# Examples with tutorial¶

The online version of this tutorial contains embedded videos.

## Bouncing sphere¶

Following example is in file doc/sphinx/tutorial/01-bouncing-sphere.py.

# basic simulation showing sphere falling ball gravity,
# bouncing against another sphere representing the support

# DATA COMPONENTS

# add 2 particles to the simulation
# they the default material (utils.defaultMat)
O.bodies.append(
[
# fixed: particle's position in space will not change (support)
# this particles is free, subject to dynamics
sphere((0, 0, 2), .5)
]
)

# FUNCTIONAL COMPONENTS

# simulation loop -- see presentation for the explanation
O.engines = [
ForceResetter(),
InsertionSortCollider([Bo1_Sphere_Aabb()]),
InteractionLoop(
[Ig2_Sphere_Sphere_ScGeom()],  # collision geometry
[Ip2_FrictMat_FrictMat_FrictPhys()],  # collision "physics"
[Law2_ScGeom_FrictPhys_CundallStrack()]  # contact law -- apply forces
),
# Apply gravity force to particles. damping: numerical dissipation of energy.
NewtonIntegrator(gravity=(0, 0, -9.81), damping=0.1)
]

# set timestep to a fraction of the critical timestep
# the fraction is very small, so that the simulation is not too fast
# and the motion can be observed
O.dt = .5e-4 * PWaveTimeStep()

# save the simulation, so that it can be reloaded later, for experimentation
O.saveTmp()


## Gravity deposition¶

Following example is in file doc/sphinx/tutorial/02-gravity-deposition.py.

# gravity deposition in box, showing how to plot and save history of data,
# and how to control the simulation while it is running by calling
# python functions from within the simulation loop

# import yade modules that we will use below

# create rectangular box from facets
O.bodies.append(geom.facetBox((.5, .5, .5), (.5, .5, .5), wallMask=31))

# create empty sphere packing
# sphere packing is not equivalent to particles in simulation, it contains only the pure geometry
sp = pack.SpherePack()
# generate randomly spheres with uniform radius distribution
sp.makeCloud((0, 0, 0), (1, 1, 1), rMean=.05, rRelFuzz=.5)
# add the sphere pack to the simulation
sp.toSimulation()

O.engines = [
ForceResetter(),
InsertionSortCollider([Bo1_Sphere_Aabb(), Bo1_Facet_Aabb()]),
InteractionLoop(
# handle sphere+sphere and facet+sphere collisions
[Ig2_Sphere_Sphere_ScGeom(), Ig2_Facet_Sphere_ScGeom()],
[Ip2_FrictMat_FrictMat_FrictPhys()],
[Law2_ScGeom_FrictPhys_CundallStrack()]
),
NewtonIntegrator(gravity=(0, 0, -9.81), damping=0.4),
# call the checkUnbalanced function (defined below) every 2 seconds
PyRunner(command='checkUnbalanced()', realPeriod=2),
# call the addPlotData function every 200 steps
]
O.dt = .5 * PWaveTimeStep()

# enable energy tracking; any simulation parts supporting it
# can create and update arbitrary energy types, which can be
# accessed as O.energy['energyName'] subsequently
O.trackEnergy = True

# if the unbalanced forces goes below .05, the packing
# is considered stabilized, therefore we stop collected
# data history and stop
def checkUnbalanced():
if unbalancedForce() < .05:
O.pause()
plot.saveDataTxt('bbb.txt.bz2')
# plot.saveGnuplot('bbb') is also possible

# collect history of data which will be plotted
# each item is given a names, by which it can be the unsed in plot.plots
# the **O.energy converts dictionary-like O.energy to plot.addData arguments

# define how to plot data: 'i' (step number) on the x-axis, unbalanced force
# on the left y-axis, all energies on the right y-axis
# (O.energy.keys is function which will be called to get all defined energies)
# None separates left and right y-axis
plot.plots = {'i': ('unbalanced', None, O.energy.keys)}

# show the plot on the screen, and update while the simulation runs
plot.plot()

O.saveTmp()


## Oedometric test¶

Following example is in file doc/sphinx/tutorial/03-oedometric-test.py.

