# ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by **Romain Gaillac** and **François-Xavier Coudert** at CNRS / Chimie
ParisTech.

If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (*J. Phys. Condens. Matter*, 2016, 28, 275201) and give the
website URL.

ELATE is open source software. Any queries or comments are welcome at

## Summary of the properties

### Input: stiffness matrix (coefficients in GPa) of H2C (Materials Project id mp-985782)

4 3 2 0 0 0 3 4 1 0 0 0 2 1 275 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2

### Average properties

Averaging scheme | Bulk modulus | Young's modulus | Shear modulus | Poisson's ratio |
---|---|---|---|---|

Voigt | K_{V} = 32.778 GPa | E_{V} = 48.33 GPa | G_{V} = 19.267 GPa | ν_{V} = 0.25425 |

Reuss | K_{R} = 3.4855 GPa | E_{R} = 2.9503 GPa | G_{R} = 1.0855 GPa | ν_{R} = 0.35892 |

Hill | K_{H} = 18.132 GPa | E_{H} = 25.717 GPa | G_{H} = 10.176 GPa | ν_{H} = 0.26361 |

### Eigenvalues of the stiffness matrix

λ_{1} |
λ_{2} |
λ_{3} |
λ_{4} |
λ_{5} |
λ_{6} |
---|---|---|---|---|---|

0.99817 GPa | 1 GPa | 1 GPa | 2 GPa | 6.9832 GPa | 275.02 GPa |

### Variations of the elastic moduli

Young's modulus | Linear compressibility | Shear modulus | Poisson's ratio | ||||||
---|---|---|---|---|---|---|---|---|---|

E_{min} | E_{max} |
β_{min} | β_{max} | G_{min} | G_{max} |
ν_{min} | ν_{max} | ||

Value | 1.7443 GPa | 273.86 GPa | 2.0866 TPa^{–1} | 143.45 TPa^{–1} | 0.49909 GPa | 4.9554 GPa | -0.28571 | 0.76654 | Value |

Anisotropy | 157 | 68.7500 | 9.929 | ∞ | Anisotropy | ||||

Axis | 1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
0.7071 0.7071 -0.0000 |
0.4985 0.5015 0.7071 |
0.0000 -0.0000 1.0000 |
-0.2260 0.2257 0.9476 |
Axis |

-0.7071 0.7071 0.0001 |
0.4985 0.5015 -0.7071 |
-0.0000 -1.0000 -0.0000 |
-0.6857 0.6541 -0.3193 |
Second axis |

## Spatial dependence of Young's modulus

Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

## Spatial dependence of linear compressibility

linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

## Spatial dependence of shear modulus

Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

## Spatial dependence of Poisson's ratio

Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane