# 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]

**GIBBON footer text**

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

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.