DEMO_febio_0002_beam_force

Below is a demonstration for:

Building geometry for a beam with hexahedral elements
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
Defining the 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
beam force loading
force control boundary condition
hexahedral elements, hex8, hex20
beam, rectangular
static, solid
hyperelastic, Ogden
displacement logfile
stress logfile

clear; close all; clc;

Plot settings

fontSize=20;
faceAlpha1=0.8;
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

%Specifying dimensions and number of elements
beamWidth=10;
sampleWidth=beamWidth; %Width
sampleThickness=4*beamWidth; %Thickness
sampleHeight=beamWidth; %Height
pointSpacings=3*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

elementType='hex20'; %'hex8' or 'hex20'

%Define applied force
appliedForce=[0 0 -2e-3];

%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=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'

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
E=meshStruct.elements; %The elements
V=meshStruct.nodes; %The nodes (vertices)
Fb=meshStruct.facesBoundary; %The boundary faces
Cb=meshStruct.boundaryMarker; %The "colors" or labels for the boundary faces
elementMaterialIndices=ones(size(E,1),1); %Element material indices

if strcmp(elementType,'hex20')
    [E,V,~,Fb]=hex8_hex20(E,V,{},Fb);
    meshStruct.elements=E;
    meshStruct.nodes=V;
    meshStruct.Fb=Fb;
end

Plotting model boundary surfaces and a cut view

hFig=cFigure;

subplot(1,2,1); hold on;
title('Model boundary surfaces and labels','FontSize',fontSize);
hp=gpatch(Fb,V,Cb,'k',faceAlpha1);
hp.Marker='.';
hp.MarkerSize=markerSize2;

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 cube. These labels can be used to define boundary conditions.

%Define supported node set
bcSupportList=unique(Fb(Cb==4,:)); %Node set part of selected face

%Prescribed force nodes
bcPrescribeList=unique(Fb(Cb==3,:)); %Node set part of selected face

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','k',0.5);

hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize);
hl(2)=plotV(V(bcPrescribeList,:),'r.','MarkerSize',markerSize);

legend(hl,{'BC support','BC prescribe'});

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.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=elementType; %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

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

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

%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.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;

%Loads section
% -> Prescribed nodal forces
nodalLoadType='force';
switch nodalLoadType
    case 'load' %Apply same force to each node
        febio_spec.Loads.nodal_load{1}.ATTR.name='PrescribedForceX';
        febio_spec.Loads.nodal_load{1}.ATTR.type='nodal_load';
        febio_spec.Loads.nodal_load{1}.ATTR.node_set=nodeSetName2;
        febio_spec.Loads.nodal_load{1}.dof='x';
        febio_spec.Loads.nodal_load{1}.scale.ATTR.lc=1;
        febio_spec.Loads.nodal_load{1}.scale.VAL=appliedForce(1)/numel(bcPrescribeList);

        febio_spec.Loads.nodal_load{2}.ATTR.name='PrescribedForceY';
        febio_spec.Loads.nodal_load{2}.ATTR.type='nodal_load';
        febio_spec.Loads.nodal_load{2}.ATTR.node_set=nodeSetName2;
        febio_spec.Loads.nodal_load{2}.dof='y';
        febio_spec.Loads.nodal_load{2}.scale.ATTR.lc=1;
        febio_spec.Loads.nodal_load{2}.scale.VAL=appliedForce(2)/numel(bcPrescribeList);

        febio_spec.Loads.nodal_load{3}.ATTR.name='PrescribedForceZ';
        febio_spec.Loads.nodal_load{3}.ATTR.type='nodal_load';
        febio_spec.Loads.nodal_load{3}.ATTR.node_set=nodeSetName2;
        febio_spec.Loads.nodal_load{3}.dof='z';
        febio_spec.Loads.nodal_load{3}.scale.ATTR.lc=1;
        febio_spec.Loads.nodal_load{3}.scale.VAL=appliedForce(3)/numel(bcPrescribeList);
    case 'force' %Apply a force vector to a collection of nodes (destributed)
        febio_spec.Loads.nodal_load{1}.ATTR.name='PrescribedForceX';
        febio_spec.Loads.nodal_load{1}.ATTR.type='nodal_force';
        febio_spec.Loads.nodal_load{1}.ATTR.node_set=nodeSetName2;
        febio_spec.Loads.nodal_load{1}.value.ATTR.lc=1;
        febio_spec.Loads.nodal_load{1}.value.VAL=appliedForce/numel(bcPrescribeList);
end

