# 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.

## 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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