3D Code for isothermal finite hyperelasticity¶
Simple stretch
Basic units: Length: mm Mass: kg Time: s Derived units: Force: milliNewtons Stress: kPa
Eric Stewart and Lallit Anand
ericstew@mit.edu and anand@mit.edu
Converted to FEniCSx by Jorge Nin jorgenin@mit.edu September 2023
In [1]:
import numpy as np
import dolfinx
from mpi4py import MPI
from petsc4py import PETSc
from dolfinx import fem, mesh, io, plot, log
from dolfinx.fem import (Constant, dirichletbc, Function, FunctionSpace, Expression )
from dolfinx.fem.petsc import NonlinearProblem
from dolfinx.nls.petsc import NewtonSolver
from dolfinx.io import XDMFFile
import ufl
from ufl import (TestFunctions, TrialFunction, Identity, grad, det, div, dev, inv, tr, sqrt, conditional , gt, dx, inner, derivative, dot, ln, split)
from datetime import datetime
from dolfinx.plot import vtk_mesh
import pyvista
pyvista.set_jupyter_backend('client')
## Define temporal parameters
Set level of detail for log messages (integer)¶
Guide:
CRITICAL = 50 errors that may lead to data corruption
ERROR = 40 things that HAVE gone wrong
WARNING = 30 things that MAY go wrong later
INFO = 20 information of general interest (includes solver info)
PROGRESS = 16 what's happening (broadly)
TRACE = 13 what's happening (in detail)
DBG = 10 sundry
In [2]:
log.set_log_level(log.LogLevel.WARNING)
Define Geometry¶
In [3]:
length = 50.0 # mm
domain = mesh.create_box(MPI.COMM_WORLD,[[0.0,0.0,0.0],[length,length,length]],[10,10,6],mesh.CellType.tetrahedron)
Visualize Gemometry¶
In [4]:
plotter = pyvista.Plotter()
vtkdata = vtk_mesh(domain, domain.topology.dim)
grid = pyvista.UnstructuredGrid(*vtkdata)
actor = plotter.add_mesh(grid, show_edges=True)
plotter.show()
plotter.close()
Widget(value="<iframe src='http://localhost:51043/index.html?ui=P_0x2a4f0dcd0_0&reconnect=auto' style='width: …
Functions for finding Differnent Areas¶
In [5]:
def xBot(x):
return np.isclose(x[0], 0)
def xTop(x):
return np.isclose(x[0], length)
def yBot(x):
return np.isclose(x[1], 0)
def yTop(x):
return np.isclose(x[1], length)
def zBot(x):
return np.isclose(x[2], 0)
def loadFace(x):
return np.logical_and(np.logical_and(np.isclose(x[2],length) , np.less_equal(x[0],length/2)) , np.less_equal(x[1], length/2))
def zTop(x):
return np.logical_and(np.isclose(x[2], length),np.logical_not(loadFace(x)))
In [6]:
boundaries = [(2,xBot),(3,yBot),(4,zBot),(5,zTop),(6,loadFace)]
facet_indices, facet_markers = [], []
fdim = domain.topology.dim - 1
for (marker, locator) in boundaries:
facets = mesh.locate_entities(domain, fdim, locator)
facet_indices.append(facets)
facet_markers.append(np.full_like(facets, marker))
facet_indices = np.hstack(facet_indices).astype(np.int32)
facet_markers = np.hstack(facet_markers).astype(np.int32)
sorted_facets = np.argsort(facet_indices)
facet_tag = mesh.meshtags(domain, fdim, facet_indices[sorted_facets], facet_markers[sorted_facets])
ds = ufl.Measure('ds', domain=domain, subdomain_data=facet_tag,metadata={'quadrature_degree': 4})
n = ufl.FacetNormal(domain)
