fourthOrderMat
Below is a demonstration of the features of the fourthOrderMat function
Contents
clear; close all; clc;
Syntax
[CM]=fourthOrderMat(C);
Description
Converts a 3x3x3x3 4th order tensor to a 9x9 matrix
Examples
Creating the stiffness tensor for Hooke's law of linear elasticity
%Constructing 4th order base tensor set I=eye(3,3); %The 2nd order identity tensor II1=dyadicProduct(I,I,1); %4th order base tensor 1 II3=dyadicProduct(I,I,3); %4th order base tensor 3 %Parameters for Hooke's law mu=1; %The shear modulus lambda=5; %The lambda lame parameter C=lambda.*II1+2.*mu.*II3; %Construct 4th order stiffness tensor
[CM]=fourthOrderMat(C)
CM =
7 0 0 0 1 0 0 0 1
0 5 0 1 0 0 0 0 0
0 0 5 0 0 0 1 0 0
0 1 0 5 0 0 0 0 0
1 0 0 0 7 0 0 0 1
0 0 0 0 0 5 0 1 0
0 0 1 0 0 0 5 0 0
0 0 0 0 0 1 0 5 0
1 0 0 0 1 0 0 0 7
GIBBON www.gibboncode.org
Kevin Mattheus Moerman, [email protected]
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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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