# 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]

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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

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