MATERIAL PARAMETERS¶
Arruda-Boyce Model
In [7]:
Gshear_0 = Constant(domain,PETSc.ScalarType(280.0)) # Ground state shear modulus
lambdaL = Constant(domain,PETSc.ScalarType(5.12)) # Locking stretch
Kbulk = Constant(domain,PETSc.ScalarType(1000.0*Gshear_0))
Simulation Control¶
In [8]:
t = 0.0 # start time
Ttot = 30 # total simulation time
trac_tot = 1.5e3 # final pressure (kPa)
numSteps = 100
dt = Ttot/numSteps # fixed step size
def distRamp(t):
return trac_tot*t/Ttot
Function Spaces¶
$$ \frac{x}{y}$$In [9]:
U2 = ufl.VectorElement("Lagrange", domain.ufl_cell(), 2) # For displacement
P1 = ufl.FiniteElement("Lagrange", domain.ufl_cell(), 1) # For pressure
TH = ufl.MixedElement([U2, P1]) # Taylor-Hood style mixed element
ME = FunctionSpace(domain, TH) # Total space for all DOFs
In [10]:
w = Function(ME)
u, p = split(w)
w_old = Function(ME)
u_old, p_old = split(w_old)
u_test, p_test = TestFunctions(ME)
dw = TrialFunction(ME)
SubRoutine¶
In [11]:
def F_calc(u):
Id = Identity(3)
F = Id + grad(u)
return F
def lambdaBar_calc(u):
F = F_calc(u)
C = F.T*F
J = det(F)
Cdis = J**(-2/3)*C
I1 = tr(Cdis)
lambdaBar = sqrt(I1/3.0)
return lambdaBar
def zeta_calc(u):
lambdaBar = lambdaBar_calc(u)
# Use Pade approximation of Langevin inverse
z = lambdaBar/lambdaL
z = conditional(gt(z,0.95), 0.95, z) # Keep simulation from blowing up
beta = z*(3.0 - z**2.0)/(1.0 - z**2.0)
zeta = (lambdaL/(3*lambdaBar))*beta
return zeta
# Generalized shear modulus for Arruda-Boyce model
def Gshear_AB_calc(u):
zeta = zeta_calc(u)
Gshear = Gshear_0 * zeta
return Gshear
#---------------------------------------------
# Subroutine for calculating the Cauchy stress
#---------------------------------------------
def T_calc(u,p):
Id = Identity(3)
F = F_calc(u)
J = det(F)
B = F*F.T
Bdis = J**(-2/3)*B
Gshear = Gshear_AB_calc(u)
T = (1/J)* Gshear * dev(Bdis) - p * Id
return T
#----------------------------------------------
# Subroutine for calculating the Piola stress
#----------------------------------------------
def Piola_calc(u, p):
Id = Identity(3)
F = F_calc(u)
J = det(F)
#
T = T_calc(u,p)
#
Tmat = J * T * inv(F.T)
return Tmat
In [12]:
F = F_calc(u)
J = det(F)
lambdaBar = lambdaBar_calc(u)
# Piola stress
Tmat = Piola_calc(u, p)
WEAK FORMS¶
In [13]:
dxs = dx(metadata={'quadrature_degree': 4})
In [14]:
# Residuals:
# Res_0: Balance of forces (test fxn: u)
# Res_1: Coupling pressure (test fxn: p)
Fcof = J*inv(F.T)
Time_cons = Constant(domain,PETSc.ScalarType(distRamp(0)))
traction = - Time_cons*dot(Fcof,n)
# The weak form for the equilibrium equation. No body force
Res_0 = inner(Tmat , grad(u_test) )*dxs- dot(traction, u_test)*ds(6)
# The weak form for the pressure
fac_p = ln(J)/J
#
Res_1 = dot( (p/Kbulk + fac_p), p_test)*dxs
# Total weak form
Res = Res_0 + Res_1
# Automatic differentiation tangent:
a = derivative(Res, w, dw)
In [15]:
#U0, submap = ME.sub(0).sub(1).collapse()
#fixed_displacement = fem.Function(U0)
#fixed_displacement.interpolate(lambda x : np.full(x.shape[1], distRamp(Time_cons)))
