%% Function name
%       moduli_halphin

%% Revised
%       30 January 2014

%% Authors
%       Michael Cohen, Trey Moore, & Autar Kaw
%       Section: All
%       Semester: Fall 2013

%% Purpose
%       Given the elastic modulii, Poisson's ratios, of a fiber and matrix,
%       as well as the fiber volume fraction, output the elastic modulii
%       and Poisson's ratios of the lamina using the Halphin and Tsai
%       method

%% Usage 
%       function [moduli] = moduli_halphin(Ef,Em,nuf,numm,Vf,xi)
% Input Variables
%       Ef=fiber elastic modulus
%       Em=matrix elastic modulus
%       nuf=fiber Poisson's ratio
%       numm=matrix Poisson's ratio
%       Vf=fiber volume fraction
%       xi=Halphin Tsai reinforcing factor
% Output Variables 
%       moduli=vector of elastic modulii and Poisson's ratio of unidirectional lamina
%       [E1 E2 nu12 G12]
% Keyword
%       elastc modulii
%       Poisson's ratio
%       Halphin and Tsai method

%% License Agreement
%       http://www.eng.usf.edu/~kaw/OCW/composites/license/limiteduse.pdf
%% Testing code
clc
clear all
%% Inputs
% Mateial: Glass/Epoxy
% Lamina: square array with circular fiber cross-sections
Ef=85E9;
Em=3.4E9;
nuf=0.2;
numm=0.3;
xi=[2 1];
fprintf('\nFiber Elastic Modulus: %g',Ef)
fprintf('\nMatrix Elastic Modulus: %g',Em)
fprintf('\nFiber Poisson''s ratio: %g',nuf)
fprintf('\nMatrix Poisson''s ratio: %g',numm)
fprintf('\nHalphin Tsai reinforcing factor for elastic moduli: %g',xi(1))
fprintf('\nHalphin Tsai reinforcing factor for shear moduli: %g',xi(2))
%% Test 1 
% Testing for a particular Vf
% Input desired Vf
Vf=0.6;
% Call function: moduli_halphin
[moduli] = moduli_halphin(Ef,Em,nuf,numm,Vf,xi);
% Results for a particular Vf
fprintf('\n\nFiber Volume Fraction: %G\n\n',Vf)
disp('Lamina Modulii and Poisson''s Ratios')
disp('____________________________________________')
fprintf('\n Ex    | %G\n Ey    | %G\n nuxy  | %G\n Gxy   | %G\n\n\n\n',...
    moduli(1),moduli(2),moduli(3),moduli(4))
%% Test 2
% Table of elastic modulii and Poisson's ratios of a Unidirectional Lamina
% as a Function of Fiber Volume Fraction
for i=1:1:11
    Vf(i)=i/10-0.1;
    [moduli] = moduli_halphin(Ef,Em,nuf,numm,Vf(i),xi);
    Ex(i)=moduli(1);
    Ey(i)=moduli(2);
    nuxy(i)=moduli(3);
    Gxy(i)=moduli(4);
end
% Table of results
disp('                  Lamina Modulii and Poisson''s Ratios')
disp('___________________________________________________________________________________')
disp('    Vf     |        Ex         |        Ey         |      nuxy     |        Gxy ')
for i=1:1:11
fprintf('   %3.2f    |     %3.4E    |     %3.4E    |     %3.4f    |     %3.4E\n',...
    Vf(i),Ex(i),Ey(i),nuxy(i),Gxy(i))
end
%% Test 3
% Graph of elastic modulii and Poisson's ratios of a Unidirectional Lamina
% as a Function of Fiber Volume Fraction
for i=1:1:101
    Vf(i)=i/10-0.1;
    [moduli] = moduli_halphin(Ef,Em,nuf,numm,Vf(i),xi);
    Ex(i)=moduli(1);
    Ey(i)=moduli(2);
    nuxy(i)=moduli(3);
    Gxy(i)=moduli(4);
end
% Plot of elastic modulus
figure
hold on
plot(Vf,Ex,'b','LineWidth',2)
plot(Vf,Ey,'r','LineWidth',2)
grid
legend('Longitudinal Elastic Modulus','Transverse Elastic Modulus')
title('Elastic Modulus vs. Fiber Volume Fraction')
xlabel('Fiber Volume Fraction')
ylabel('Elastic Modulus')
hold off
% Plot of Poisson's ratio
figure
hold on
plot(Vf,nuxy,'b','LineWidth',2)
grid
legend('Poisson''s Ratio')
title('Poisson''s Ratio vs. Fiber Volume Fraction')
xlabel('Fiber Volume Fraction')
ylabel('Poisson''s Ratio')
hold off
% Plot of shear modulus
figure
hold on
plot(Vf,Gxy,'b','LineWidth',2)
grid
legend('Shear Modulus')
title('Shear Modulus vs. Fiber Volume Fraction')
xlabel('Fiber Volume Fraction')
ylabel('Shear Modulus')
hold off