# gravity deposition, continuing with oedometric test after stabilization
# shows also how to run parametric studies with yade-batch

# The components of the batch are:
# 1. table with parameters, one set of parameters per line (ccc.table)
#
#

# load parameters from file if run in batch
# default values are used if not run from batch
# make rMean, rRelFuzz, maxLoad accessible directly as variables later

# create box with free top, and ceate loose packing inside the box
O.bodies.append(geom.facetBox((.5, .5, .5), (.5, .5, .5), wallMask=31))
sp = pack.SpherePack()
sp.makeCloud((0, 0, 0), (1, 1, 1), rMean=rMean, rRelFuzz=rRelFuzz)
sp.toSimulation()

O.engines = [
ForceResetter(),
# sphere, facet, wall
InsertionSortCollider([Bo1_Sphere_Aabb(), Bo1_Facet_Aabb(), Bo1_Wall_Aabb()]),
InteractionLoop(
# the loading plate is a wall, we need to handle sphere+sphere, sphere+facet, sphere+wall
[Ig2_Sphere_Sphere_ScGeom(), Ig2_Facet_Sphere_ScGeom(), Ig2_Wall_Sphere_ScGeom()],
[Ip2_FrictMat_FrictMat_FrictPhys()],
[Law2_ScGeom_FrictPhys_CundallStrack()]
),
NewtonIntegrator(gravity=(0, 0, -9.81), damping=0.5),
# the label creates an automatic variable referring to this engine
# we use it below to change its attributes from the functions called
PyRunner(command='checkUnbalanced()', realPeriod=2, label='checker'),
]
O.dt = .5 * PWaveTimeStep()

# (the last engine) one after another; this sequence defines progression of different stages of the
# simulation, as each of the functions, when the condition is satisfied, updates 'checker' to call
# the next function when it is run from within the simulation next time

# check whether the gravity deposition has already finished
# if so, add wall on the top of the packing and start the oedometric test
def checkUnbalanced():
# at the very start, unbalanced force can be low as there is only few contacts, but it does not mean the packing is stable
if O.iter < 5000:
return
# the rest will be run only if unbalanced is < .1 (stabilized packing)
if unbalancedForce() > .1:
return
# add plate at the position on the top of the packing
# the maximum finds the z-coordinate of the top of the topmost particle
O.bodies.append(wall(max([b.state.pos + b.shape.radius for b in O.bodies if isinstance(b.shape, Sphere)]), axis=2, sense=-1))
global plate  # without this line, the plate variable would only exist inside this function
plate = O.bodies[-1]  # the last particles is the plate
# Wall objects are "fixed" by default, i.e. not subject to forces
# prescribing a velocity will therefore make it move at constant velocity (downwards)
plate.state.vel = (0, 0, -.1)
# start plotting the data now, it was not interesting before
O.engines = O.engines + [PyRunner(command='addPlotData()', iterPeriod=200)]
# next time, do not call this function anymore, but the next one (unloadPlate) instead

plate.state.vel *= -1

# O.tags can be used to retrieve unique identifiers of the simulation
# if running in batch, subsequent simulation would overwrite each other's output files otherwise
# d (or description) is simulation description (composed of parameter values)
# while the id is composed of time and process number
plot.saveDataTxt(O.tags['d.id'] + '.txt')
O.pause()

if not isinstance(O.bodies[-1].shape, Wall):
return
Fz = O.forces.f(plate.id)
plot.addData(Fz=Fz, w=plate.state.pos - plate.state.refPos, unbalanced=unbalancedForce(), i=O.iter)

# besides unbalanced force evolution, also plot the displacement-force diagram
plot.plots = {'i': ('unbalanced',), 'w': ('Fz',)}
plot.plot()

