DEMO_febio_0027_layer_spatially_varying_material

Below is a demonstration for:

Building geometry for a cube with hexahedral 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
DEFINING AND VISUALIZING THE PARAMETER MAP
BUILD MODEL
SET UP 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
uniaxial loading
compression, tension, compressive, tensile
displacement control, displacement boundary condition
hexahedral elements, hex8
cube, box, rectangular
static, solid
hyperelastic, Ogden
displacement logfile
SED logfile

clear; close all; clc;

Plot settings

fontSize=15;
faceAlpha1=0.8;
faceAlpha2=1;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize1=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=[febioFebFileNamePart,'.txt']; %FEBio log file name
febioLogFileName_disp=[febioFebFileNamePart,'_disp_out.txt']; %Log file name for exporting displacement
febioLogFileName_sed=[febioFebFileNamePart,'_sed_out.txt']; %Log file name for exporting strain energy density

%Geometry parameters
fontSizeImage=15;
imagePadAmount=4;
numElemLayers=5;
displacementMagnitude=-0.2.*numElemLayers;

% FEA control settings
numTimeSteps=5; %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

E_youngs_min=1; %Lowest Youngs modulus
E_youngs_max=100; %Highest Youngs modulus
nu=0.4; %Poissons ratio

DEFINING AND VISUALIZING THE PARAMETER MAP

%Create text image
G=flipud(textImage('GIBBON','Arial',fontSizeImage,imagePadAmount));

%Thicken image
S=repmat(G,[1 1 numElemLayers]);

%Normalize data
S=S-min(S(:)); %Subtract minimum -> range [0-...]
S=S./max(S(:)); %Devide by max -> range [0-1]

%Use scaling data S to generate element Youngs moduli
E_youngs_elem=S(:).*(E_youngs_max-E_youngs_min)+E_youngs_min;

BUILD MODEL

%Create hexahedral elements with function based colors
[E,V,C]=ind2patch(true(size(S)),S,'hu');

F=element2patch(E);

[F]=element2patch(E);

%Get boundary faces for light plotting
[indBoundary]=tesBoundary(F);
Fb=F(indBoundary,:);

Plotting model boundary surfaces and a cut view

%Create mesh struct for plotting
meshStruct.elements=E;
meshStruct.elementData=E_youngs_elem;
meshStruct.nodes=V;
meshStruct.faces=F;

hFig=cFigure; hold on;
title('Cut view of material parameter: Youngs modulus [MPa]','FontSize',fontSize);
optionStruct.hFig=hFig;
optionStruct.cutDir=3;
optionStruct.cutSide=-1;
meshView(meshStruct,optionStruct);
colormap(gca,gray(250));
caxis([E_youngs_min E_youngs_max]);
axisGeom(gca,fontSize);

drawnow;

SET UP BOUNDARY CONDITIONS

%List of nodes for applying displacement
logicTopNodes=abs(V(:,3)-max(V(:,3)))<=max(eps(V(:,3)));
bcPrescribeList=find(logicTopNodes);

%List of nodes to fix
logicBottomNodes=abs(V(:,3)-min(V(:,3)))<=max(eps(V(:,3)));
bcSupportList=find(logicBottomNodes);

Visualize BC's

cFigure; hold on;
title('Boundary conditions','FontSize',fontSize);
gpatch(Fb,V,'kw','none',0.4);
hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize1);
hl(2)=plotV(V(bcPrescribeList,:),'r.','MarkerSize',markerSize1);
legend(hl,{'BC full support','BC prescribed displacement'})
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';
dataMapName1='MaterialParameterMap1';
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.ATTR.type='map'; %Calls for mapping of parameter
febio_spec.Material.material{1}.E=dataMapName1; %Calls for mapping of parameter
febio_spec.Material.material{1}.v=nu;

% 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='hex8'; %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=mrow(bcSupportList);

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

%MeshData secion
%-> Element data
febio_spec.MeshData.ElementData.ATTR.name=dataMapName1;
febio_spec.MeshData.ElementData.ATTR.elem_set=partName1;
febio_spec.MeshData.ElementData.elem.ATTR.lid=(1:1:size(E,1))';
febio_spec.MeshData.ElementData.elem.VAL=E_youngs_elem;

%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;

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.element_data{1}.ATTR.file=febioLogFileName_sed;
febio_spec.Output.logfile.element_data{1}.ATTR.data='sed';
febio_spec.Output.logfile.element_data{1}.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='external';%'internal';

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

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-------->    RUNNING/MONITORING FEBIO JOB    <-------- 20-Apr-2023 10:46:20
FEBio path: /home/kevin/FEBioStudio2/bin/febio4
# Attempt removal of existing log files                20-Apr-2023 10:46:20
 * Removal succesful                                   20-Apr-2023 10:46:20
# Attempt removal of existing .xplt files              20-Apr-2023 10:46:20
 * Removal succesful                                   20-Apr-2023 10:46:20
# Starting FEBio...                                    20-Apr-2023 10:46:20
  Max. total analysis time is: Inf s
 * Waiting for log file creation                       20-Apr-2023 10:46:20
   Max. wait time: 30 s
 * Log file found.                                     20-Apr-2023 10:46:20
# Parsing log file...                                  20-Apr-2023 10:46:20
    number of iterations   : 3                         20-Apr-2023 10:46:21
    number of reformations : 3                         20-Apr-2023 10:46:21
------- converged at time : 0.2                        20-Apr-2023 10:46:21
    number of iterations   : 3                         20-Apr-2023 10:46:22
    number of reformations : 3                         20-Apr-2023 10:46:22
------- converged at time : 0.4                        20-Apr-2023 10:46:22
    number of iterations   : 3                         20-Apr-2023 10:46:22
    number of reformations : 3                         20-Apr-2023 10:46:22
------- converged at time : 0.6                        20-Apr-2023 10:46:22
    number of iterations   : 3                         20-Apr-2023 10:46:23
    number of reformations : 3                         20-Apr-2023 10:46:23
------- converged at time : 0.8                        20-Apr-2023 10:46:23
    number of iterations   : 3                         20-Apr-2023 10:46:24
    number of reformations : 3                         20-Apr-2023 10:46:24
------- converged at time : 1                          20-Apr-2023 10:46:24
 Elapsed time : 0:00:04                                20-Apr-2023 10:46:24
 N O R M A L   T E R M I N A T I O N
# Done                                                 20-Apr-2023 10:46:24
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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 element stress from a log file

    dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_sed),0,1);

    %Access data
    E_energy=dataStruct.data;

Plotting the simulated results using anim8 to visualize and animate deformations

    [CV]=faceToVertexMeasure(E,V,E_energy(:,:,end));

    % Create basic view and store graphics handle to initiate animation
    hf=cFigure; %Open figure
    gtitle([febioFebFileNamePart,': Press play to animate']);
    title('$\sigma_{zz}$ [MPa]','Interpreter','Latex')
    hp=gpatch(Fb,V_DEF(:,:,end),CV,'k',1); %Add graphics object to animate

    hp.FaceColor='interp';

    axisGeom(gca,fontSize);
    colormap(gjet(250)); colorbar;
    caxis([min(E_energy(:)) max(E_energy(:))]/8);
    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

        [CV]=faceToVertexMeasure(E,V,E_energy(:,:,qt));

        %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),CV}; %Property values for to set in order to animate
    end
    anim8(hf,animStruct); %Initiate animation feature
    drawnow;

end

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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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