DEMO_FEBio_block_uniaxial_compression_fibre_reinforced_v1p2

Below is a demonstration for: 1) Building an FEBio model for uniaxial compression 2) Running the model 3) Importing displacement and force results 4) Plotting Cauchy stress, displacement results

Contents

clear; close all; clc;

warning off;

Plot settings

figColor='w'; figColorDef='white';
fontSize=20;
faceAlpha1=0.8;
faceAlpha2=1;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize=25;
lineWidth=3;

Control parameters

% path names
filePath=mfilename('fullpath');
savePath=fullfile(fileparts(filePath),'data','temp');

modelName=fullfile(savePath,'tempModel');

%Specifying dimensions and number of elements
sampleWidth=10;
sampleThickness=10;
sampleHeight=10;
pointSpacings=2*ones(1,3);
initialArea=sampleWidth*sampleThickness;

numElementsWidth=round(sampleWidth/pointSpacings(1));
numElementsThickness=round(sampleThickness/pointSpacings(2));
numElementsHeight=round(sampleHeight/pointSpacings(3));

stretchLoad=0.7;
displacementMagnitude=[0 0 (stretchLoad*sampleHeight)-sampleHeight];

%Material parameter set
c1=1e-3;
m1=12;
ksi=c1*100;
beta=3;
k_factor=1e3;
alphaFib=1/3*pi;

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;
faceBoundaryMarker=box1.faceBoundaryMarker;

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

elementMaterialIndices=ones(size(E,1),1);
% Plotting boundary surfaces
hf=figuremax(figColor,figColorDef);
title('Model surfaces','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;
patch('Faces',Fb,'Vertices',V,'FaceColor','flat','CData',faceBoundaryMarker,'FaceAlpha',faceAlpha2,'lineWidth',edgeWidth,'edgeColor',edgeColor);

colormap(jet(6)); colorbar;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;
drawnow;

DEFINE BC's

%Define faces
logicFace=faceBoundaryMarker==1;
Fr=Fb(logicFace,:);
bcSupportList_X=unique(Fr(:));

logicFace=faceBoundaryMarker==3;
Fr=Fb(logicFace,:);
bcSupportList_Y=unique(Fr(:));

logicFace=faceBoundaryMarker==5;
Fr=Fb(logicFace,:);
bcSupportList_Z=unique(Fr(:));

%Define line support
bcSupportList_X_axis=bcSupportList_Y(ismember(bcSupportList_Y,bcSupportList_Z));
bcSupportList_Y_axis=bcSupportList_X(ismember(bcSupportList_X,bcSupportList_Z));

%Prescribed displacement nodes
logicPrescribe=faceBoundaryMarker==6;
Fr=Fb(logicPrescribe,:);
bcPrescribeList=unique(Fr(:));
bcPrescribeMagnitudes=displacementMagnitude(ones(1,numel(bcPrescribeList)),:);

Visualize BC's

hf=figuremax(figColor,figColorDef);
title('Model BCs','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;

patch('Faces',Fb,'Vertices',V,'FaceColor','flat','CData',faceBoundaryMarker,'FaceAlpha',faceAlpha2,'lineWidth',edgeWidth,'edgeColor',edgeColor);

plotV(V(bcSupportList_Z,:),'b.','MarkerSize',markerSize);
plotV(V(bcPrescribeList,:),'k.','MarkerSize',markerSize);
plotV(V(bcSupportList_X_axis,:),'g.','MarkerSize',markerSize*2);
plotV(V(bcSupportList_Y_axis,:),'r.','MarkerSize',markerSize*2);

set(gca,'FontSize',fontSize);
colormap(jet(6)); colorbar;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;
drawnow;

DEFINE FIBRE DIRECTIONS

[R,~]=euler2DCM([0,alphaFib,0]);
v_fib=(R*[0 0 1]')';

V_fib=v_fib(ones(size(E,1),1),:);

Visualize fibre direction vectors

[Ff,Vf,Cf]=quiver3Dpatch(VE(:,1),VE(:,2),VE(:,3),V_fib(:,1),V_fib(:,2),V_fib(:,3),ones(size(V_fib,1),1),min(pointSpacings).*ones(1,2));

hf=figuremax(figColor,figColorDef);
title('Fibre vectors','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;

patch('Faces',Fb,'Vertices',V,'FaceColor',0.5.*ones(1,3),'FaceAlpha',faceAlpha1,'edgeColor','k');
patch('Faces',Ff,'Vertices',Vf,'FaceColor','k','FaceAlpha',1,'edgeColor','none');

set(gca,'FontSize',fontSize);
colormap(jet(6)); colorbar;
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;  grid on;
drawnow;

