def _solve(self, current_state: dict, **kwargs) -> dict:
span = [
(2 - pa) * s
for pa, s in zip(self._periodic_axes,
current_state['maximum_tangential_force'].shape)
]
if not self._pre_solve_checks or span != self._last_span:
self._check(span)
self._last_span = span
domain = current_state['contact_nodes']
conv_func = plan_convolve(current_state['maximum_tangential_force'],
self._im_total,
domain,
circular=self._periodic_axes)
# if the displacements are provided by another sub model or we have a set displacement we just have one set
# of bccg iterations:
if self.displacement_from_sub_model:
displacement = current_state['rigid_body_displacement_' +
self.direction]
else:
displacement = kwargs[f'rigid_body_displacement_{self.direction}']
set_displacement = float(displacement) * np.ones(
current_state['maximum_tangential_force'].shape)
x0 = self.previous_result if self.previous_result is not None else \
current_state['maximum_tangential_force']/2
min_pressure = np.array(
-1 * current_state['maximum_tangential_force'][domain])
loads_in_domain, failed = bccg(
conv_func, set_displacement[domain], self._tol, self._max_it,
x0[domain], min_pressure,
current_state['maximum_tangential_force'][domain])
loads_in_domain = slippy.asnumpy(loads_in_domain)
full_loads = np.zeros_like(current_state['maximum_tangential_force'])
full_loads[domain] = loads_in_domain
stick_nodes = np.logical_and(
domain, full_loads <
(0.99 * current_state['maximum_tangential_force']))
rtn_dict = dict()
rtn_dict['stick_nodes'] = stick_nodes
tangential_deformation = slippy.asnumpy(
conv_func(loads_in_domain, True))
rtn_dict['loads_' + self.component[0]] = full_loads
if 'total_displacement_' + self.component[0] in current_state:
rtn_dict['total_displacement_' +
self.component[0]] += tangential_deformation
else:
rtn_dict['total_displacement_' +
self.component[0]] = tangential_deformation
slip_distance = set_displacement - tangential_deformation
slip_distance[stick_nodes] = 0
slip_distance[np.logical_not(domain)] = 0
rtn_dict['slip_distance'] = slip_distance
return rtn_dict
def test_elastic_coupled():
mat = core.Elastic('steel_6', {'E': 200e9, 'v': 0.3})
np.random.seed(0)
loads1 = np.random.rand(16, 16)
loads2 = np.random.rand(16, 16)
directions = 'xyzx'
for i in range(3):
dir_1 = directions[i]
dir_2 = directions[i + 1]
loads_in_direction = {dir_1: loads1, dir_2: loads2}
displacement = mat.displacement_from_surface_loads(loads_in_direction,
grid_spacing=0.01,
simple=True)
loads_calc = mat.loads_from_surface_displacement(
displacements=displacement, grid_spacing=0.01, simple=True)
for direction in [dir_1, dir_2]:
npt.assert_allclose(loads_in_direction[direction],
slippy.asnumpy(loads_calc[direction]),
atol=0.02)
displacement = mat.displacement_from_surface_loads(loads_in_direction,
grid_spacing=0.01,
simple=False)
loads_calc = mat.loads_from_surface_displacement(
displacements=displacement, grid_spacing=0.01, simple=False)
for direction in [dir_1, dir_2]:
npt.assert_allclose(loads_in_direction[direction],
slippy.asnumpy(loads_calc[direction]),
atol=0.02)
def p_and_k(self,
target_load: float,
pressure_guess: np.ndarray = None,
add_to_cache: bool = True):
""" Solve the set contact problem using the Polonsky and Keer algorithm
Parameters
----------
target_load: float
The target total load
pressure_guess: array, optional (None)
The initial guess for the pressure solution, if none is supplied the last converged solution is used if
there is no last converged solution a flat array (ones) is used.
add_to_cache: bool
If True the result will be cached
Returns
-------
None
Notes
-----
The results from this method can be accessed by accessing the results property of this class, this will
automatically fill in displacement for both surfaces and the rigid body interference result.
The contact nodes property must be set to None before using this method, this remakes the convolution function.
