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jameskermode committed Jul 5, 2023
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47 changes: 47 additions & 0 deletions docs/applications/elastic_constants.ipynb
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"# Elastic Constants\n",
"\n",
"Solids respond to small external loads through a reversible elastic response. The strength of the response is characterized by the elastic moduli. {py:mod}`matscipy.elasticity` implements functions for computing elastic moduli from small deformation of atomistic systems that consider potential symmetries of the underlying atomic system, in particular for crystals. {py:mod}`matscipy.elasticity` also implements analytic calculation of elastic moduli for some interatomic potentials, described in more detail below. The computation of elastic moduli is a basic prerequisite for multi-scale modelling of materials, as they are the most basic parameters of continuum material models.\n",
"\n",
"In this tutorial, we will go over different ways that `matscipy` can compute elastic constants of an atomic configuration.\n",
"\n",
"## Problem setup"
]
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4 changes: 0 additions & 4 deletions docs/applications/elastic_constants.rst

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2 changes: 1 addition & 1 deletion docs/applications/index.rst
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Expand Up @@ -7,4 +7,4 @@ Application domains

elastic_constants
plasticity
fracture_mechanics
fracture_mechanics
12 changes: 6 additions & 6 deletions docs/calculators/manybody.ipynb
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"\n",
"`matscipy` implements support for generic manybody potentials. The class `matscipy.calculators.manybody.Manybody` implements the functional form\n",
"\n",
"$$\n",
"```{math}\n",
" U\n",
" =\n",
" \\frac{1}{2}\n",
" \\sum_{\\substack{ij\\\\ i\\neq j}}\n",
" U_2(r^2_{ij}) + U_\\text{m}(r^2_{ij}, \\xi_{ij})\n",
"$$\n",
"```\n",
"\n",
"with\n",
"\n",
"$$\n",
"```{math}\n",
" \\xi_{ij} \n",
" = \n",
" \\sum_{\\substack{k\\\\ k\\neq i,j}} \n",
" \\Xi(r^2_{ij}, r^2_{ik}, r^2_{jk})\n",
"$$\n",
"```\n",
"\n",
"as described, e.g. by [Müser et al.](https://doi.org/10.1080/23746149.2022.2093129) and [Grießer et al.](https://doi.org/10.48550/arXiv.2302.08754). On top of energies and forces, the calculator can compute second derivatives (with respect to positions and strain degrees of freedom). Explicit functional forms of $U_2$, $U_\\text{m}$ and $\\Xi$ are implemented for a number of potential."
"as described, e.g. by [Müser et al.](https://doi.org/10.1080/23746149.2022.2093129) and [Grießer et al.](https://doi.org/10.48550/arXiv.2302.08754). On top of energies and forces, the calculator can compute second derivatives (with respect to positions and strain degrees of freedom). Explicit functional forms of {math}`U_2`, {math}`U_\\text{m}` and {math}`\\Xi` are implemented for a number of potential."
]
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{
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"source": [
"## Kumagai potential\n",
"\n",
"The following example compute the elastic constants of a small representation of amorphous silicon using the potential by [Kumagai et al.](https://doi.org/10.1016/j.commatsci.2006.07.013)."
"The following example computes the elastic constants of a small representation of amorphous silicon using the potential by [Kumagai et al.](https://doi.org/10.1016/j.commatsci.2006.07.013)."
]
},
{
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1 change: 1 addition & 0 deletions docs/conf.py
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'sphinx.ext.autodoc',
'sphinx.ext.napoleon',
'sphinx.ext.autosummary',
'sphinx.ext.mathjax',
'myst_nb'
]

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