dofs1 = fem.locate_dofs_topological(ME.sub(0).sub(0), facet_tag.dim, facet_tag.find(2))
dofs2 = fem.locate_dofs_topological(ME.sub(0).sub(1), facet_tag.dim, facet_tag.find(3))
dofs3 = fem.locate_dofs_topological(ME.sub(0).sub(0), facet_tag.dim, facet_tag.find(6))
dofs4 = fem.locate_dofs_topological(ME.sub(0).sub(1), facet_tag.dim, facet_tag.find(6))
dofs5 = fem.locate_dofs_topological(ME.sub(0).sub(2), facet_tag.dim, facet_tag.find(4))
bcs_1 = dirichletbc(0.0, dofs1,ME.sub(0).sub(0)) # u1 fix - xBot
bcs_2 = dirichletbc(0.0, dofs2, ME.sub(0).sub(1)) # u2 fix - yBot
bcs_3 = dirichletbc(0.0,dofs3 ,ME.sub(0).sub(0)) # u3 fix - zBot
bcs_4 = dirichletbc(0.0, dofs4, ME.sub(0).sub(1)) # u2 fix - yBot
bcx_5 = dirichletbc(0.0,dofs5 ,ME.sub(0).sub(2)) # u3 fix - zBot
#
bcs = [bcs_1, bcs_2, bcs_3, bcs_4,bcx_5]
Non Linear Variational¶
In [16]:
#Setting up visualziation
import pyvista
import matplotlib
import cmasher as cmr
import os
if not os.path.exists("results"):
# Create a new directory because it does not exist
os.makedirs("results")
pyvista.set_jupyter_backend('client')
plotter = pyvista.Plotter()
plotter.open_gif("results/3D_cube_footing.gif")
V = fem.FunctionSpace(domain,U2) ## Difference
u_n = fem.Function(V)
u_ex = Expression(w.sub(0),V.element.interpolation_points())
u_n.interpolate(u_ex)
topology, cells, geometry = plot.vtk_mesh(u_n.function_space)
function_grid = pyvista.UnstructuredGrid(topology, cells, geometry)
values = np.zeros((geometry.shape[0], 3))
#u0 = w.sub(0).collapse()
values[:, :len(u_n)] = u_n.x.array.reshape(geometry.shape[0], len(u_n))
function_grid["u"] = values
function_grid.set_active_vectors("u")
# Warp mesh by deformation
warped = function_grid.warp_by_vector("u", factor=0)
warped.set_active_vectors("u")
cmap = cmr.get_sub_cmap(matplotlib.colormaps.get_cmap("jet"), 0.1, 0.9,N=6)
# Add mesh to plotter and visualize
actor = plotter.add_mesh(warped, show_edges=True, lighting=False, clim=[0, 67.5],cmap=cmap)
# Compute magnitude of displacement to visualize in GIF
Vs = fem.FunctionSpace(domain, ("Lagrange", 2))
magnitude = fem.Function(Vs)
us = fem.Expression(u_n[1], Vs.element.interpolation_points())
magnitude.interpolate(us)
warped["mag"] = magnitude.x.array
#plotter.view_xy()
#plotter.camera.position=[5,25,200]
#plotter.camera.focal_point=[5,40,0]
plotter.write_frame()
In [17]:
## Functions for visualization
U1 = ufl.VectorElement("Lagrange", domain.ufl_cell(), 1)
V2 = fem.FunctionSpace(domain, U1)#Vector function space
V1 = fem.FunctionSpace(domain, P1)#Scalar function space
u_r = Function(V2)
u_r.name = "disp"
p_r = Function(V1)
p_r.name = "p"
J_vis = Function(V1)
J_vis.name = "J"
J_expr = Expression(J,V1.element.interpolation_points())
lambdaBar_Vis = Function(V1)
lambdaBar_Vis.name = "lambdaBar"
lambdaBar_expr = Expression(lambdaBar,V1.element.interpolation_points())
P11 = Function(V1)
P11.name = "P11"
P11_expr = Expression(Tmat[0,0],V1.element.interpolation_points())
P22 = Function(V1)
P22.name = "P22"
P22_expr = Expression(Tmat[1,1],V1.element.interpolation_points())
