%% Function name
%   beta_micro

%% Revised:
%   28 January 2014

%% Author
%   Kevin Reilly, Trey Moore, & Autar Kaw
%   Section: All
%   Semester: Fall 2013

%% Purpose
%       Given elastic modulii and Poisson's ratios for a fiber and matrix, 
%       coefficient of moisture expansion of a matrix, as well as a fiber 
%       volume ratio, output coefficient of moisture expansion in the local
%       directions for the specified unidirectional lamina.

%% Usage 
%       function [beta12] = beta_micro(Ef,Em,nuf,numm,betam,Vf)
% Input variables
%       Ef=fiber modulus
%       Em=matrix modulus
%       nuf=fiber Poisson's ratio
%       numm=matrix Poisson's ratio
%       betam= moisture expansion of matrix
%       Vf=fiber volume fraction
% Output variables 
%       beta12=vector of moisture expansion of unidirectional lamina
%       [beta12]=[beta1 beta2 beta12]
% Keywords
%       coefficient of moisture expansion

%% License Agreement
%       http://www.eng.usf.edu/~kaw/OCW/composites/license/limiteduse.pdf

%% Testing Code
clc
clear all
%% Inputs
% Material: Glass/Epoxy
Ef=230e+09;
Em=3.4e+09;
nuf=0.3;
numm=0.2;
betam=0.33;
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('\nMatrix Coefficient of Moisture Expansion: %g',betam)
%% Test 1 
% Testing for a particular Vf
% Input desired Vf
Vf=0.7;
% Call function: beta_micro
[beta12] = beta_micro(Ef,Em,nuf,numm,betam,Vf);
% Results for a particular Vf
fprintf('\n\nFiber Volume Fraction: %G\n\n',Vf)
disp('      Lamina Coefficient of Moisture Expansion')
disp('___________________________________________________')
fprintf('\n beta1  | %G\n beta2  | %G\n beta12 | %G\n\n\n\n',...
    beta12(1),beta12(2),beta12(3))
%% Test 2
% Table of Moisture Expansion Coefficients of a Unidirectional Lamina
% as a Function of Fiber Volume Fraction
for i=1:1:11
    Vf(i)=i/10-0.1;
    [beta12] = beta_micro(Ef,Em,nuf,numm,betam,Vf(i));
    beta1(i)=beta12(1);
    beta2(i)=beta12(2);
    beta_12(i)=beta12(3);
end
% Table of results
disp('          Lamina Coefficient of Moisture Expansion')
disp('______________________________________________________________')
disp('    Vf     |     beta1      |      beta2    |     beta12   ')
for i=1:1:11
fprintf('   %3.2f    |  %E  |   %E  |        %g\n',Vf(i),beta1(i),...
    beta2(i),beta_12(i))
end
%% Test 3
% Graph of Moisture Expansion Coefficients of a Unidirectional Lamina
% as a Function of Fiber Volume Fraction
for i=1:1:101
    Vf(i)=i/100-0.01;
    [beta12] = beta_micro(Ef,Em,nuf,numm,betam,Vf(i));
    beta1(i)=beta12(1);
    beta2(i)=beta12(2);
    beta_12(i)=beta12(3);
end
hold on
plot(Vf,beta1,'LineWidth',2)
plot(Vf,beta2,'r','LineWidth',2)
plot(Vf,beta_12,'m','LineWidth',2)
grid
legend('beta1','beta2','beta12')
title('Coefficient of Moisture Expansion vs. Fiber Volume Fraction')
xlabel('Fiber Volume Fraction')
ylabel('Coefficient of Moisture Expansion')
hold off