MVT_strain_invariants.m

% MVT_strain_invariants - calculate inveriants of square symmetric matrix
%
% Return I_E, II_E and III_E for a strain or strain rate tensor. I_E is the
% trace and gives the volume change, II_E is a measure of strain magnitude
% and III_E is the determinant. These do not change if the tensor is
% rotated.
%
% Usage:
%     [I_E, II_E, III_E] = MVT_strain_invariants(E)
%         E must be a 3*3 symmetric real matrix.
%
% See also: MVT_decompose_Lijs

% Copyright (c) 2013, Andrew Walker
% All rights reserved.
% 
% Redistribution and use in source and binary forms, 
% with or without modification, are permitted provided 
% that the following conditions are met:
% 
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%      above copyright notice, this list of conditions 
%      and the following disclaimer.
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%    * Neither the name of the University of Bristol nor the names 
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% 
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function [I_E, II_E, III_E] = MVT_strain_invariants(E)

    s = size(E);
    assert((s(1) == 3), '1st dimension of strain(rate) matrix must be 3');
    assert((s(2) == 3), '2nd dimension of strain(rate) matrix must be 3');
    
    if length(s) == 2
        % This is a scalar calculation (one input matrix)
        [I_E, II_E, III_E] = scalar_strain_invariants(E);
    elseif length(s) == 3
        I_E = zeros(1,s(3));
        II_E = zeros(1,s(3));
        III_E = zeros(1,s(3));
        for i = 1:s(3)
            [I_E(i), II_E(i), III_E(i)] = ...
                scalar_strain_invariants(E(:,:,i));
        end
    else
        error('Argument must be 3x3xn or 3x3');
    end    
end

function [I_E, II_E, III_E] = scalar_strain_invariants(E)
        I_E = trace(E);
        II_E = 0.5*(trace(E)^2-trace(E^2));
        II_E = trace(E*E');
        III_E = det(E);
end