P33 = Function(V1)
P33.name = "P33"
P33_expr = Expression(Tmat[2,2],V1.element.interpolation_points())
T = Tmat*F.T/J
T0 = T - (1/3)*tr(T)*Identity(3)
Mises = sqrt((3/2)*inner(T0, T0))
Mises_Vis= Function(V1,name="Mises")
Mises_expr = Expression(Mises,V1.element.interpolation_points())
def InterpAndSave(t,file):
u_r.interpolate(w.sub(0))
p_r.interpolate(w.sub(1))
J_vis.interpolate(J_expr)
P11.interpolate(P11_expr)
P22.interpolate(P22_expr)
P33.interpolate(P33_expr)
lambdaBar_Vis.interpolate(lambdaBar_expr)
Mises_Vis.interpolate(Mises_expr)
file.write_function(u_r,t)
file.write_function(p_r,t)
file.write_function(J_vis,t)
file.write_function(P11,t)
file.write_function(P22,t)
file.write_function(P33,t)
file.write_function(lambdaBar_Vis,t)
file.write_function(Mises_Vis,t)
pointForStress = [0,0,length]
bb_tree = dolfinx.geometry.bb_tree(domain,domain.topology.dim)
cell_candidates = dolfinx.geometry.compute_collisions_points(bb_tree, pointForStress)
colliding_cells = dolfinx.geometry.compute_colliding_cells(domain, cell_candidates, pointForStress)
In [18]:
startTime = datetime.now()
#"-mcpu=apple-m1"
jit_options ={"cffi_extra_compile_args":["-O3","-ffast-math","-mcpu=apple-m1"]}
problem = NonlinearProblem(Res, w, bcs, a,jit_options=jit_options)
solver = NewtonSolver(MPI.COMM_WORLD, problem)
solver.convergence_criterion = "incremental"
solver.rtol = 1e-8
solver.atol = 1e-8
solver.max_it = 50
solver.report = True
ksp = solver.krylov_solver
opts = PETSc.Options()
option_prefix = ksp.getOptionsPrefix()
opts[f"{option_prefix}ksp_type"] = "preonly"
opts[f"{option_prefix}pc_type"] = "lu"
#opts[f"{option_prefix}pc_hypre_type"] = "boomeramg"
opts[f"{option_prefix}pc_factor_mat_solver_type"] = "mumps"
opts[f"{option_prefix}ksp_max_it"] = 30
ksp.setFromOptions()
totSteps = numSteps+1
timeHist0 = np.zeros(shape=[totSteps])
step = "Strech"
t = 0
ii = 0
xdmf = XDMFFile(domain.comm, "results/3D_cube_footing.xdmf", "w")
xdmf.write_mesh(domain)
InterpAndSave(t,xdmf)
print("------------------------------------")
print("Simulation Start")
print("------------------------------------")
# Store start time
startTime = datetime.now()
while (round(t + dt, 9) <= Ttot):
# increment time
t += dt
# increment counter
ii += 1
# update time variables in time-dependent BCs
Time_cons.value = distRamp(t)
# Solve the problem
try:
(iter, converged) = solver.solve(w)
except: # Break the loop if solver fails
print( "Ended Early")
break
w.x.scatter_forward()
# Write output to *.xdmf file
#writeResults(t)
#print(u0.x.array-w.x.array[dofs])
#Visualizing GIF
u_n.interpolate(u_ex)
function_grid["u"][:, :len(u_n)] = u_n.x.array.reshape(geometry.shape[0], len(u_n))
magnitude.interpolate(us)
warped.set_active_scalars("mag")
warped_n = function_grid.warp_by_vector(factor=1)
plotter.update_coordinates(warped_n.points.copy(), render=False)
plotter.update_scalars(magnitude.x.array,render = False)
plotter.write_frame()
# Update DOFs for next step
w_old.x.array[:] = w.x.array
#SAVING RESULT
InterpAndSave(t,xdmf)