CONSTRUCTING FEB MODEL

FEB_struct.febio_spec.version='1.2';

FEB_struct.Module.Type='solid';

% Defining file names
FEB_struct.run_filename=[modelName,'.feb']; %FEB file name
FEB_struct.run_logname=[modelName,'.txt']; %FEBio log file name

%Geometry section
FEB_struct.Geometry.Nodes=V;
FEB_struct.Geometry.Elements={E}; %The element sets
FEB_struct.Geometry.ElementType={'hex8'}; %The element types
FEB_struct.Geometry.ElementMat={elementMaterialIndices};

%Material section
k=0.5.*(c1+ksi)*k_factor;
Mat1.type='uncoupled solid mixture';
% Mat1.props={'k'};
% Mat1.vals={k};
Mat11.type='Ogden';
Mat11.props={'c1','m1','k'};
Mat11.vals={c1,m1,k};
Mat11.aniso_type='none';
Mat12.type='fiber-exp-pow-uncoupled';
Mat12.props={'ksi','alpha','beta','theta','phi','k'};
Mat12.vals={ksi,1e-20,beta,0,0,k};
Mat12.aniso_type='none';
Mat1.Mats={Mat11 Mat12};

%Collect materials in cell array
FEB_struct.Materials={Mat1};

%Adding fibre direction, construct local orthonormal basis vectors
[a,d]=vectorOrthogonalPair(V_fib);

VF_E=zeros(size(V_fib,1),size(V_fib,2),2);
VF_E(:,:,1)=a; %a1 ~ e1 ~ X or first direction
VF_E(:,:,2)=d; %a2 ~ e2 ~ Y or second direction
%Vf_E %a3 ~ e3 ~ Z, third direction, or fibre direction

FEB_struct.Geometry.ElementData.MatAxis.ElementIndices=1:1:size(E,1);
FEB_struct.Geometry.ElementData.MatAxis.Basis=VF_E;


%Step specific control sections
FEB_struct.Control.AnalysisType='static';
FEB_struct.Control.Properties={'time_steps','step_size',...
    'max_refs','max_ups',...
    'dtol','etol','rtol','lstol'};
FEB_struct.Control.Values={10,0.1,...
    15,0,...
    0.001,0.01,0,0.9};
FEB_struct.Control.TimeStepperProperties={'dtmin','dtmax','max_retries','opt_iter','aggressiveness'};
FEB_struct.Control.TimeStepperValues={1e-5,0.1,10,10,1};

%Adding BC information
FEB_struct.Boundary.FixList={bcSupportList_Y_axis,bcSupportList_X_axis,bcSupportList_Z};
FEB_struct.Boundary.FixType={'x','y','z'};

FEB_struct.Boundary.PrescribeList={bcPrescribeList};
FEB_struct.Boundary.PrescribeType={'z'};
FEB_struct.Boundary.PrescribeValues={displacementMagnitude(ones(numel(bcPrescribeList),1),3)};
FEB_struct.Boundary.PrescribeTypes={'relative'};
FEB_struct.Boundary.LoadCurveIds=1;

%Load curves
FEB_struct.LoadData.LoadCurves.id=1;
FEB_struct.LoadData.LoadCurves.type={'linear'};
FEB_struct.LoadData.LoadCurves.loadPoints={[0 0;1 1;]};

%Adding output requests
FEB_struct.Output.VarTypes={'displacement','stress','relative volume','shell thickness'};

%Specify log file output
run_disp_output_name=[FEB_struct.run_filename(1:end-4),'_node_out.txt'];
run_force_output_name=[FEB_struct.run_filename(1:end-4),'_force_out.txt'];
FEB_struct.run_output_names={run_disp_output_name,run_force_output_name};
FEB_struct.output_types={'node_data','node_data'};
FEB_struct.data_types={'ux;uy;uz','Rx;Ry;Rz'};

SAVING .FEB FILE

FEB_struct.disp_opt=0; %Display waitbars option
febStruct2febFile_v1p2(FEB_struct);
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- Writing FEBio XML object --- 23-Sep-2014 12:31:45
Adding Module level
Adding Globals level
Adding Material level
Adding Geometry level
----> Adding node field
----> Adding element field
----> Adding hex8 element entries....
----> Adding element data field
----> MatAxis data entries found
Adding Output level
----> Adding plotfile field
----> Adding logfile field
Adding Boundary level
----> Defining fix type boundary conditions
----> Defining prescribe type boundary conditions
Adding LoadData level
----> Defining load curves
Writing .feb file
--- Done --- 23-Sep-2014 12:31:45

