DEMO_febio_0057_diamond_lattice_compression_01

Below is a demonstration for:

Building the geometry for the diaomond lattice with pentahedral and tetrahedral elements
Defining the boundary conditions
Coding the febio structure
Running the model
Importing and visualizing the displacement and stress results

Keywords
Plot settings
Control parameters
Create diamond lattice
DEFINE BC's
Check porosity
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
compression, tension, compressive, tensile
displacement control, displacement boundary condition
pentahedral penta6
tetrahedral tet4
cube, box, rectangular
Lattice
static, solid
hyperelastic, Ogden
displacement logfile
stress logfile

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=0.8;
faceAlpha2=1;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize=25;
markerSize2=10;
cMap=gjet(4);

Control parameters

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

% Defining file names
febioFebFileNamePart='tempModel';
febioFebFileName=fullfile(savePath,[febioFebFileNamePart,'.feb']); %FEB file name
febioLogFileName=fullfile(savePath,[febioFebFileNamePart,'.txt']); %FEBio log file name
febioLogFileName_disp=[febioFebFileNamePart,'_disp_out.txt']; %Log file name for exporting displacement
febioLogFileName_force=[febioFebFileNamePart,'_force_out.txt']; %Log file name for exporting force
febioLogFileName_stress=[febioFebFileNamePart,'_stress_out.txt']; %Log file name for exporting stress
febioLogFileName_stiffness=[febioFebFileNamePart,'_stiffness_out.txt']; %Log file name for exporting stiffness

%Geometry parameters
sampleSize=10;
nRepeat=3;
strutThickness=0.3; %Set the strut thickness
nSubPenta=2; %Number of subdivisions of the pentahedra in length direction
latticePhaseType=1;  % 1 = "bubble" centred, 2 = vertex centred, 3 = nested

%Define applied displacement
appliedStrain=0.3; %Linear strain (Only used to compute applied stretch)
loadingOption='compression'; % or 'tension'
switch loadingOption
    case 'compression'
        stretchLoad=1-appliedStrain; %The applied stretch for uniaxial loading
    case 'tension'
        stretchLoad=1+appliedStrain; %The applied stretch for uniaxial loading
end
displacementMagnitude=(stretchLoad*sampleSize)-sampleSize; %The displacement magnitude

%Material parameter set
E_youngs1=0.1; %Material Young's modulus
nu1=0.4; %Material Poisson's ratio

% 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

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

Create diamond lattice

[Ep,Et,V]=diamondLattice(sampleSize,nRepeat,strutThickness,latticePhaseType);
[Ep,V]=subPenta(Ep,V,nSubPenta,3); %Sub-divide pentahedra

Visualization of lattice meshes

% Convert tetrahedra and pentahedra to faces
[Ft]=element2patch(Et,[],'tet4');
[Fp]=element2patch(Ep,[],'penta6');

cFigure; hold on;
hpl=gpatch(Fp,V,'rw','r',0.5);
hpl(end+1)=gpatch(Ft,V,'gw','g',0.5);
legend(hpl,{'Pentahedral triangles','Pentahedra quads','Tetrahedral triangles'});
axisGeom;
camlight headlight;
drawnow;

DEFINE BC's

Z=V(:,3);
logicTop=Z>=(max(Z(:))-eps(max(Z(:))));
logicBottom=Z<min(Z(:))+eps(min(Z(:)));

bcPrescribeList=find(logicTop);
bcSupportList=find(logicBottom);

cFigure; hold on;
gpatch(Fp,V,'w','none',0.25);
gpatch(Ft,V,'w','none',0.25);
hl2(1)=plotV(V(bcPrescribeList,:),'r.','MarkerSize',markerSize);
hl2(2)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize);
legend(hl2,{'BC prescribe','BC support'});
axisGeom;
camlight headlight;
drawnow;