# Store displacement at a particular point at this time
timeHist0[ii] = w.sub(0).sub(2).eval([0, 0, length],colliding_cells[0])[0] # time history of displacement
#
# Print progress of calculation
if ii%1 == 0:
now = datetime.now()
current_time = now.strftime("%H:%M:%S")
print("Step: {} | Simulation Time: {} s, Wallclock Time: {}".\
format(step, round(t,4), current_time))
print("Iterations: {}".format(iter))
print()
plotter.close()
print("-----------------------------------------")
print("End computation")
# Report elapsed real time for the analysis
endTime = datetime.now()
elapseTime = endTime - startTime
print("------------------------------------------")
print("Elapsed real time: {}".format(elapseTime))
print("------------------------------------------")
xdmf.close()
------------------------------------ Simulation Start ------------------------------------ Step: Strech | Simulation Time: 0.3 s, Wallclock Time: 20:20:40 Iterations: 4 Step: Strech | Simulation Time: 0.6 s, Wallclock Time: 20:20:42 Iterations: 4 Step: Strech | Simulation Time: 0.9 s, Wallclock Time: 20:20:43 Iterations: 4 Step: Strech | Simulation Time: 1.2 s, Wallclock Time: 20:20:45 Iterations: 4 Step: Strech | Simulation Time: 1.5 s, Wallclock Time: 20:20:46 Iterations: 4 Step: Strech | Simulation Time: 1.8 s, Wallclock Time: 20:20:48 Iterations: 4 Step: Strech | Simulation Time: 2.1 s, Wallclock Time: 20:20:49 Iterations: 4 Step: Strech | Simulation Time: 2.4 s, Wallclock Time: 20:20:51 Iterations: 4 Step: Strech | Simulation Time: 2.7 s, Wallclock Time: 20:20:52 Iterations: 4 Step: Strech | Simulation Time: 3.0 s, Wallclock Time: 20:20:54 Iterations: 4 Step: Strech | Simulation Time: 3.3 s, Wallclock Time: 20:20:55 Iterations: 4 Step: Strech | Simulation Time: 3.6 s, Wallclock Time: 20:20:57 Iterations: 4 Step: Strech | Simulation Time: 3.9 s, Wallclock Time: 20:20:58 Iterations: 4 Step: Strech | Simulation Time: 4.2 s, Wallclock Time: 20:21:00 Iterations: 4 Step: Strech | Simulation Time: 4.5 s, Wallclock Time: 20:21:01 Iterations: 4 Step: Strech | Simulation Time: 4.8 s, Wallclock Time: 20:21:03 Iterations: 4 Step: Strech | Simulation Time: 5.1 s, Wallclock Time: 20:21:04 Iterations: 4 Step: Strech | Simulation Time: 5.4 s, Wallclock Time: 20:21:05 Iterations: 4 Step: Strech | Simulation Time: 5.7 s, Wallclock Time: 20:21:07 Iterations: 4 Step: Strech | Simulation Time: 6.0 s, Wallclock Time: 20:21:08 Iterations: 4 Step: Strech | Simulation Time: 6.3 s, Wallclock Time: 20:21:10 Iterations: 4 Step: Strech | Simulation Time: 6.6 s, Wallclock Time: 20:21:11 Iterations: 4 Step: Strech | Simulation Time: 6.9 s, Wallclock Time: 20:21:13 Iterations: 4 Step: Strech | Simulation Time: 7.2 s, Wallclock Time: 20:21:14 Iterations: 4 Step: Strech | Simulation Time: 7.5 s, Wallclock Time: 20:21:16 Iterations: 4 Step: Strech | Simulation Time: 7.8 s, Wallclock Time: 20:21:17 Iterations: 4 Step: Strech | Simulation Time: 8.1 s, Wallclock Time: 20:21:19 Iterations: 4 Step: Strech | Simulation Time: 