scikit-elasticity

A library for working with anisotropic elasticity in Python

Features

All functionality is implemented in "vectorized" form, i.e. multidimensional arrays are handled without explicit loops in Python. Hence, despited being a pure Python library (if the dependency on NumPy and SciPy is ignored), it is suitable for large scale calculations.

Homogenization

Calculation of effective stiffness

Conversions

Represent 2nd and 4th order tensors in compressed Voigt or Mandel notation. Including support for rotations, which is based on the Python implementation of the conventions by Rowenhorst et al.

Stiffness or Compliance Matrices

Initialize stiffness or compliance matrices for different crystal systems.

Installation

Development

From the base directory run export PYTHONPATH=:$PWD/skel:$PYTHONPATH.

To get the correct version, also run versioningit -w from the root directory of the package. This requires to have versioningit installed.

From source

python -m pip install .

Usage

import skel
import damask
import numpy as np

N = 100000
C_Fe = skel.Hooke.C('cubic',C_11=232.2e9,C_12=136.4e9,C_44=117.0e9)
C_Al = skel.Hooke.C('cubic',C_11=106.9e9,C_12=60.5e9,C_44=28.4e9)
C_Cu = skel.Hooke.C('cubic',C_11=168.9e9,C_12=121.8e9,C_44=75.8e9)
C_Mg = skel.Hooke.C('hexagonal',C_11=59.5e9,C_12=25.6e9,C_44=16.5e9,C_33=61.7e9,C_13=21.5e9)
O = damask.Rotation.from_random(N,rng_seed=20191102)
for label,C in zip(['Fe','Al','Cu','Mg'],[C_Fe,C_Al,C_Cu,C_Mg]):
    print(f'== {label} ==')
    ve = skel.VolumeElement(C,O)
    with np.printoptions(precision=2,suppress=True):
        print('Reuss\n',ve.C_Reuss/1e9)
        print('Voigt\n',ve.C_Voigt/1e9)
        print('Hill\n',ve.C_Hill/1e9)
        print('Self-consistent\n',ve.C_sc/1e9)

# https://www.sciencedirect.com/science/article/abs/pii/0956715195901698 (fig 6)
# https://doi.org/10.1080/02670836.2016.1231746
def texture_Ni(N_grains,rng):
    Eulers = [[[59,37,63],.30], # S
              [[90,35,45],.20], # Cu
              [[35,45,90],.15]] # Brass
    directions = [[[np.pi/4.,0.],[0.,0.],.10]]
    O = damask.Rotation.from_random(N_grains \
                                    - sum(int(N_grains*_[1]) for _ in Eulers)\
                                    - sum(int(N_grains*_[2]) for _ in directions),rng_seed=rng)
    for eu,v in Eulers:
        p = damask.Orientation.from_Euler_angles(phi=eu,degrees=True,lattice='cI')
        O = O.append(damask.Rotation.from_spherical_component(p,50,int(N_grains*v),degrees=True,rng_seed=rng))
    for c,s,v in directions:
        O = O.append(damask.Rotation.from_fiber_component(c,s,np.deg2rad(20),shape=int(N_grains*v),rng_seed=rng))
    return O

C_Ni = skel.Hooke.C('cubic',C_11=251.0e+9,C_12=150.0e+9,C_44=123.7e+9)
ve = skel.VolumeElement(C_Ni,texture_Ni(2000,2))
C = skel.Voigt.to_3x3x3x3_compliance(np.linalg.inv(ve.C_sc))
print('E_x',skel.Hooke.E(C,[1,0,0])/1e9)
print('E_y',skel.Hooke.E(C,[0,1,0])/1e9)
print('E_z',skel.Hooke.E(C,[0,0,1])/1e9)

Contact

Martin Diehl
KU Leuven
[email protected]