voigtMap

Below is a demonstration of the features of the voigtMap function

Contents

clear; close all; clc;

Syntax

cVoigt=voigtMap(c);

Description

This function converts the fourth order tensor c (a 3x3x3x3 array) into a 6x6 Voigt mapped array.

Examples

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;

Derive Voigt mapped tensor

Cv=voigtMap(C)

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

Using symbolic variables

try

    %Lame parameters for Hooke's law
    syms mu lambda; %Create symbolic parameters

    %Construct 4th order stiffness tensor
    C=lambda.*II1+2.*mu.*II3;

Derive Voigt mapped tensor

    Cv=voigtMap(C)

 
Cv =
 
[lambda + 2*mu,        lambda,        lambda,  0,  0,  0]
[       lambda, lambda + 2*mu,        lambda,  0,  0,  0]
[       lambda,        lambda, lambda + 2*mu,  0,  0,  0]
[            0,             0,             0, mu,  0,  0]
[            0,             0,             0,  0, mu,  0]
[            0,             0,             0,  0,  0, mu]
 

end

s=rand(3,3);
S=s*s'

Sv=voigtMap(S)

S =

    0.6545    0.2841    0.3007
    0.2841    0.4401    0.2010
    0.3007    0.2010    0.7841


Sv =

    0.6545
    0.4401
    0.7841
    0.4020
    0.6014
    0.5681

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

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Published with MATLAB® R2023a