8.4 s, Wallclock Time: 20:21:20 Iterations: 4 Step: Strech | Simulation Time: 8.7 s, Wallclock Time: 20:21:22 Iterations: 4 Step: Strech | Simulation Time: 9.0 s, Wallclock Time: 20:21:23 Iterations: 4 Step: Strech | Simulation Time: 9.3 s, Wallclock Time: 20:21:25 Iterations: 4 Step: Strech | Simulation Time: 9.6 s, Wallclock Time: 20:21:26 Iterations: 4 Step: Strech | Simulation Time: 9.9 s, Wallclock Time: 20:21:28 Iterations: 4 Step: Strech | Simulation Time: 10.2 s, Wallclock Time: 20:21:29 Iterations: 4 Step: Strech | Simulation Time: 10.5 s, Wallclock Time: 20:21:31 Iterations: 4 Step: Strech | Simulation Time: 10.8 s, Wallclock Time: 20:21:32 Iterations: 4 Step: Strech | Simulation Time: 11.1 s, Wallclock Time: 20:21:34 Iterations: 4 Step: Strech | Simulation Time: 11.4 s, Wallclock Time: 20:21:35 Iterations: 4 Step: Strech | Simulation Time: 11.7 s, Wallclock Time: 20:21:37 Iterations: 4 Step: Strech | Simulation Time: 12.0 s, Wallclock Time: 20:21:38 Iterations: 4 Step: Strech | Simulation Time: 12.3 s, Wallclock Time: 20:21:40 Iterations: 4 Step: Strech | Simulation Time: 12.6 s, Wallclock Time: 20:21:41 Iterations: 4 Step: Strech | Simulation Time: 12.9 s, Wallclock Time: 20:21:43 Iterations: 4 Step: Strech | Simulation Time: 13.2 s, Wallclock Time: 20:21:44 Iterations: 4 Step: Strech | Simulation Time: 13.5 s, Wallclock Time: 20:21:46 Iterations: 4 Step: Strech | Simulation Time: 13.8 s, Wallclock Time: 20:21:47 Iterations: 4 Step: Strech | Simulation Time: 14.1 s, Wallclock Time: 20:21:49 Iterations: 4 Step: Strech | Simulation Time: 14.4 s, Wallclock Time: 20:21:50 Iterations: 4 Step: Strech | Simulation Time: 14.7 s, Wallclock Time: 20:21:52 Iterations: 4 Step: Strech | Simulation Time: 15.0 s, Wallclock Time: 20:21:53 Iterations: 4 Step: Strech | Simulation Time: 15.3 s, Wallclock Time: 20:21:55 Iterations: 4 Step: Strech | Simulation Time: 15.6 s, Wallclock Time: 20:21:56 Iterations: 4 Step: Strech | Simulation Time: 15.9 s, Wallclock Time: 20:21:58 Iterations: 4 Step: Strech | Simulation Time: 16.2 s, Wallclock Time: 20:21:59 Iterations: 4 Step: Strech | Simulation Time: 16.5 s, Wallclock Time: 20:22:01 Iterations: 4 Step: Strech | Simulation Time: 16.8 s, Wallclock Time: 20:22:03 Iterations: 4 Step: Strech | Simulation Time: 17.1 s, Wallclock Time: 20:22:04 Iterations: 4 Step: Strech | Simulation Time: 17.4 s, Wallclock Time: 20:22:06 Iterations: 4 Step: Strech | Simulation Time: 17.7 s, Wallclock Time: 20:22:07 Iterations: 4 Step: Strech | Simulation Time: 18.0 s, Wallclock Time: 20:22:09 Iterations: 4 Step: Strech | Simulation Time: 18.3 s, Wallclock Time: 20:22:10 Iterations: 4 Step: Strech | Simulation Time: 18.6 s, Wallclock Time: 20:22:12 Iterations: 4 Step: Strech | Simulation Time: 18.9 s, Wallclock Time: 20:22:13 Iterations: 4 Step: Strech | Simulation Time: 19.2 s, Wallclock Time: 20:22:15 Iterations: 4 Step: Strech | Simulation Time: 19.5 s, Wallclock Time: 20:22:16 Iterations: 4 Step: Strech | Simulation Time: 19.8 s, Wallclock