,end),'w','none',0.25); %Add graphics object to animate

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([min(F_primary_contact_pressure_mat(:)) max(F_primary_contact_pressure_mat(:))]);
    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

        %Set entries in animation structure
        animStruct.Handles{qt}=[hp hp hp2]; %Handles of objects to animate
        animStruct.Props{qt}={'Vertices','CData','Vertices'}; %Properties of objects to animate
        animStruct.Set{qt}={V_DEF(:,:,qt),F_primary_contact_pressure_mat(:,:,qt),V_DEF(:,:,qt)}; %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.

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.

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