# 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.

## 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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