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visualisation_example.py
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#!/usr/bin/env python3
# -*- coding:utf-8 -*-
"""
@file visualisation_example.py
@author Richard Leute <richard.leute@imtek.uni-freiburg.de>
@date 14 Jan 2019
@brief small example of how one can use the visualisation tools:
gradient_integration() and vtk_export()
@section LICENSE
Copyright © 2019 Till Junge, Richard Leute
µSpectre is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation, either version 3, or (at
your option) any later version.
µSpectre is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with µSpectre; see the file COPYING. If not, write to the
Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
Additional permission under GNU GPL version 3 section 7
If you modify this Program, or any covered work, by linking or combining it
with proprietary FFT implementations or numerical libraries, containing parts
covered by the terms of those libraries' licenses, the licensors of this
Program grant you additional permission to convey the resulting work.
"""
import numpy as np
import sys
import os
sys.path.append("language_bindings/python/")
import muSpectre as µ
import muSpectre.gradient_integration as gi
import muSpectre.vtk_export as vt_ex
### Input parameters ###
#----------------------#
#general
resolutions = [71, 71, 3]
lengths = [1.0, 1.0, 0.2]
Nx, Ny, Nz = resolutions
formulation = µ.Formulation.finite_strain
Young = [10, 20] #Youngs modulus for each phase
Poisson = [0.3, 0.4] #Poissons ratio for each phase
#solver
newton_tol = 1e-6 #tolerance for newton algo
cg_tol = 1e-6 #tolerance for cg algo
equil_tol = 1e-6 #tolerance for equilibrium
maxiter = 100
verbose = 0
# sinusoidal bump
d = 10 #thickness of the phase with higher elasticity in pixles
l = Nx//3 #length of bump
h = Ny//4 #height of bump
low_y = (Ny-d)//2 #lower y-boundary of phase
high_y = low_y+d #upper y-boundary of phase
left_x = (Nx-l)//2 #boundaries in x direction left
right_x = left_x + l #boundaries in x direction right
x = np.arange(l)
p_y = h*np.sin(np.pi/(l-1)*x) #bump function
xy_bump = np.ones((l,h,Nz)) #grid representing bumpx
for i, threshold in enumerate(np.round(p_y)):
xy_bump[i,int(threshold):,:] = 0
phase = np.zeros(resolutions, dtype=int) #0 for surrounding matrix
phase[:, low_y:high_y, :] = 1
phase[left_x:right_x, high_y:high_y+h, :] = xy_bump
### Run muSpectre ###
#-------------------#
cell = µ.Cell(resolutions,
lengths,
formulation)
mat = µ.material.MaterialLinearElastic4_3d.make(cell, "material")
for i, pixel in enumerate(cell):
#add Young and Poisson depending on the material index
m_i = phase.flatten()[i] #m_i = material index / phase index
mat.add_pixel(pixel, Young[m_i], Poisson[m_i])
cell.initialise() #initialization of fft to make faster fft
DelF = np.array([[0 , 0.7, 0],
[0 , 0 , 0],
[0 , 0 , 0]])
solver_newton = µ.solvers.SolverCG(cell, cg_tol, maxiter, verbose)
result = µ.solvers.newton_cg(cell, DelF, solver_newton,
newton_tol, equil_tol, verbose)
# print solver results
print('\n\nstatus messages of OptimizeResults:')
print('-----------------------------------')
print('success: ', result.success)
print('status: ', result.status)
print('message: ', result.message)
print('# iterations: ', result.nb_it)
print('# cell evaluations: ', result.nb_fev)
print('formulation: ', result.formulation)
### Visualisation ###
#-------------------#
#integration of the deformation gradient field
placement_n, x = gi.compute_placement(result, lengths, resolutions, order = 0)
### some fields which can be added to the visualisation
#2-tensor field containing the first Piola Kirchhoff stress
PK1 = gi.reshape_gradient(result.stress, resolutions)
#scalar field containing the distance to the origin O
distance_O = np.linalg.norm(placement_n, axis=-1)
#random fields
center_shape = tuple(np.array(x.shape[:-1])-1)#shape of the center point grid
dim = len(resolutions)
scalar_c = np.random.random(center_shape)
vector_c = np.random.random(center_shape + (dim,))
tensor2_c = np.random.random(center_shape + (dim,dim))
scalar_n = np.random.random(x.shape[:-1])
vector_n = np.random.random(x.shape[:-1] + (dim,))
tensor2_n = np.random.random(x.shape[:-1] + (dim,dim))
#write dictionaries with cell data and point data
c_data = {"scalar field" : scalar_c,
"vector field" : vector_c,
"2-tensor field" : tensor2_c,
"PK1 stress" : PK1,
"phase" : phase}
p_data = {"scalar field" : scalar_n,
"vector field" : vector_n,
"2-tensor field" : tensor2_n,
"distance_O" : distance_O}
vt_ex.vtk_export(fpath = "visualisation_example",
x_n = x,
placement = placement_n,
point_data = p_data,
cell_data = c_data)
print("The file 'visualisation_example.vtr' was successfully written!\n"
"You can open it for example with paraview or some other software:\n"
"paraview visualisation_example.vtr")

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