DEMO_febio_0041_beam_L_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
Control parameters
CREATING MESHED BOX
Make last element set "h" heigh
Find side faces to extrude
Merging element sets
Refining elements
DEFINE BC's
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=15;
faceAlpha1=0.8;
faceAlpha2=1;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize=50;
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_force=[febioFebFileNamePart,'_force_out.txt']; %Log file name for exporting force

%Specifying dimensions and number of elements
L=85.4;
h=5.6;
b=50;
t=45;
phi=10;

sampleWidth=5.6;
sampleThickness=b;
sampleHeight=L+h;

numElementsWidth=round(sampleWidth/h);
numElementsThickness=round(sampleThickness/h);
numElementsHeight=round(sampleHeight/h);

appliedForce=2800;

E_youngs1=6550; % 6.55e10 Pa = 65.5 GPa = 6550 MPa
v1=0.3;
E_youngs2=7200; %72 Gpa = 7200
v2=0.3;

nRefine=0;

% FEA control settings
numTimeSteps=20; %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

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

CREATING MESHED BOX

%Create box 1
boxDim=[sampleWidth sampleThickness sampleHeight]; %Dimensions
boxEl=[numElementsWidth numElementsThickness numElementsHeight]; %Number of elements
[box1]=hexMeshBox(boxDim,boxEl);
E=box1.E;
V=box1.V;
Fb=box1.Fb;
Cb=box1.faceBoundaryMarker;

X=V(:,1); Y=V(:,2); Z=V(:,3);
VE=[mean(X(E),2) mean(Y(E),2) mean(Z(E),2)];

% Plotting boundary surfaces cFigure; hold on; title('Model surfaces','FontSize',fontSize); gpatch(Fb,V,Cb,'k',faceAlpha1); colormap(gjet(6)); icolorbar; axisGeom; camlight headlight; set(gca,'FontSize',fontSize); drawnow;

Make last element set "h" heigh

F_bottom=Fb(Cb==5,:);

logicBottomElements=any(ismember(E,F_bottom),2);
E_bottom=E(logicBottomElements,:);
[FE_bottom,~]=element2patch(E_bottom);

indV_FE_bottom=unique(FE_bottom(:));
mean_E_bottom=mean(V(indV_FE_bottom,:),1);

Z=V(:,3);
zMax=max(V(indV_FE_bottom,3));
zThreshold=zMax-(h/2);

indV_bottom=unique(F_bottom(:));
indV_bottomTop=indV_FE_bottom(V(indV_FE_bottom,3)>zThreshold);
% V(indV_bottomTop,3)=min(V(:,3))+h;

Find side faces to extrude

F_side=Fb(Cb==2,:);

logicSideBottom=all(ismember(F_side,indV_FE_bottom),2);
F_side_bottom=F_side(logicSideBottom,:);

layerThickness=t-h;
numStepsExtrude=ceil(layerThickness/h)+1;
dirSet=1;
[Eq,Vq,Fq_start,Fq_end]=quadThick(F_side_bottom,V,dirSet,layerThickness,numStepsExtrude);

[Fq,~]=element2patch(Eq);

Merging element sets

F_top=Fb(Cb==6,:);
F_force=Fq_end;

F_force=F_force+size(V,1);
Eq=Eq+size(V,1);

elementMaterialIndices=[ones(size(E,1),1); 2*ones(size(Eq,1),1);];
E=[E;Eq];
V=[V;Vq];

[~,ind1,ind2]=unique(pround(V,5),'rows');
V=V(ind1,:);
E=ind2(E);
F_top=ind2(F_top);
F_force=ind2(F_force);

[FE,CE]=element2patch(E,elementMaterialIndices);

Plotting boundary surfaces

cFigure; hold on;
title('Model surfaces','FontSize',fontSize);

gpatch(FE,V,CE,'k',1);

gpatch(F_force,V,'y','y',1);
gpatch(F_top,V,'g','g',1);
% plotV(V,'k.','MarkerSize',25);

colormap(gjet(4)); icolorbar;

axisGeom;
camlight headlight;
set(gca,'FontSize',fontSize);
drawnow;

