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

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/.