%% 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

%% Code
function[beta12]=beta_micro(Ef,Em,nuf,numm,betam,Vf)
% Finding Longitudinal Elastic Modulus in Local Direction
E1=Ef*Vf+Em*(1-Vf);
% Finding Major Poisson's Ratio in Local Direction
nu12=nuf*Vf+numm*(1-Vf);
% Finding Coefficient of Moisture Expansions in Local Longitudinal and Local
% Transverse Directions
beta1=(betam*(1-Vf)*Em)/((Ef*Vf)+(Em*(1-Vf)));
beta2=((1+numm)*(beta1/betam)*(E1/Em)*(betam))-(beta1*nu12);
% Results in vector form
[beta12]=[beta1;beta2;0];
end