DEMO_febio_0041_beam_L_force

Below is a demonstration for:

Contents

Keywords

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=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

%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);

forceMagnitude=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

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);

% Plotting boundary surfaces cFigure; hold on; title('Model surfaces','FontSize',fontSize); gpatch(Fb,V,0.5*ones(1,3),'none',0.2); % gpatch(F_bottom,V,'g','k',1); % gpatch(FE_bottom,V,'g','k',0.9); gpatch(F_side_bottom,V,'r','k',1); gpatch(Fq,Vq,'r','k',0.5);

% gpatch(Fq_start,Vq,'b','k',1); % gpatch(Fq_end,Vq,'b','k',1);

plotV(V(indV_bottom,:),'b.','MarkerSize',25); plotV(V(indV_bottomTop,:),'y.','MarkerSize',25);

plotV(Vq,'k.','MarkerSize',25);

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

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);

[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,:);

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=(forceMagnitude.*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='2.5';

%Module section
febio_spec.Module.ATTR.type='solid';

%Control section
febio_spec.Control.analysis.ATTR.type='static';
febio_spec.Control.time_steps=numTimeSteps;
febio_spec.Control.step_size=1/numTimeSteps;
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;
febio_spec.Control.max_refs=max_refs;
febio_spec.Control.max_ups=max_ups;

%Material section
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;

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;

%Geometry section
% -> Nodes
febio_spec.Geometry.Nodes{1}.ATTR.name='nodeSet_all'; %The node set name
febio_spec.Geometry.Nodes{1}.node.ATTR.id=(1:size(V,1))'; %The node id's
febio_spec.Geometry.Nodes{1}.node.VAL=V; %The nodel coordinates

% -> Elements
febio_spec.Geometry.Elements{1}.ATTR.type='hex8'; %Element type of this set
febio_spec.Geometry.Elements{1}.ATTR.mat=1; %material index for this set
febio_spec.Geometry.Elements{1}.ATTR.name='Beam_part1'; %Name of the element set
febio_spec.Geometry.Elements{1}.elem.ATTR.id=(1:1:nnz(elementMaterialIndices==1))'; %Element id's
febio_spec.Geometry.Elements{1}.elem.VAL=E(elementMaterialIndices==1,:);

febio_spec.Geometry.Elements{2}.ATTR.type='hex8'; %Element type of this set
febio_spec.Geometry.Elements{2}.ATTR.mat=2; %material index for this set
febio_spec.Geometry.Elements{2}.ATTR.name='Beam_part2'; %Name of the element set
febio_spec.Geometry.Elements{2}.elem.ATTR.id=nnz(elementMaterialIndices==1)+(1:1:nnz(elementMaterialIndices==2))'; %Element id's
febio_spec.Geometry.Elements{2}.elem.VAL=E(elementMaterialIndices==2,:);

% -> NodeSets
febio_spec.Geometry.NodeSet{1}.ATTR.name='bcSupportList';
febio_spec.Geometry.NodeSet{1}.node.ATTR.id=bcSupportList(:);

febio_spec.Geometry.NodeSet{2}.ATTR.name='bcPrescribeList';
febio_spec.Geometry.NodeSet{2}.node.ATTR.id=bcPrescribeList(:);

%Boundary condition section
% -> Fix boundary conditions
febio_spec.Boundary.fix{1}.ATTR.bc='x';
febio_spec.Boundary.fix{1}.ATTR.node_set=febio_spec.Geometry.NodeSet{1}.ATTR.name;
febio_spec.Boundary.fix{2}.ATTR.bc='y';
febio_spec.Boundary.fix{2}.ATTR.node_set=febio_spec.Geometry.NodeSet{1}.ATTR.name;
febio_spec.Boundary.fix{3}.ATTR.bc='z';
febio_spec.Boundary.fix{3}.ATTR.node_set=febio_spec.Geometry.NodeSet{1}.ATTR.name;

