DEMO_febio_0004_beam_twist

Below is a demonstration for:

Contents

Keywords

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'

%Define applied torsion angle
alphaRotTotal=2*pi;%0.5*pi; %Total twist angle
numSteps=50; %Number of steps

%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=30; %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

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;
    quadType='quad8';
else
    quadType='quad4';
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;

Create rigid body end plate for rotation constraint

Fr=Fb(Cb==3,:); %The faces for the beam end

%Nodes part of the rigid body
indRigid=unique(Fr(:));

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

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,'w','k',0.5);

hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize);
hl(2)=gpatch(Fr,V,'rw','k',1);
plotV(V(indRigid,:),'r.','MarkerSize',markerSize);
legend(hl,{'BC support','Rigid body'});

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;

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=mean(V(indRigid,:),1);

%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

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

% -> 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;

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

%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';

%Rigid section
% -> Prescribed rigid body boundary conditions
febio_spec.Rigid.rigid_constraint{1}.ATTR.name='RotFix_1';
febio_spec.Rigid.rigid_constraint{1}.ATTR.type='fix';
febio_spec.Rigid.rigid_constraint{1}.rb=2;
febio_spec.Rigid.rigid_constraint{1}.dofs='Ru,Rw';

febio_spec.Rigid.rigid_constraint{2}.ATTR.name='RotPrescribe_1';
febio_spec.Rigid.rigid_constraint{2}.ATTR.type='prescribe';
febio_spec.Rigid.rigid_constraint{2}.rb=2;
febio_spec.Rigid.rigid_constraint{2}.dof='Rv';
febio_spec.Rigid.rigid_constraint{2}.value.ATTR.lc=1;
febio_spec.Rigid.rigid_constraint{2}.value.VAL=alphaRotTotal;

%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=',';

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='external';%'internal';

[runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-------->    RUNNING/MONITORING FEBIO JOB    <-------- 11-Dec-2020 12:18:05
FEBio path: /home/kevin/FEBioStudio/bin/febio3
# Attempt removal of existing log files                11-Dec-2020 12:18:05
 * Removal succesful                                   11-Dec-2020 12:18:05
# Attempt removal of existing .xplt files              11-Dec-2020 12:18:05
 * Removal succesful                                   11-Dec-2020 12:18:05
# Starting FEBio...                                    11-Dec-2020 12:18:05
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       11-Dec-2020 12:18:05
   Max. wait time: 30 s
 * Log file found.                                     11-Dec-2020 12:18:05
# Parsing log file...                                  11-Dec-2020 12:18:05
    number of iterations   : 8                         11-Dec-2020 12:18:06
    number of reformations : 8                         11-Dec-2020 12:18:06
------- converged at time : 0.0333333                  11-Dec-2020 12:18:06
    number of iterations   : 8                         11-Dec-2020 12:18:07
    number of reformations : 8                         11-Dec-2020 12:18:07
------- converged at time : 0.0622455                  11-Dec-2020 12:18:07
    number of iterations   : 7                         11-Dec-2020 12:18:07
    number of reformations : 7                         11-Dec-2020 12:18:07
------- converged at time : 0.0873288                  11-Dec-2020 12:18:07
    number of iterations   : 6                         11-Dec-2020 12:18:07
    number of reformations : 6                         11-Dec-2020 12:18:07
------- converged at time : 0.110576                   11-Dec-2020 12:18:07
    number of iterations   : 6                         11-Dec-2020 12:18:08
    number of reformations : 6                         11-Dec-2020 12:18:08
------- converged at time : 0.133824                   11-Dec-2020 12:18:08
    number of iterations   : 6                         11-Dec-2020 12:18:08
    number of reformations : 6                         11-Dec-2020 12:18:08
------- converged at time : 0.157071                   11-Dec-2020 12:18:08
    number of iterations   : 6                         11-Dec-2020 12:18:08
    number of reformations : 6                         11-Dec-2020 12:18:08
------- converged at time : 0.180318                   11-Dec-2020 12:18:08
    number of iterations   : 6                         11-Dec-2020 12:18:08
    number of reformations : 6                         11-Dec-2020 12:18:08
------- converged at time : 0.203566                   11-Dec-2020 12:18:08
    number of iterations   : 6                         11-Dec-2020 12:18:09
    number of reformations : 6                         11-Dec-2020 12:18:09
------- converged at time : 0.226813                   11-Dec-2020 12:18:09
    number of iterations   : 6                         11-Dec-2020 12:18:09
    number of reformations : 6                         11-Dec-2020 12:18:09
------- converged at time : 0.250061                   11-Dec-2020 12:18:09
    number of iterations   : 6                         11-Dec-2020 12:18:09
    number of reformations : 6                         11-Dec-2020 12:18:09
------- converged at time : 0.273308                   11-Dec-2020 12:18:09
    number of iterations   : 6                         11-Dec-2020 12:18:09
    number of reformations : 6                         11-Dec-2020 12:18:09
------- converged at time : 0.296555                   11-Dec-2020 12:18:09
    number of iterations   : 6                         11-Dec-2020 12:18:10
    number of reformations : 6                         11-Dec-2020 12:18:10
------- converged at time : 0.319803                   11-Dec-2020 12:18:10
    number of iterations   : 6                         11-Dec-2020 12:18:10
    number of reformations : 6                         11-Dec-2020 12:18:10
------- converged at time : 0.34305                    11-Dec-2020 12:18:10
    number of iterations   : 6                         11-Dec-2020 12:18:10
    number of reformations : 6                         11-Dec-2020 12:18:10
------- converged at time : 0.366297                   11-Dec-2020 12:18:10
    number of iterations   : 6                         11-Dec-2020 12:18:10
    number of reformations : 6                         11-Dec-2020 12:18:10
------- converged at time : 0.389545                   11-Dec-2020 12:18:10
    number of iterations   : 6                         11-Dec-2020 12:18:11
    number of reformations : 6                         11-Dec-2020 12:18:11
------- converged at time : 0.412792                   11-Dec-2020 12:18:11
    number of iterations   : 6                         11-Dec-2020 12:18:11
    number of reformations : 6                         11-Dec-2020 12:18:11
------- converged at time : 0.43604                    11-Dec-2020 12:18:11
    number of iterations   : 6                         11-Dec-2020 12:18:11
    number of reformations : 6                         11-Dec-2020 12:18:11
------- converged at time : 0.459287                   11-Dec-2020 12:18:11
    number of iterations   : 6                         11-Dec-2020 12:18:11
    number of reformations : 6                         11-Dec-2020 12:18:11
------- converged at time : 0.482534                   11-Dec-2020 12:18:11
    number of iterations   : 6                         11-Dec-2020 12:18:12
    number of reformations : 6                         11-Dec-2020 12:18:12
------- converged at time : 0.505782                   11-Dec-2020 12:18:12
    number of iterations   : 6                         11-Dec-2020 12:18:12
