defMetrics

Below is a demonstration of the features of the defMetrics function

Contents

clear; close all; clc;

Syntax

[D_out]=defMetrics(F_cell,strain_type);

Description

Computes various deformation metrics using the input cell array F_cell which contains deformation gradient tensors.

Examples

F_uni = [1.5 0.0 0.0;...
         0.0 1.0 0.0;...
         0.0 0.0 1.0];

F_shear=[1.0 0.5 0.0;...
         0.0 1.0 0.0;...
         0.0 0.0 1.0];

F_hydro=[1.5 0.0 0.0;...
         0.0 1.0 0.0;...
         0.0 0.0 1.0];

F_rand=1+0.25*(rand(3,3)-0.5);

F_cell={F_uni,F_shear,F_hydro,F_rand};

% 1 = Biot (linear) strain tensor
% 2 = Hencky (logarithmic/natural) strain tensor
% 3 = Green-Lagrange strain tensor
strain_type=2;
[D_out]=defMetrics(F_cell,strain_type);

D_out
D_out = 

  struct with fields:

        F: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
        C: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
       Cp: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
        U: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
        E: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
        Q: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
     Qeig: {[3×3 double]  [3×3 double]  [3×3 double]  [3×3 double]}
    Emaxp: [0.4055 0.2475 0.4055 1.0991]
    Emidp: [0 0 0 -2.0953]
    Eminp: [0 -0.2475 0 -3.8301]
    Lmaxp: [1.5000 1.2808 1.5000 3.0015]
    Lmidp: [1 1 1 0.1230]
    Lminp: [1 0.7808 1 0.0217]
     Eoct: [0.1911 0.2021 0.1911 2.0416]
      Exx: [0.4055 -0.0600 0.4055 -1.2228]
      Exy: [0 0.2401 0 1.6179]
      Exz: [0 0 0 0.7245]
      Eyx: [0 0.2401 0 1.6179]
      Eyy: [0 0.0600 0 -2.0641]
      Eyz: [0 0 0 1.7114]
      Ezx: [0 0 0 0.7245]
      Ezy: [0 0 0 1.7114]
      Ezz: [0 0 0 -1.5394]

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

GIBBON footer text

License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2006-2023 Kevin Mattheus Moerman and the GIBBON contributors

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.