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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Published with MATLAB® R2023a