%Loads section
% -> Prescribed nodal forces
febio_spec.Loads.nodal_load{1}.ATTR.bc='x';
febio_spec.Loads.nodal_load{1}.ATTR.node_set=febio_spec.Geometry.NodeSet{2}.ATTR.name;
febio_spec.Loads.nodal_load{1}.scale.ATTR.lc=1;
febio_spec.Loads.nodal_load{1}.scale.VAL=1;
febio_spec.Loads.nodal_load{1}.value=bcPrescribedForce(1);

febio_spec.Loads.nodal_load{2}.ATTR.bc='y';
febio_spec.Loads.nodal_load{2}.ATTR.node_set=febio_spec.Geometry.NodeSet{2}.ATTR.name;
febio_spec.Loads.nodal_load{2}.scale.ATTR.lc=1;
febio_spec.Loads.nodal_load{2}.scale.VAL=1;
febio_spec.Loads.nodal_load{2}.value=bcPrescribedForce(2);

febio_spec.Loads.nodal_load{3}.ATTR.bc='z';
febio_spec.Loads.nodal_load{3}.ATTR.node_set=febio_spec.Geometry.NodeSet{2}.ATTR.name;
febio_spec.Loads.nodal_load{3}.scale.ATTR.lc=1;
febio_spec.Loads.nodal_load{3}.scale.VAL=1;
febio_spec.Loads.nodal_load{3}.value=bcPrescribedForce(3);

%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{1}.VAL=1:size(V,1);

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=',';
febio_spec.Output.logfile.node_data{2}.VAL=1:size(V,1);

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.disp_log_on=1; %Display convergence information in the command window
febioAnalysis.runMode='external';%'internal';
febioAnalysis.t_check=0.25; %Time for checking log file (dont set too small)
febioAnalysis.maxtpi=1e99; %Max analysis time
febioAnalysis.maxLogCheckTime=3; %Max log file checking time

[runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- STARTING FEBIO JOB --- 04-Jun-2019 13:16:03
Waiting for log file...
Proceeding to check log file...04-Jun-2019 13:16:04
------- converged at time : 0.05
------- converged at time : 0.1
------- converged at time : 0.15
------- converged at time : 0.2
------- converged at time : 0.25
------- converged at time : 0.3
------- converged at time : 0.35
------- converged at time : 0.4
------- converged at time : 0.45
------- converged at time : 0.5
------- converged at time : 0.55
------- converged at time : 0.6
------- converged at time : 0.65
------- converged at time : 0.7
------- converged at time : 0.75
------- converged at time : 0.8
------- converged at time : 0.85
------- converged at time : 0.9
------- converged at time : 0.95
------- converged at time : 1
--- Done --- 04-Jun-2019 13:16:05

Import FEBio results

if runFlag==1 %i.e. a succesful run
    % Importing nodal displacements from a log file
    [time_mat, N_disp_mat,~]=importFEBio_logfile(fullfile(savePath,febioLogFileName_disp)); %Nodal displacements
    time_mat=[0; time_mat(:)]; %Time

    N_disp_mat=N_disp_mat(:,2:end,:);
    sizImport=size(N_disp_mat);
    sizImport(3)=sizImport(3)+1;
    N_disp_mat_n=zeros(sizImport);
    N_disp_mat_n(:,:,2:end)=N_disp_mat;
    N_disp_mat=N_disp_mat_n;
    DN=N_disp_mat(:,:,end);
    DN_magnitude=sqrt(sum(DN(:,3).^2,2));
    V_def=V+DN;
    [CF]=vertexToFaceMeasure(Fb,DN_magnitude);

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']);
    hp=gpatch(Fb,V_def,CF,'k',1); %Add graphics object to animate
    hp.Marker='.';
    hp.MarkerSize=markerSize2;

    gpatch(Fb,V,0.5*ones(1,3),'none',0.25); %A static graphics object

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([0 max(DN_magnitude)]);
    axis([min(V_def(:,1)) max(V_def(:,1)) min(V_def(:,2)) max(V_def(:,2)) min(V_def(:,3)) max(V_def(:,3))]); %Set axis limits statically
    camlight headlight;

    % Set up animation features
    animStruct.Time=time_mat; %The time vector
    for qt=1:1:size(N_disp_mat,3) %Loop over time increments
        DN=N_disp_mat(:,:,qt); %Current displacement
        DN_magnitude=sqrt(sum(DN.^2,2)); %Current displacement magnitude
        V_def=V+DN; %Current nodal coordinates
        [CF]=vertexToFaceMeasure(Fb,DN_magnitude); %Current color data to use

        %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,CF}; %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]

GIBBON footer text

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) 2019 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/.