O.run()
# when running with yade-batch, the script must not finish until the simulation is done fully
# this command will wait for that (has no influence in the non-batch mode)
waitIfBatch()


### Batch table¶

To run the same script doc/sphinx/tutorial/03-oedometric-test.py in batch mode to test different parameters, execute command yade-batch 03-oedometric-test.table 03-oedometric-test.py, also visit page http://localhost:9080 to see the batch simulation progress.

rMean rRelFuzz maxLoad
.05 .1 1e6
.05 .2 1e6
.05 .3 1e6


## Periodic simple shear¶

Following example is in file doc/sphinx/tutorial/04-periodic-simple-shear.py.

# encoding: utf-8

# script for periodic simple shear test, with periodic boundary
# first compresses to attain some isotropic stress (checkStress),
# then loads in shear (checkDistorsion)
#
# the initial packing is either regular (hexagonal), with empty bands along the boundary,
# or periodic random cloud of spheres
#
# material friction angle is initially set to zero, so that the resulting packing is dense
# (sphere rearrangement is easier if there is no friction)
#

# setup the periodic boundary
from __future__ import print_function
O.periodic = True
O.cell.hSize = Matrix3(2, 0, 0, 0, 2, 0, 0, 0, 2)

# the "if 0:" block will be never executed, therefore the "else:" block will be
# to use cloud instead of regular packing, change to "if 1:" or something similar
if 0:
# create cloud of spheres and insert them into the simulation
sp = pack.SpherePack()
sp.makeCloud((0, 0, 0), (2, 2, 2), rMean=.1, rRelFuzz=.6, periodic=True)
# insert the packing into the simulation
sp.toSimulation(color=(0, 0, 1))  # pure blue
else:
# in this case, add dense packing
O.bodies.append(pack.regularHexa(pack.inAlignedBox((0, 0, 0), (2, 2, 2)), radius=.1, gap=0, color=(0, 0, 1)))

# create "dense" packing by setting friction to zero initially
O.materials.frictionAngle = 0

# simulation loop (will be run at every step)
O.engines = [
ForceResetter(),
InsertionSortCollider([Bo1_Sphere_Aabb()]),
InteractionLoop(
# interaction loop
[Ig2_Sphere_Sphere_ScGeom()],
[Ip2_FrictMat_FrictMat_FrictPhys()],
[Law2_ScGeom_FrictPhys_CundallStrack()]
),
NewtonIntegrator(damping=.4),
# run checkStress function (defined below) every second
# the label is arbitrary, and is used later to refer to this engine
PyRunner(command='checkStress()', realPeriod=1, label='checker'),
# record data for plotting every 100 steps; addData function is defined below
]

# set the integration timestep to be 1/2 of the "critical" timestep
O.dt = .5 * PWaveTimeStep()

# prescribe isotropic normal deformation (constant strain rate)
# of the periodic cell
O.cell.velGrad = Matrix3(-.1, 0, 0, 0, -.1, 0, 0, 0, -.1)

# when to stop the isotropic compression (used inside checkStress)
limitMeanStress = -5e5

# called every second by the PyRunner engine
def checkStress():
# stress tensor as the sum of normal and shear contributions
# Matrix3.Zero is the intial value for sum(...)
stress = getStress().trace() / 3.
print('mean stress', stress)
# if mean stress is below (bigger in absolute value) limitMeanStress, start shearing
if stress < limitMeanStress:
# apply constant-rate distorsion on the periodic cell
O.cell.velGrad = Matrix3(0, 0, .1, 0, 0, 0, 0, 0, 0)
# change the function called by the checker engine
# (checkStress will not be called anymore)
checker.command = 'checkDistorsion()'
# block rotations of particles to increase tanPhi, if desired
# disabled by default
if 0:
for b in O.bodies:
# block X,Y,Z rotations, translations are free
b.state.blockedDOFs = 'XYZ'
# stop rotations if any, as blockedDOFs block accelerations really
b.state.angVel = (0, 0, 0)
# set friction angle back to non-zero value
# tangensOfFrictionAngle is computed by the Ip2_* functor from material
# for future contacts change material (there is only one material for all particles)
# for existing contacts, set contact friction directly
for i in O.interactions:
i.phys.tangensOfFrictionAngle = tan(.5)