Refining elements

C=[1:1:size(E,1)]';
if nRefine>0
    splitMethod=1;
    [E,V,C,CV]=subHex(E,V,nRefine,splitMethod);
end
elementMaterialIndices=elementMaterialIndices(C);

E1=E(elementMaterialIndices==1,:);
E2=E(elementMaterialIndices==2,:);

[FE,CF]=element2patch(E,C);
[D]=patchEdgeLengths(FE,V);

indTop=find(V(:,3)>(max(V(:,3))-max(D(:))/2));
indForce=find(V(:,1)>(max(V(:,1))-max(D(:))/2));


logicTopFaces=all(ismember(FE,indTop),2);
logicForceFaces=all(ismember(FE,indForce),2);

F_top=FE(logicTopFaces,:);
F_force=FE(logicForceFaces,:);
indBoundaryFaces=tesBoundary(FE,V);
Fb=FE(indBoundaryFaces,:);

Warning: Second input (vertices) no longer required. Update code to avoid
future error.

Plotting boundary surfaces

cFigure; hold on;
title('Model surfaces','FontSize',fontSize);

gpatch(Fb,V,0.5*ones(1,3),'k',1);

gpatch(F_force,V,'r','k',1);
gpatch(F_top,V,'g','k',1);

plotV(V(indTop,:),'b.','MarkerSize',25);
plotV(V(indForce,:),'y.','MarkerSize',25);
% plotV(V,'k.','MarkerSize',25);

% colormap(gjet(6)); icolorbar;
axisGeom;
camlight headlight;
set(gca,'FontSize',fontSize);
drawnow;

DEFINE BC's

%Supported nodes
bcSupportList=unique(F_top(:));

%Prescribed force nodes
bcPrescribeList=unique(F_force(:));
numForceNodes=numel(bcPrescribeList);

forceNormVec=[0 0 -1];
[R]=euler2DCM([0 phi/180*pi 0]);
forceNormVec=(R*forceNormVec')';

bcPrescribedForce=(appliedForce.*forceNormVec)/numForceNodes;

Visualize BC's

cFigure; hold on;
title('Boundary conditions','FontSize',fontSize);

gpatch(Fb,V,0.75*ones(1,3),'k',1);

plotV(V(bcSupportList,:),'b.','MarkerSize',markerSize);
plotV(V(bcPrescribeList,:),'r.','MarkerSize',markerSize);

quiverVec(V(bcPrescribeList,:),bcPrescribedForce(ones(numel(bcPrescribeList),1),:),25,'r');

axisGeom;
camlight headlight;
set(gca,'FontSize',fontSize);
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='neo-Hookean';
febio_spec.Material.material{1}.ATTR.id=1;
febio_spec.Material.material{1}.E=E_youngs1;
febio_spec.Material.material{1}.v=v1;

materialName2='Material2';
febio_spec.Material.material{2}.ATTR.name=materialName2;
febio_spec.Material.material{2}.ATTR.type='neo-Hookean';
febio_spec.Material.material{2}.ATTR.id=2;
febio_spec.Material.material{2}.E=E_youngs2;
febio_spec.Material.material{2}.v=v2;

%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='hex8'; %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);

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=materialName2;

%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
febio_spec.Loads.nodal_load{1}.ATTR.name='PrescribedForce';
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=bcPrescribedForce;

%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;