    number of reformations : 6                         11-Dec-2020 12:18:12
------- converged at time : 0.529029                   11-Dec-2020 12:18:12
    number of iterations   : 6                         11-Dec-2020 12:18:12
    number of reformations : 6                         11-Dec-2020 12:18:12
------- converged at time : 0.552276                   11-Dec-2020 12:18:12
    number of iterations   : 6                         11-Dec-2020 12:18:12
    number of reformations : 6                         11-Dec-2020 12:18:12
------- converged at time : 0.575524                   11-Dec-2020 12:18:12
    number of iterations   : 6                         11-Dec-2020 12:18:13
    number of reformations : 6                         11-Dec-2020 12:18:13
------- converged at time : 0.598771                   11-Dec-2020 12:18:13
    number of iterations   : 6                         11-Dec-2020 12:18:13
    number of reformations : 6                         11-Dec-2020 12:18:13
------- converged at time : 0.622019                   11-Dec-2020 12:18:13
    number of iterations   : 6                         11-Dec-2020 12:18:13
    number of reformations : 6                         11-Dec-2020 12:18:13
------- converged at time : 0.645266                   11-Dec-2020 12:18:13
    number of iterations   : 6                         11-Dec-2020 12:18:14
    number of reformations : 6                         11-Dec-2020 12:18:14
------- converged at time : 0.668513                   11-Dec-2020 12:18:14
    number of iterations   : 6                         11-Dec-2020 12:18:14
    number of reformations : 6                         11-Dec-2020 12:18:14
------- converged at time : 0.691761                   11-Dec-2020 12:18:14
    number of iterations   : 6                         11-Dec-2020 12:18:14
    number of reformations : 6                         11-Dec-2020 12:18:14
------- converged at time : 0.715008                   11-Dec-2020 12:18:14
    number of iterations   : 6                         11-Dec-2020 12:18:14
    number of reformations : 6                         11-Dec-2020 12:18:14
------- converged at time : 0.738255                   11-Dec-2020 12:18:14
    number of iterations   : 6                         11-Dec-2020 12:18:15
    number of reformations : 6                         11-Dec-2020 12:18:15
------- converged at time : 0.761503                   11-Dec-2020 12:18:15
    number of iterations   : 6                         11-Dec-2020 12:18:15
    number of reformations : 6                         11-Dec-2020 12:18:15
------- converged at time : 0.78475                    11-Dec-2020 12:18:15
    number of iterations   : 8                         11-Dec-2020 12:18:15
    number of reformations : 8                         11-Dec-2020 12:18:15
------- converged at time : 0.807998                   11-Dec-2020 12:18:15
    number of iterations   : 6                         11-Dec-2020 12:18:15
    number of reformations : 6                         11-Dec-2020 12:18:15
------- converged at time : 0.828175                   11-Dec-2020 12:18:15
    number of iterations   : 6                         11-Dec-2020 12:18:16
    number of reformations : 6                         11-Dec-2020 12:18:16
------- converged at time : 0.848353                   11-Dec-2020 12:18:16
    number of iterations   : 6                         11-Dec-2020 12:18:16
    number of reformations : 6                         11-Dec-2020 12:18:16
------- converged at time : 0.86853                    11-Dec-2020 12:18:16
    number of iterations   : 6                         11-Dec-2020 12:18:16
    number of reformations : 6                         11-Dec-2020 12:18:16
------- converged at time : 0.888708                   11-Dec-2020 12:18:16
    number of iterations   : 6                         11-Dec-2020 12:18:16
    number of reformations : 6                         11-Dec-2020 12:18:16
------- converged at time : 0.908885                   11-Dec-2020 12:18:16
    number of iterations   : 6                         11-Dec-2020 12:18:17
    number of reformations : 6                         11-Dec-2020 12:18:17
------- converged at time : 0.929063                   11-Dec-2020 12:18:17
    number of iterations   : 6                         11-Dec-2020 12:18:17
    number of reformations : 6                         11-Dec-2020 12:18:17
------- converged at time : 0.94924                    11-Dec-2020 12:18:17
    number of iterations   : 6                         11-Dec-2020 12:18:17
    number of reformations : 6                         11-Dec-2020 12:18:17
------- converged at time : 0.969417                   11-Dec-2020 12:18:17
    number of iterations   : 6                         11-Dec-2020 12:18:17
    number of reformations : 6                         11-Dec-2020 12:18:17
------- converged at time : 0.989595                   11-Dec-2020 12:18:17
    number of iterations   : 4                         11-Dec-2020 12:18:18
    number of reformations : 4                         11-Dec-2020 12:18:18
------- converged at time : 1                          11-Dec-2020 12:18:18
 Elapsed time : 0:00:12                                11-Dec-2020 12:18:18
 N O R M A L   T E R M I N A T I O N
# Done                                                 11-Dec-2020 12:18:18
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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';
    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, gibbon.toolbox@gmail.com

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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 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/.