RUNNING FEBIO JOB

% FEBioRunStruct.FEBioPath='C:\Progra~1\FEBio1p8\febio.exe';
% FEBioRunStruct.FEBioPath='C:\Progra~1\FEBio2p0\bin\FEBio2x64.exe';
% FEBioRunStruct.FEBioPath='C:\Program Files\febio-2.1.1\bin\FEBio2.exe';
FEBioRunStruct.run_filename=FEB_struct.run_filename;
FEBioRunStruct.run_logname=FEB_struct.run_logname;
FEBioRunStruct.disp_on=1;
FEBioRunStruct.disp_log_on=1;
FEBioRunStruct.runMode='external';%'internal';
FEBioRunStruct.t_check=0.25; %Time for checking log file (dont set too small)
FEBioRunStruct.maxtpi=1e99; %Max analysis time
FEBioRunStruct.maxLogCheckTime=3;

%-------------------------------------------------------------------
[rundFlag]=runMonitorFEBio(FEBioRunStruct);%START FEBio NOW!!!!!!!!
%-------------------------------------------------------------------
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--- STARTING FEBIO JOB --- 23-Sep-2014 12:31:45
Waiting for log file...
Proceeding to check log file...23-Sep-2014 12:31:46
------- converged at time : 0.1
------- converged at time : 0.2
------- converged at time : 0.3
------- converged at time : 0.4
------- converged at time : 0.5
------- converged at time : 0.6
------- converged at time : 0.7
------- converged at time : 0.75
------- converged at time : 0.81
------- converged at time : 0.878
------- converged at time : 0.9152
------- converged at time : 0.96496
------- converged at time : 1
--- Done --- 23-Sep-2014 12:31:47

IMPORTING NODAL DISPLACEMENT RESULTS

Importing nodal displacements from a log file

[~, N_disp_mat,~]=importFEBio_logfile(FEB_struct.run_output_names{1}); %Nodal displacements

DN=N_disp_mat(:,2:end,end); %Final nodal displacements

CREATING NODE SET IN DEFORMED STATE

V_def=V+DN;
DN_magnitude=sqrt(sum(DN.^2,2));

Plotting the deformed model

[CF]=vertexToFaceMeasure(Fb,DN_magnitude);

hf1=figuremax(figColor,figColorDef);
title('The deformed model','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;

hps=patch('Faces',Fb,'Vertices',V_def,'FaceColor','flat','CData',CF);

view(3); axis tight;  axis equal;  grid on;
colormap jet; colorbar;
% camlight headlight;
set(gca,'FontSize',fontSize);
drawnow;

IMPORTING NODAL FORCES

Importing nodal forces from a log file

[time_mat, N_force_mat,~]=importFEBio_logfile(FEB_struct.run_output_names{2}); %Nodal displacements

FZ_set=N_force_mat(bcPrescribeList,end,:); %Final nodal displacements

DERIVING STRESS METRICS

%Get Z forces
FZ=sum(N_force_mat(bcPrescribeList,end,:),1);
FZ=[0; FZ(:)]; %Mean top surface nodal forces

%Derive applied stretch
DZ_set=N_disp_mat(bcPrescribeList,end,:); %Final nodal displacements
DZ_set=mean(DZ_set,1);
stretch_sim=(DZ_set+sampleHeight)./sampleHeight;
stretch_sim=[1; stretch_sim(:)];

%Derive simulated Cauchy stress (alternatively import stress and take the mean)
currentArea=initialArea./stretch_sim;
stress_cauchy_sim=FZ./currentArea; %Cauchy stress
stress_cauchy_sim=stress_cauchy_sim.*1e3; %Scale to kPa
hf1=figuremax(figColor,figColorDef);
title('Stretch stress curves','FontSize',fontSize);
xlabel('\lambda Stretch [.]','FontSize',fontSize); ylabel('\sigma Cauchy stress [kPa]','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on;

plot(stretch_sim,stress_cauchy_sim,'r.-','lineWidth',lineWidth,'markerSize',markerSize);

view(2); axis tight;  grid on;
set(gca,'FontSize',fontSize);
drawnow;

GIBBON

Kevin M. Moerman (kevinmoerman@hotmail.com)