Check porosity

vol_tet=sum(tetVol(Et,V)); %Volume of tetrahedra
vol_penta=sum(pentaVol(Ep,V));  %Volume of pentahedra
vol_lattice=vol_tet+vol_penta; %Total lattice volume
porosity_lattice=vol_lattice./sampleSize.^3; %Porosity

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.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='neo-Hookean';
febio_spec.Material.material{1}.ATTR.id=1;
febio_spec.Material.material{1}.E=E_youngs1;
febio_spec.Material.material{1}.v=nu1;

% Mesh section
% -> Nodes
febio_spec.Mesh.Nodes{1}.ATTR.name='Object1'; %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='penta6'; %Element type
febio_spec.Mesh.Elements{1}.elem.ATTR.id=(1:1:size(Ep,1))'; %Element id's
febio_spec.Mesh.Elements{1}.elem.VAL=Ep; %The element matrix

partName2='Part2';
febio_spec.Mesh.Elements{2}.ATTR.name=partName2; %Name of this part
febio_spec.Mesh.Elements{2}.ATTR.type='tet4'; %Element type
febio_spec.Mesh.Elements{2}.elem.ATTR.id=size(Ep,1)+(1:1:size(Et,1))'; %Element id's
febio_spec.Mesh.Elements{2}.elem.VAL=Et; %The element matrix

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

nodeSetName2='bcPrescribeList';
febio_spec.Mesh.NodeSet{2}.ATTR.name=nodeSetName2;
febio_spec.Mesh.NodeSet{2}.VAL=mrow(bcPrescribeList);

%MeshDomains section
febio_spec.MeshDomains.SolidDomain{1}.ATTR.name=partName1;
febio_spec.MeshDomains.SolidDomain{1}.ATTR.mat=materialName1;

febio_spec.MeshDomains.SolidDomain{2}.ATTR.name=partName2;
febio_spec.MeshDomains.SolidDomain{2}.ATTR.mat=materialName1;

%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;

febio_spec.Boundary.bc{2}.ATTR.name='zero_displacement_xy';
febio_spec.Boundary.bc{2}.ATTR.type='zero displacement';
febio_spec.Boundary.bc{2}.ATTR.node_set=nodeSetName2;
febio_spec.Boundary.bc{2}.x_dof=1;
febio_spec.Boundary.bc{2}.y_dof=1;
febio_spec.Boundary.bc{2}.z_dof=0;

febio_spec.Boundary.bc{3}.ATTR.name='prescibed_displacement_z';
febio_spec.Boundary.bc{3}.ATTR.type='prescribed displacement';
febio_spec.Boundary.bc{3}.ATTR.node_set=nodeSetName2;
febio_spec.Boundary.bc{3}.dof='z';
febio_spec.Boundary.bc{3}.value.ATTR.lc=1;
febio_spec.Boundary.bc{3}.value.VAL=displacementMagnitude;
febio_spec.Boundary.bc{3}.relative=0;

%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.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=',';

% Plotfile section
febio_spec.Output.plotfile.compression=0;

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;
febioAnalysis.maxLogCheckTime=10; %Max log file checking time