# called from the 'checker' engine periodically, during the shear phase
def checkDistorsion():
# if the distorsion value is >.3, exit; otherwise do nothing
if abs(O.cell.trsf[0, 2]) > .5:
# save data from addData(...) before exiting into file
# use O.tags['id'] to distinguish individual runs of the same simulation
plot.saveDataTxt(O.tags['id'] + '.txt')
# exit the program
#import sys
#sys.exit(0) # no error (0)
O.pause()

# called periodically to store data history
# get the stress tensor (as 3x3 matrix)
stress = sum(normalShearStressTensors(), Matrix3.Zero)
# give names to values we are interested in and save them
plot.addData(exz=O.cell.trsf[0, 2], szz=stress[2, 2], sxz=stress[0, 2], tanPhi=(stress[0, 2] / stress[2, 2]) if stress[2, 2] != 0 else 0, i=O.iter)
# color particles based on rotation amount
for b in O.bodies:
# rot() gives rotation vector between reference and current position
b.shape.color = scalarOnColorScale(b.state.rot().norm(), 0, pi / 2.)

# define what to plot (3 plots in total)
## exz(i), [left y axis, separate by None:] szz(i), sxz(i)
## szz(exz), sxz(exz)
## tanPhi(i)
# note the space in 'i ' so that it does not overwrite the 'i' entry
plot.plots = {'i': ('exz', None, 'szz', 'sxz'), 'exz': ('szz', 'sxz'), 'i ': ('tanPhi',)}

# better show rotation of particles
Gl1_Sphere.stripes = True

# open the plot on the screen
plot.plot()

O.saveTmp()


## 3d postprocessing¶

Following example is in file doc/sphinx/tutorial/05-3d-postprocessing.py. This example will run for 20000 iterations, saving *.png snapshots, then it will make a video 3d.mpeg out of those snapshots.

# demonstrate 3d postprocessing with yade
#
# 1. qt.SnapshotEngine saves images of the 3d view as it appears on the screen periodically
#    makeVideo is then used to make real movie from those images
# 2. VTKRecorder saves data in files which can be opened with Paraview
#    see the User's manual for an intro to Paraview

# generate loose packing
sp = pack.SpherePack()
sp.makeCloud((0, 0, 0), (2, 2, 2), rMean=.1, rRelFuzz=.6, periodic=True)
# add to scene, make it periodic
sp.toSimulation()

O.engines = [
ForceResetter(),
InsertionSortCollider([Bo1_Sphere_Aabb()]),
InteractionLoop(
# interaction loop
[Ig2_Sphere_Sphere_ScGeom()],
[Ip2_FrictMat_FrictMat_FrictPhys()],
[Law2_ScGeom_FrictPhys_CundallStrack()]
),
NewtonIntegrator(damping=.4),
# save data for Paraview
VTKRecorder(fileName='3d-vtk-', recorders=['all'], iterPeriod=1000),
# save data from Yade's own 3d view
qt.SnapshotEngine(fileBase='3d-', iterPeriod=200, label='snapshot'),
# this engine will be called after 20000 steps, only once
PyRunner(command='finish()', iterPeriod=20000)
]
O.dt = .5 * PWaveTimeStep()

# prescribe constant-strain deformation of the cell
O.cell.velGrad = Matrix3(-.1, 0, 0, 0, -.1, 0, 0, 0, -.1)

# we must open the view explicitly (limitation of the qt.SnapshotEngine)
qt.View()

# this function is called when the simulation is finished
def finish():
# snapshot is label of qt.SnapshotEngine
# the 'snapshots' attribute contains list of all saved files
makeVideo(snapshot.snapshots, '3d.mpeg', fps=10, bps=10000)
O.pause()

# set parameters of the renderer, to show network chains rather than particles
# these settings are accessible from the Controller window, on the second tab ("Display") as well
rr.shape = False
rr.intrPhys = True


## Periodic triaxial test¶

Following example is in file doc/sphinx/tutorial/06-periodic-triaxial-test.py.