"""
if self.max_pressure < np.inf:
raise ValueError(
"Polonsky and Keer algorithm cannot be used with a maximum pressure"
)
if pressure_guess is None:
pressure_guess = self._last_converged_loads or np.ones_like(
self._just_touching_gap)
failed, pressure, gap = polonsky_and_keer(
self.conv_func, pressure_guess, self._just_touching_gap,
target_load, self._grid_spacing, self._tol, self._max_it)
total_displacement = self.conv_func(pressure)
self._results = {
'loads_z':
pressure,
'total_displacement_z':
total_displacement,
'interference':
np.mean((slippy.asnumpy(self._just_touching_gap) +
slippy.asnumpy(total_displacement))[slippy.asnumpy(
pressure > 0)]),
'converged':
not failed
}
if add_to_cache:
self.add_to_cache(self._results['interference'], target_load,
pressure, failed)
def solve(self, current_state: dict) -> dict:
span = current_state['maximum_tangential_force'].shape
if not self._pre_solve_checks or span != self._last_span:
self._check(span)
self._last_span = span
domain = current_state['contact_nodes']
conv_func_full = plan_convolve(self._im_total, self._im_total, domain,
circular=self._periodic_axes)
# if the displacements are provided by another sub model or we have a set displacement we just have one set
# of bccg iterations:
if not self.load_controlled:
if self.update_displacement:
set_displacement = self.displacement_upd(current_state['time'])
elif self.displacement_from_sub_model:
set_displacement = current_state['rigid_body_displacement']
else:
set_displacement = self.displacement
try:
set_displacement = float(set_displacement)*np.ones_like(current_state['maximum_tangential_force'])
except TypeError:
pass
x0 = self.previous_result if self.previous_result is not None else set_displacement/np.sum(self._im_total)
loads_in_domain, failed = bccg(conv_func_full, set_displacement[domain], self._tol,
self._max_it, x0[domain], 0,
current_state['maximum_tangential_force'][domain])
loads_in_domain = slippy.asnumpy(loads_in_domain)
full_loads = np.zeros_like(current_state['maximum_tangential_force'])
full_loads[domain] = loads_in_domain
stick_nodes = np.logical_and(domain, full_loads < (0.99 * current_state['maximum_tangential_force']))
current_state['stick_nodes'] = stick_nodes
tangential_deformation = slippy.asnumpy(conv_func_full(loads_in_domain, True))
loads = current_state['loads']._asdict() if 'loads' in current_state else dict()
loads[self.component[0]] = full_loads
current_state['loads'] = Loads(**loads)
td = 'total_displacement'
all_displacements = current_state[td]._asdict() if td in current_state else dict()
if self.component[0] in all_displacements and all_displacements[self.component[0]] is not None:
all_displacements[self.component[0]] += tangential_deformation
else:
all_displacements[self.component[0]] = tangential_deformation
current_state[td] = Displacements(**all_displacements)
slip_distance = set_displacement-tangential_deformation
slip_distance[stick_nodes] = 0
slip_distance[np.logical_not(domain)] = 0
current_state['slip_distance'] = slip_distance
return current_state
else:
raise NotImplementedError('Load controlled partial slip is not yet implemented')
def test_materials_basic():
# check that one of influence matrix or displacement from loading is given
for material in core.materials._IMMaterial._subclass_registry:
if material in exceptions:
continue
try:
mat_params = material_parameters[material.material_type]
except KeyError:
raise AssertionError(
f"Material test parameters are not specified, for material {material.material_type}"
)
mat_instance = material(**mat_params[0])
max_load = mat_params[1].pop('_max_load', 1)
np.random.seed(0)
loads = np.random.rand(16, 16) * max_load
# check that the loads and displacement functions are inverse of each other
for direction in {'x', 'y', 'z'}:
load_in_direction = {direction: loads}
displacement = mat_instance.displacement_from_surface_loads(
load_in_direction, **mat_params[1])
set_disp = displacement[direction]
loads_calc = mat_instance.loads_from_surface_displacement(
displacements={direction: set_disp}, **mat_params[2])
npt.assert_allclose(loads,
slippy.asnumpy(loads_calc[direction]),
atol=max_load * 0.02)
def solve(self, current_state: dict) -> dict:
if 'converged' in current_state and not current_state['converged']:
print(
f"SUB MODEL: {self.name}, Solution did not converge, no wear")
return current_state
if self.no_time:
just_touching_gap = current_state['just_touching_gap']
if self.plastic_def_this_step is None or (
'new_step' in current_state and current_state['new_step']):
self.plastic_def_this_step = np.zeros_like(just_touching_gap)
# need to sort out the discrepancy between the current just touching gap and the one used for the model
gap = (just_touching_gap - current_state['interference'] +
current_state['total_displacement_z'] +
self.plastic_def_this_step)
else:
# just use the current just touching gap and interference
gap = slippy.asnumpy(current_state['gap'])
# just_touching_gap = current_state['just_touching_gap']
# gap = (just_touching_gap - current_state['interference'] + current_state['total_displacement_z'])
max_load = min(self.model.surface_1.material.max_load,
self.model.surface_2.material.max_load)
idx = np.logical_and(