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

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-------->    RUNNING/MONITORING FEBIO JOB    <-------- 20-Apr-2023 18:06:18
FEBio path: /home/kevin/FEBioStudio2/bin/febio4
# Attempt removal of existing log files                20-Apr-2023 18:06:18
 * Removal succesful                                   20-Apr-2023 18:06:18
# Attempt removal of existing .xplt files              20-Apr-2023 18:06:19
 * Removal succesful                                   20-Apr-2023 18:06:19
# Starting FEBio...                                    20-Apr-2023 18:06:19
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       20-Apr-2023 18:06:19
   Max. wait time: 30 s
 * Log file found.                                     20-Apr-2023 18:06:19
# Parsing log file...                                  20-Apr-2023 18:06:19
    number of iterations   : 8                         20-Apr-2023 18:06:19
    number of reformations : 8                         20-Apr-2023 18:06:19
------- converged at time : 0.05                       20-Apr-2023 18:06:19
    number of iterations   : 8                         20-Apr-2023 18:06:19
    number of reformations : 8                         20-Apr-2023 18:06:19
------- converged at time : 0.1                        20-Apr-2023 18:06:19
    number of iterations   : 7                         20-Apr-2023 18:06:19
    number of reformations : 7                         20-Apr-2023 18:06:19
------- converged at time : 0.15                       20-Apr-2023 18:06:19
    number of iterations   : 7                         20-Apr-2023 18:06:19
    number of reformations : 7                         20-Apr-2023 18:06:19
------- converged at time : 0.2                        20-Apr-2023 18:06:19
    number of iterations   : 7                         20-Apr-2023 18:06:19
    number of reformations : 7                         20-Apr-2023 18:06:19
------- converged at time : 0.25                       20-Apr-2023 18:06:19
    number of iterations   : 6                         20-Apr-2023 18:06:20
    number of reformations : 6                         20-Apr-2023 18:06:20
------- converged at time : 0.3                        20-Apr-2023 18:06:20
    number of iterations   : 6                         20-Apr-2023 18:06:20
    number of reformations : 6                         20-Apr-2023 18:06:20
------- converged at time : 0.35                       20-Apr-2023 18:06:20
    number of iterations   : 6                         20-Apr-2023 18:06:20
    number of reformations : 6                         20-Apr-2023 18:06:20
------- converged at time : 0.4                        20-Apr-2023 18:06:20
    number of iterations   : 6                         20-Apr-2023 18:06:20
    number of reformations : 6                         20-Apr-2023 18:06:20
------- converged at time : 0.45                       20-Apr-2023 18:06:20
    number of iterations   : 6                         20-Apr-2023 18:06:20
    number of reformations : 6                         20-Apr-2023 18:06:20
------- converged at time : 0.5                        20-Apr-2023 18:06:20
    number of iterations   : 5                         20-Apr-2023 18:06:20
    number of reformations : 5                         20-Apr-2023 18:06:20
------- converged at time : 0.55                       20-Apr-2023 18:06:20
    number of iterations   : 5                         20-Apr-2023 18:06:20
    number of reformations : 5                         20-Apr-2023 18:06:20
------- converged at time : 0.6                        20-Apr-2023 18:06:20
    number of iterations   : 5                         20-Apr-2023 18:06:20
    number of reformations : 5                         20-Apr-2023 18:06:20
------- converged at time : 0.65                       20-Apr-2023 18:06:20
    number of iterations   : 5                         20-Apr-2023 18:06:20
    number of reformations : 5                         20-Apr-2023 18:06:20
------- converged at time : 0.7                        20-Apr-2023 18:06:20
    number of iterations   : 4                         20-Apr-2023 18:06:20
    number of reformations : 4                         20-Apr-2023 18:06:20
------- converged at time : 0.75                       20-Apr-2023 18:06:20
    number of iterations   : 4                         20-Apr-2023 18:06:20
    number of reformations : 4                         20-Apr-2023 18:06:20
------- converged at time : 0.8                        20-Apr-2023 18:06:20
    number of iterations   : 4                         20-Apr-2023 18:06:20
    number of reformations : 4                         20-Apr-2023 18:06:20
------- converged at time : 0.85                       20-Apr-2023 18:06:20
    number of iterations   : 4                         20-Apr-2023 18:06:20
    number of reformations : 4                         20-Apr-2023 18:06:20
------- converged at time : 0.9                        20-Apr-2023 18:06:20
    number of iterations   : 4                         20-Apr-2023 18:06:21
    number of reformations : 4                         20-Apr-2023 18:06:21
------- converged at time : 0.95                       20-Apr-2023 18:06:21
    number of iterations   : 4                         20-Apr-2023 18:06:21
    number of reformations : 4                         20-Apr-2023 18:06:21
------- converged at time : 1                          20-Apr-2023 18:06:21
 Elapsed time : 0:00:02                                20-Apr-2023 18:06:21
 N O R M A L   T E R M I N A T I O N
# Done                                                 20-Apr-2023 18:06:21
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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)]);

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.

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/.