Elaston

Elaston is a simple and lightweight module for linear elasticity calculations.

Installation

We will offer pip and conda at some point. For now, you can install the package by cloning the repository and running the following command in the root directory:

pip install .

Features

Calculation of elastic constants
Stress, strain and displacement field around dislocations using anisotropic elasticity
Stress, strain and displacement field around point defects

Usage

Examples I: Get bulk modulus from the elastic tensor:

from elaston import LinearElasticity

medium = LinearElasticity(C_11=211.0, C_12=130.0, C_44=82.0)  # Fe
medium_voigt = medium.get_voigt_average()
parameters = medium_voigt.get_elastic_moduli()
print(parameters['bulk_modulus'])

Example II: Get strain field around a point defect:

import numpy as np
medium = LinearElasticity(C_11=211.0, C_12=130.0, C_44=82.0)
random_positions = np.random.random((10, 3)) - 0.5
dipole_tensor = np.eye(3)
print(medium.get_point_defect_strain(random_positions, dipole_tensor))

Example III: Get stress field around a dislocation:

import numpy as np
medium = LinearElasticity(C_11=211.0, C_12=130.0, C_44=82.0)
random_positions = np.random.random((10, 3)) - 0.5
# Burgers vector of a screw dislocation in bcc Fe
burgers_vector = np.array([0, 0, 2.86 * np.sqrt(3) / 2])
print(medium.get_dislocation_stress(random_positions, burgers_vector))

Example IV: Estimate the distance between partial dislocations:

medium = LinearElasticity(C_11=110.5, C_12=64.8, C_44=30.9)  # Al
lattice_constant = 4.05
partial_one = np.array([-0.5, 0, np.sqrt(3) / 2]) * lattice_constant
partial_two = np.array([0.5, 0, np.sqrt(3) / 2]) * lattice_constant
distance = 100
stress_one = medium.get_dislocation_stress([0, distance, 0], partial_one)
print('Choose `distance` in the way that the value below corresponds to SFE')
medium.get_dislocation_force(stress_one, [0, 1, 0], partial_two)