# dyadicProduct

Below is a demonstration of the features of the `dyadicProduct` function

## Contents

```
clear; close all; clc;
```

## Syntax

`C=dyadicProduct(A,B,r);`

## Description

Computes dyadic products of two second order tensors yielding a fourth-order tensor. See Curnier et al. 1994 and Ateshian et al. 2009

## Examples

## Example 1: Constructing fourth-order stiffness tensors

Creating the stiffness tensor for Hooke's law of linear elasticity

%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 %Parameters for Hooke's law mu=1; %The shear modulus lambda=5; %The lambda lame parameter %Construct 4th order stiffness tensor C=lambda.*II1+2.*mu.*II3

C(:,:,1,1) = 7 0 0 0 5 0 0 0 5 C(:,:,2,1) = 0 1 0 1 0 0 0 0 0 C(:,:,3,1) = 0 0 1 0 0 0 1 0 0 C(:,:,1,2) = 0 1 0 1 0 0 0 0 0 C(:,:,2,2) = 5 0 0 0 7 0 0 0 5 C(:,:,3,2) = 0 0 0 0 0 1 0 1 0 C(:,:,1,3) = 0 0 1 0 0 0 1 0 0 C(:,:,2,3) = 0 0 0 0 0 1 0 1 0 C(:,:,3,3) = 5 0 0 0 5 0 0 0 7

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*Kevin Mattheus Moerman*, [email protected]

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