apple

tutorial_example.py
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			#!/usr/bin/env python3

			import numpy as np
			import muSpectre as msp
			import matplotlib.pyplot as plt


			## currently, muSpectre is restricted to odd-numbered resolutions for
			## reasons explained in T.W.J. de Geus, J. Vondřejc, J. Zeman,
			## R.H.J. Peerlings, M.G.D. Geers, Finite strain FFT-based non-linear
			## solvers made simple, Computer Methods in Applied Mechanics and
			## Engineering, Volume 318, 2017
			## https://doi.org/10.1016/j.cma.2016.12.032
			resolution = [51, 51]
			center = np.array([r//2 for r in resolution])
			incl = resolution[0]//5


			## Domain dimensions
			lengths = [7., 5.]
			## formulation (small_strain or finite_strain)
			formulation = msp.Formulation.small_strain

			## build a computational domain
			rve = msp.SystemFactory(resolution,
			lengths,
			formulation)

			## define the material properties of the matrix and inclusion
			hard = msp.material.MaterialLinearElastic1_2d.make(
			rve, "hard", 10e9, .33)
			soft = msp.material.MaterialLinearElastic1_2d.make(
			rve, "soft", 70e9, .33)

			## assign each pixel to exactly one material
			for i, pixel in enumerate(rve):
			if np.linalg.norm(center - np.array(pixel),2)<incl:
			hard.add_pixel(pixel)
			else:
			soft.add_pixel(pixel)

			## define the convergence tolerance for the Newton-Raphson increment
			tol = 1e-5
			## tolerance for the solver of the linear system
			cg_tol = 1e-8


			## Macroscopic strain
			Del0 = np.array([[.0, .0],
			[0, .03]])
			Del0 = .5*(Del0 + Del0.T)


			maxiter = 50 ## for linear system solver

			## Choose a solver for the linear systems. Currently avaliable:
			## SolverCG, SolverCGEigen, SolverBiCGSTABEigen, SolverGMRESEigen,
			## SolverDGMRESEigen, SolverMINRESEigen.
			## See Reference for explanations
			solver = msp.solvers.SolverCGEigen(rve, cg_tol, maxiter, verbose=True)


			## Verbosity levels:
			## 0: silent,
			## 1: info about Newton-Raphson loop,
			verbose = 1

			## Choose a solution strategy. Currently available:
			## de_geus: is discribed in de Geus et al. see Ref above
			## newton_cg: classical Newton-Conjugate Gradient solver. Recommended
			result = msp.solvers.newton_cg(rve, Del0, solver, tol, verbose)

			print(result)

			## visualise e.g., stress in y-direction
			stress = result.stress
			## stress is stored in a flatten stress tensor per pixel, i.e., a
			## dim^2 × prod(resolution_i) array, so it needs to be reshaped
			stress = stress.T.reshape(*resolution, 2, 2)

			plt.pcolormesh(stress[:, :, 1, 1])
			plt.colorbar()
			plt.show()

muSpectre/bin/tutorial_example.py5d59f1e9dcfafeat/apple

tutorial_example.pyView Options

muSpectre/bin/tutorial_example.py
5d59f1e9dcfafeat/apple

tutorial_example.py
View Options