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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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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