ivoigtMap

Below is a demonstration of the features of the ivoigtMap function

Contents

clear; close all; clc;

Syntax

c=ivoigtMap(cVoigt);

Description

This function reverses Voigt mapped tensors from their Voigt array for back to their tensorial form.

Examples

Example 1: The Voigt mapping of the elasticity tensor for Hooke's law with Lame parameters

%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;

Cv=voigtMap(C) % Voigt map version

Cr=ivoigtMap(Cv)

Cv =

     7     3     3     0     0     0
     3     7     3     0     0     0
     3     3     7     0     0     0
     0     0     0     2     0     0
     0     0     0     0     2     0
     0     0     0     0     0     2


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

s=rand(3,3);
S=s*s'

Sv=voigtMap(S)

Sr=ivoigtMap(Sv)

S =

    1.0700    0.8442    0.8164
    0.8442    0.9254    0.6173
    0.8164    0.6173    1.0834


Sv =

    1.0700
    0.9254
    1.0834
    1.2346
    1.6329
    1.6884


Sr =

    1.0700    0.8442    0.8164
    0.8442    0.9254    0.6173
    0.8164    0.6173    1.0834

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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Published with MATLAB® R2023a