Time: 20:22:18 Iterations: 4 Step: Strech | Simulation Time: 20.1 s, Wallclock Time: 20:22:19 Iterations: 4 Step: Strech | Simulation Time: 20.4 s, Wallclock Time: 20:22:21 Iterations: 4 Step: Strech | Simulation Time: 20.7 s, Wallclock Time: 20:22:22 Iterations: 4 Step: Strech | Simulation Time: 21.0 s, Wallclock Time: 20:22:24 Iterations: 4 Step: Strech | Simulation Time: 21.3 s, Wallclock Time: 20:22:26 Iterations: 4 Step: Strech | Simulation Time: 21.6 s, Wallclock Time: 20:22:27 Iterations: 4 Step: Strech | Simulation Time: 21.9 s, Wallclock Time: 20:22:29 Iterations: 4 Step: Strech | Simulation Time: 22.2 s, Wallclock Time: 20:22:30 Iterations: 4 Step: Strech | Simulation Time: 22.5 s, Wallclock Time: 20:22:32 Iterations: 4 Step: Strech | Simulation Time: 22.8 s, Wallclock Time: 20:22:33 Iterations: 4 Step: Strech | Simulation Time: 23.1 s, Wallclock Time: 20:22:35 Iterations: 4 Step: Strech | Simulation Time: 23.4 s, Wallclock Time: 20:22:36 Iterations: 4 Step: Strech | Simulation Time: 23.7 s, Wallclock Time: 20:22:38 Iterations: 4 Step: Strech | Simulation Time: 24.0 s, Wallclock Time: 20:22:39 Iterations: 4 Step: Strech | Simulation Time: 24.3 s, Wallclock Time: 20:22:41 Iterations: 4 Step: Strech | Simulation Time: 24.6 s, Wallclock Time: 20:22:42 Iterations: 4 Step: Strech | Simulation Time: 24.9 s, Wallclock Time: 20:22:44 Iterations: 4 Step: Strech | Simulation Time: 25.2 s, Wallclock Time: 20:22:46 Iterations: 4 Step: Strech | Simulation Time: 25.5 s, Wallclock Time: 20:22:47 Iterations: 4 Step: Strech | Simulation Time: 25.8 s, Wallclock Time: 20:22:49 Iterations: 4 Step: Strech | Simulation Time: 26.1 s, Wallclock Time: 20:22:50 Iterations: 4 Step: Strech | Simulation Time: 26.4 s, Wallclock Time: 20:22:52 Iterations: 4 Step: Strech | Simulation Time: 26.7 s, Wallclock Time: 20:22:53 Iterations: 4 Step: Strech | Simulation Time: 27.0 s, Wallclock Time: 20:22:55 Iterations: 4 Step: Strech | Simulation Time: 27.3 s, Wallclock Time: 20:22:56 Iterations: 4 Step: Strech | Simulation Time: 27.6 s, Wallclock Time: 20:22:58 Iterations: 4 Step: Strech | Simulation Time: 27.9 s, Wallclock Time: 20:22:59 Iterations: 4 Step: Strech | Simulation Time: 28.2 s, Wallclock Time: 20:23:01 Iterations: 4 Step: Strech | Simulation Time: 28.5 s, Wallclock Time: 20:23:02 Iterations: 4 Step: Strech | Simulation Time: 28.8 s, Wallclock Time: 20:23:04 Iterations: 4 Step: Strech | Simulation Time: 29.1 s, Wallclock Time: 20:23:06 Iterations: 4 Step: Strech | Simulation Time: 29.4 s, Wallclock Time: 20:23:07 Iterations: 4 Step: Strech | Simulation Time: 29.7 s, Wallclock Time: 20:23:09 Iterations: 4 Step: Strech | Simulation Time: 30.0 s, Wallclock Time: 20:23:10 Iterations: 4 ----------------------------------------- End computation ------------------------------------------ Elapsed real time: 0:02:35.500574 ------------------------------------------
In [19]:
from IPython.display import Image
display(Image(data=open("results/3D_cube_footing.gif",'rb').read(), format='png'))
