DEMO_visualization_von_mises_plasticity_01

Below is a demonstration for:

Contents

clear; close all; clc

Plot settings.

fontSizeAxis=25;
fontSizeText=35;
colorSet=viridis(3);
lineWidth1=1;
lineWidth2=3;
lineWidthAxis=3;
f=3;

Control parameters

s=1; %Yield stress

Create ellipsoids

t=linspace(0,2*pi,1000); %Angular coordinates
x=s*cos(t);
y=s*sqrt(3).*sin(t);
z=zeros(size(x));
v=[x(:) y(:) z(:)]; %Ellipse coordinates

%Make cylinder "slices" ellipses by rotating above ellipse
R12=euler2DCM([0 0 (45/180)*pi]);
v12=v*R12;

R13_1=euler2DCM([0 (90/180)*pi 0]);
R13_2=euler2DCM([(135/180)*pi 0 0]);
v13=v*R13_1*R13_2;

R23_1=euler2DCM([(90/180)*pi 0 0]);
R23_2=euler2DCM([0 (-45/180)*pi 0 ]);
v23=v*R23_1*R23_2;

Creating cylinder data

% Creating input structure
inputStruct.cylRadius=s;
inputStruct.numRadial=250;
inputStruct.cylHeight=2*sqrt(2)*s;
inputStruct.numHeight=10;
inputStruct.meshType='quad';
[F,V,C]=patchcylinder(inputStruct);
Q=euler2DCM([0 pi/2 0]);
V=V*Q;

R1=euler2DCM([0 asin(1/sqrt(3)) 0]);
R2=euler2DCM([0 0 -(45/180)*pi]);
V=V*R1*R2;

[x1,y1]=meshgrid(-f*s:1:f*s);
z1=zeros(size(x1));

[x2,z2]=meshgrid(-f*s:1:f*s);
y2=zeros(size(x2));

[y3,z3]=meshgrid(-f*s:1:f*s);
x3=zeros(size(y3));

%Visualize
hf=cFigure; hold on;

h4=gpatch(F,V,'rw','none',0.5);
surf(x1,y1,z1,'EdgeColor','k','faceColor',1*ones(1,3),'EdgeAlpha',0.5,'FaceAlpha',0.1,'LineWidth',lineWidth1);
surf(x2,y2,z2,'EdgeColor','k','faceColor',1*ones(1,3),'EdgeAlpha',0.5,'FaceAlpha',0.1,'LineWidth',lineWidth1);
surf(x3,y3,z3,'EdgeColor','k','faceColor',1*ones(1,3),'EdgeAlpha',0.5,'FaceAlpha',0.1,'LineWidth',lineWidth1);

h1=quiverVec([0 0 0],[1 0 0],f*s,colorSet(1,:));
h2=quiverVec([0 0 0],[0 1 0],f*s,colorSet(2,:));
h3=quiverVec([0 0 0],[0 0 1],f*s,colorSet(3,:));

h5=plotV([-1 -1 -1; 1 1 1],'k--','LineWidth',lineWidth2); %Hydrostatic axis

h6=plotV(v12,'r-','LineWidth',lineWidth2);
h6.Color=(colorSet(1,:)+colorSet(2,:))/2;

h7=plotV(v13,'r-','LineWidth',lineWidth2);
h7.Color=(colorSet(1,:)+colorSet(3,:))/2;

h8=plotV(v23,'r-','LineWidth',lineWidth2);
h8.Color=(colorSet(2,:)+colorSet(3,:))/2;

hAxis=gca;
hAxis.XRuler.FirstCrossoverValue  = 0; % X crossover with Y axis
hAxis.YRuler.FirstCrossoverValue  = 0; % Y crossover with X axis
hAxis.ZRuler.FirstCrossoverValue  = 0; % Z crossover with X axis
hAxis.XRuler.SecondCrossoverValue = 0; % X crossover with Z axis
hAxis.YRuler.SecondCrossoverValue = 0; % Y crossover with Z axis
hAxis.ZRuler.SecondCrossoverValue = 0; % Z crossover with Y axis

text(0.5+f*s,0,0,'$\sigma_1$','Interpreter','Latex','FontSize',fontSizeText);
text(0,0.5+f*s,0,'$\sigma_2$','Interpreter','Latex','FontSize',fontSizeText);
text(0,0,0.5+f*s,'$\sigma_3$','Interpreter','Latex','FontSize',fontSizeText);

xticks(-f*s:1:f*s);
yticks(-f*s:1:f*s);
zticks(-f*s:1:f*s);

legend([h1 h2 h3 h4 h5 h6 h7 h8],{'$\sigma_1$ axis','$\sigma_2$ axis','$\sigma_3$ axis',...
                           'Von Mises yield surface',...
                           'Hydrostatic line',...
                           'yield ellipse $\sigma_3=0$','yield ellipse $\sigma_2=0$','yield ellipse $\sigma_1=0$'...
                           },'Interpreter','Latex');

axis tight; axis equal; axis vis3d; view(3); %box on;
camlight headlight;
axis(f*s*[-1 1 -1 1 -1 1])
set(gca,'FontSize',fontSizeAxis,'LineWidth',lineWidthAxis);
gdrawnow;

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.

Copyright (C) 2006-2022 Kevin Mattheus Moerman and the GIBBON contributors

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Published with MATLAB® R2022a