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

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-------->    RUNNING/MONITORING FEBIO JOB    <-------- 27-Apr-2023 13:48:28
FEBio path: /home/kevin/FEBioStudio2/bin/febio4
# Attempt removal of existing log files                27-Apr-2023 13:48:28
 * Removal succesful                                   27-Apr-2023 13:48:28
# Attempt removal of existing .xplt files              27-Apr-2023 13:48:29
 * Removal succesful                                   27-Apr-2023 13:48:29
# Starting FEBio...                                    27-Apr-2023 13:48:29
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       27-Apr-2023 13:48:29
   Max. wait time: 10 s
 * Log file found.                                     27-Apr-2023 13:48:29
# Parsing log file...                                  27-Apr-2023 13:48:29
    number of iterations   : 3                         27-Apr-2023 13:48:29
    number of reformations : 3                         27-Apr-2023 13:48:29
------- converged at time : 0.1                        27-Apr-2023 13:48:29
    number of iterations   : 3                         27-Apr-2023 13:48:29
    number of reformations : 3                         27-Apr-2023 13:48:29
------- converged at time : 0.2                        27-Apr-2023 13:48:29
    number of iterations   : 3                         27-Apr-2023 13:48:30
    number of reformations : 3                         27-Apr-2023 13:48:30
------- converged at time : 0.3                        27-Apr-2023 13:48:30
    number of iterations   : 3                         27-Apr-2023 13:48:30
    number of reformations : 3                         27-Apr-2023 13:48:30
------- converged at time : 0.4                        27-Apr-2023 13:48:30
    number of iterations   : 3                         27-Apr-2023 13:48:30
    number of reformations : 3                         27-Apr-2023 13:48:30
------- converged at time : 0.5                        27-Apr-2023 13:48:30
    number of iterations   : 3                         27-Apr-2023 13:48:30
    number of reformations : 3                         27-Apr-2023 13:48:30
------- converged at time : 0.6                        27-Apr-2023 13:48:30
    number of iterations   : 3                         27-Apr-2023 13:48:30
    number of reformations : 3                         27-Apr-2023 13:48:30
------- converged at time : 0.7                        27-Apr-2023 13:48:30
    number of iterations   : 3                         27-Apr-2023 13:48:31
    number of reformations : 3                         27-Apr-2023 13:48:31
------- converged at time : 0.8                        27-Apr-2023 13:48:31
    number of iterations   : 3                         27-Apr-2023 13:48:31
    number of reformations : 3                         27-Apr-2023 13:48:31
------- converged at time : 0.9                        27-Apr-2023 13:48:31
    number of iterations   : 3                         27-Apr-2023 13:48:31
    number of reformations : 3                         27-Apr-2023 13:48:31
------- converged at time : 1                          27-Apr-2023 13:48:31
 Elapsed time : 0:00:02                                27-Apr-2023 13:48:31
 N O R M A L   T E R M I N A T I O N
# Done                                                 27-Apr-2023 13:48:31
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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 nodal forces from a log file

    dataStructForce=importFEBio_logfile(fullfile(savePath,febioLogFileName_force),0,1);
    F_applied=squeeze(sum(dataStructForce.data(bcPrescribeList,:,:),1))';

    f_sum_x=F_applied(:,1);
    f_sum_y=F_applied(:,2);
    f_sum_z=F_applied(:,3);

Visualize force data

    cFigure; hold on;
    xlabel('Time [s]','Interpreter','Latex'); ylabel('Force [N]','Interpreter','Latex');
    hp1=plot(timeVec,f_sum_x,'r-','LineWidth',3);
    hp2=plot(timeVec,f_sum_y,'g-','LineWidth',3);
    hp3=plot(timeVec,f_sum_z,'b-','LineWidth',3);
    legend([hp1 hp2 hp3],{'$F_x$','$F_y$','$F_z$'},'Interpreter','Latex');
    grid on; box on; axis square; axis tight;
    set(gca,'FontSize',fontSize);
    drawnow;

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']);
    hp1=gpatch(Ft,V_DEF(:,:,end),DN_magnitude,'k',1);
    hp1.FaceColor='interp';
    hp2=gpatch(Fp{1},V_DEF(:,:,end),DN_magnitude,'k',1);
    hp2.FaceColor='interp';
    hp3=gpatch(Fp{2},V_DEF(:,:,end),DN_magnitude,'k',1);
    hp3.FaceColor='interp';

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    clim([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}=[hp1 hp1 hp2 hp2 hp3 hp3]; %Handles of objects to animate
        animStruct.Props{qt}={'Vertices','CData','Vertices','CData','Vertices','CData'}; %Properties of objects to animate
        animStruct.Set{qt}={V_DEF(:,:,qt),DN_magnitude,V_DEF(:,:,qt),DN_magnitude,V_DEF(:,:,qt),DN_magnitude}; %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.

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