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)