%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=',';

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    <-------- 20-Apr-2023 10:37:48
FEBio path: /home/kevin/FEBioStudio2/bin/febio4
# Attempt removal of existing log files                20-Apr-2023 10:37:48
 * Removal succesful                                   20-Apr-2023 10:37:48
# Attempt removal of existing .xplt files              20-Apr-2023 10:37:48
 * Removal succesful                                   20-Apr-2023 10:37:48
# Starting FEBio...                                    20-Apr-2023 10:37:48
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       20-Apr-2023 10:37:48
   Max. wait time: 30 s
 * Log file found.                                     20-Apr-2023 10:37:48
# Parsing log file...                                  20-Apr-2023 10:37:48
    number of iterations   : 7                         20-Apr-2023 10:37:48
    number of reformations : 7                         20-Apr-2023 10:37:48
------- converged at time : 0.1                        20-Apr-2023 10:37:48
    number of iterations   : 7                         20-Apr-2023 10:37:48
    number of reformations : 7                         20-Apr-2023 10:37:48
------- converged at time : 0.192656                   20-Apr-2023 10:37:48
    number of iterations   : 7                         20-Apr-2023 10:37:49
    number of reformations : 7                         20-Apr-2023 10:37:49
------- converged at time : 0.278513                   20-Apr-2023 10:37:49
    number of iterations   : 7                         20-Apr-2023 10:37:49
    number of reformations : 7                         20-Apr-2023 10:37:49
------- converged at time : 0.358076                   20-Apr-2023 10:37:49
    number of iterations   : 7                         20-Apr-2023 10:37:49
    number of reformations : 7                         20-Apr-2023 10:37:49
------- converged at time : 0.43181                    20-Apr-2023 10:37:49
    number of iterations   : 6                         20-Apr-2023 10:37:49
    number of reformations : 6                         20-Apr-2023 10:37:49
------- converged at time : 0.50015                    20-Apr-2023 10:37:49
    number of iterations   : 6                         20-Apr-2023 10:37:50
    number of reformations : 6                         20-Apr-2023 10:37:50
------- converged at time : 0.568489                   20-Apr-2023 10:37:50
    number of iterations   : 6                         20-Apr-2023 10:37:50
    number of reformations : 6                         20-Apr-2023 10:37:50
------- converged at time : 0.636828                   20-Apr-2023 10:37:50
    number of iterations   : 6                         20-Apr-2023 10:37:50
    number of reformations : 6                         20-Apr-2023 10:37:50
------- converged at time : 0.705167                   20-Apr-2023 10:37:50
    number of iterations   : 6                         20-Apr-2023 10:37:50
    number of reformations : 6                         20-Apr-2023 10:37:50
------- converged at time : 0.773507                   20-Apr-2023 10:37:50
    number of iterations   : 6                         20-Apr-2023 10:37:50
    number of reformations : 6                         20-Apr-2023 10:37:50
------- converged at time : 0.841846                   20-Apr-2023 10:37:50
    number of iterations   : 6                         20-Apr-2023 10:37:51
    number of reformations : 6                         20-Apr-2023 10:37:51
------- converged at time : 0.910185                   20-Apr-2023 10:37:51
    number of iterations   : 6                         20-Apr-2023 10:37:51
    number of reformations : 6                         20-Apr-2023 10:37:51
------- converged at time : 0.978524                   20-Apr-2023 10:37:51
    number of iterations   : 4                         20-Apr-2023 10:37:51
    number of reformations : 4                         20-Apr-2023 10:37:51
------- converged at time : 1                          20-Apr-2023 10:37:51
 Elapsed time : 0:00:03                                20-Apr-2023 10:37:51
 N O R M A L   T E R M I N A T I O N
# Done                                                 20-Apr-2023 10:37:51
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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)]);

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';
    gpatch(Fb,V,0.5*ones(1,3),'k',0.25); %A static graphics object

    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;

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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