kelvinUnMap
Below is a demonstration of the features of the kelvinUnMap function
Contents
clear; close all; clc;
Syntax
[C]=kelvinUnMap(cKelvin);
Description
This function transforms the Kelvin mapped tensor cKelvin to the normal tensorial representation C.
Examples
Example 1: Mapping a Kelvin mapped tensor to the normal tensorial representation
%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 %Lame parameters for Hooke's law mu=2; %The shear modulus lambda=3; %The lambda lame parameter %Construct 4th order stiffness tensor C=lambda.*II1+2.*mu.*II3;
Derive Kelvin mapped tensor
Ck=kelvinMap(C) Cr=kelvinUnMap(Ck)
Ck =
7.0000 3.0000 3.0000 0 0 0
3.0000 7.0000 3.0000 0 0 0
3.0000 3.0000 7.0000 0 0 0
0 0 0 4.0000 0 0
0 0 0 0 4.0000 0
0 0 0 0 0 4.0000
Cr(:,:,1,1) =
7 0 0
0 3 0
0 0 3
Cr(:,:,2,1) =
0 2 0
2 0 0
0 0 0
Cr(:,:,3,1) =
0 0 2
0 0 0
2 0 0
Cr(:,:,1,2) =
0 2 0
2 0 0
0 0 0
Cr(:,:,2,2) =
3 0 0
0 7 0
0 0 3
Cr(:,:,3,2) =
0 0 0
0 0 2
0 2 0
Cr(:,:,1,3) =
0 0 2
0 0 0
2 0 0
Cr(:,:,2,3) =
0 0 0
0 0 2
0 2 0
Cr(:,:,3,3) =
3 0 0
0 3 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.
Copyright (C) 2006-2023 Kevin Mattheus Moerman and the GIBBON contributors
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