# encoding: utf-8

# periodic triaxial test simulation
#
# The initial packing is either
#
# 1. random cloud with uniform distribution, or
# 2. cloud with specified granulometry (radii and percentages), or
# 3. cloud of clumps, i.e. rigid aggregates of several particles
#
# The triaxial consists of 2 stages:
#
# 1. isotropic compaction, until sigmaIso is reached in all directions;
#    this stage is ended by calling compactionFinished()
# 2. constant-strain deformation along the z-axis, while maintaining
#    constant stress (sigmaIso) laterally; this stage is ended by calling
#    triaxFinished()
#
# Controlling of strain and stresses is performed via PeriTriaxController,
# of which parameters determine type of control and also stability
# condition (maxUnbalanced) so that the packing is considered stabilized
# and the stage is done.
#

from __future__ import print_function
sigmaIso = -1e5

#import matplotlib
#matplotlib.use('Agg')

# generate loose packing
from yade import pack, qt, plot

O.periodic = True
sp = pack.SpherePack()
if 0:
## uniform distribution
sp.makeCloud((0, 0, 0), (2, 2, 2), rMean=.1, rRelFuzz=.3, periodic=True)
else:
## create packing from clumps
# configuration of one clump
c1 = pack.SpherePack([((0, 0, 0), .03333), ((.03, 0, 0), .017), ((0, .03, 0), .017)])
# make cloud using the configuration c1 (there could c2, c3, ...; selection between them would be random)
sp.makeClumpCloud((0, 0, 0), (2, 2, 2), [c1], periodic=True, num=500)

# setup periodic boundary, insert the packing
sp.toSimulation()

O.engines = [
ForceResetter(),
InsertionSortCollider([Bo1_Sphere_Aabb()]),
InteractionLoop([Ig2_Sphere_Sphere_ScGeom()], [Ip2_FrictMat_FrictMat_FrictPhys()], [Law2_ScGeom_FrictPhys_CundallStrack()]),
PeriTriaxController(
label='triax',
# specify target values and whether they are strains or stresses
goal=(sigmaIso, sigmaIso, sigmaIso),
# type of servo-control
dynCell=True,
maxStrainRate=(10, 10, 10),
# wait until the unbalanced force goes below this value
maxUnbalanced=.1,
relStressTol=1e-3,
# call this function when goal is reached and the packing is stable
doneHook='compactionFinished()'
),
NewtonIntegrator(damping=.2),
]
O.dt = .5 * PWaveTimeStep()

unbalanced=unbalancedForce(),
i=O.iter,
sxx=triax.stress,
syy=triax.stress,
szz=triax.stress,
exx=triax.strain,
eyy=triax.strain,
ezz=triax.strain,
# save all available energy data
Etot=O.energy.total(),
**O.energy
)

# enable energy tracking in the code
O.trackEnergy = True

# define what to plot
plot.plots = {
'i': ('unbalanced',),
'i ': ('sxx', 'syy', 'szz'),
' i': ('exx', 'eyy', 'ezz'),
# energy plot
' i ': (O.energy.keys, None, 'Etot'),
}
# show the plot
plot.plot()

def compactionFinished():
# set the current cell configuration to be the reference one
O.cell.trsf = Matrix3.Identity
# change control type: keep constant confinement in x,y, 20% compression in z
triax.goal = (sigmaIso, sigmaIso, -.2)