current_state['loads_z'] >= max_load,
np.logical_and(gap < 0, current_state['contact_nodes']))
total_wear = -gap[idx]
if self.no_time:
self.plastic_def_this_step[idx] += total_wear
if total_wear.size:
tpd = np.sum(total_wear) * self.model.surface_1.grid_spacing**2 * (
self.p_surf_1 + self.p_surf_2)
else:
tpd = np.array(0.0)
results = {'total_plastic_deformation': tpd}
if self.p_surf_1 > 0:
y_pts = current_state['surface_1_points'][0][idx]
x_pts = current_state['surface_1_points'][1][idx]
surface_1_wear = total_wear * self.p_surf_1
results['wear_plastic_surface_1'] = surface_1_wear
self.model.surface_1.wear(self.name, x_pts, y_pts, surface_1_wear)
if self.p_surf_2 > 0:
y_pts = current_state['surface_2_points'][0][idx]
x_pts = current_state['surface_2_points'][1][idx]
surface_2_wear = total_wear * self.p_surf_2
results['wear_plastic_surface_2'] = surface_2_wear
self.model.surface_2.wear(self.name, x_pts, y_pts, surface_2_wear)
print(f"SUB MODEL: {self.name}, total deformation: {tpd}")
return results
def __call__(self, height, current_state=None):
# If the height guess is in the cache that can be out load guess
height = float(height)
if height in self.cache_heights:
total_load = self.cache_total_load[self.cache_heights.index(
height)]
print(
f"Returning bound value from cache: height: {height:.4}, total_load {total_load:.4}"
)
return total_load - self._set_load
pressure_initial_guess = self.get_loads_from_cache(height)
self.it += 1
# if im mats we can save some time here mostly by not moving data to and from the gpu
if self.im_mats:
z = -self._just_touching_gap + height
if not self.set_contact_nodes:
self.contact_nodes = z > 0 # this will remake the conv function as a side effect
contact_nodes = self.contact_nodes
if not np.any(contact_nodes):
print('no contact nodes')
total_load = 0
full_loads = np.zeros(contact_nodes.shape)
failed = False
else:
if pressure_initial_guess is None:
pressure_initial_guess = np.zeros(z.shape)
z_in = z[contact_nodes]
pressure_guess_in = pressure_initial_guess[contact_nodes]
loads_in_domain, failed = bccg(self.conv_func, z_in, self._tol,
self._max_it, pressure_guess_in,
0, self.max_pressure)
loads_in_domain = slippy.asnumpy(loads_in_domain)
self._results = {
'loads_in_domain': loads_in_domain,
'domain': self.contact_nodes,
'interference': height
}
total_load = float(
np.sum(loads_in_domain) * self._grid_spacing**2)
if not failed:
full_loads = np.zeros(contact_nodes.shape)
full_loads[contact_nodes] = loads_in_domain
self._last_converged_loads = full_loads
else:
full_loads = None
self.add_to_cache(height, total_load, full_loads, failed)
if failed:
# noinspection PyUnboundLocalVariable
print(
f'Failed: total load: {total_load}, height {height}, max_load {np.max(loads_in_domain)}'
)
self.last_call_failed = True
else:
print(
f'Solved: interference: {height}\tTotal load: {total_load}\tTarget load: {self._set_load}'
)
self.last_call_failed = False
return total_load - self._set_load
# else use the basic form
loads, total_disp, disp_1, disp_2, contact_nodes, failed = \
solve_normal_interference(height, gap=self._just_touching_gap,
model=self._model,
current_state=current_state,
adhesive_pressure=self._adhesion_model,
contact_nodes=self.contact_nodes,
max_iter=self._max_it,
material_options=self._material_options,
tol=self._tol,
initial_guess_loads=pressure_initial_guess)
self._results['loads_z'] = loads
self._results['total_displacement'] = total_disp
self._results['surface_1_displacement'] = disp_1
self._results['surface_2_displacement'] = disp_2
self._results['contact_nodes'] = contact_nodes
self._results['interference'] = height
total_load = np.sum(loads.flatten()) * self._grid_spacing**2
self._results['total_normal_load'] = total_load
if failed:
self.last_call_failed = True
print(
f'Failed: total load: {total_load}, height {height}, max_load {np.max(loads.flatten())}'
)
else:
self.last_call_failed = False
print(
f'Interference is: {height}\tTotal load is: {total_load}\tTarget load is: {self._set_load}'
)
self.add_to_cache(height, total_load, loads, failed)
return total_load - self._set_load
def rey(self,
target_load: float = None,
target_mean_gap: float = None,
add_to_cache: bool = True):
""" Solve the contact problem using the Rey algorithm
Parameters
----------
target_load: float
The target total load
target_mean_gap: float
The target mean gap
add_to_cache: bool
If True the result will be cached
Returns
-------
None
Notes
-----
The results from this method can be accessed by accessing the results property of this class, this will
automatically fill in displacement for both surfaces and the rigid body interference result.
The contact nodes property must be set to None before using this method, this remakes the convolution function.
"""
if not self._zero_frequency_zero:
raise ValueError(
"Rey solver requires a zero frequency value of 0, set in material definitions"
)
if not all(self._periodic_axes):
raise ValueError(
"Rey solver requires fully periodic contact, set periodic axes to True in step definition"
)
if self.max_pressure < np.inf:
raise ValueError(
"Rey algorithm cannot be used with a maximum pressure")
if target_load is None:
target_mean_pressure = None
else:
target_mean_pressure = target_load / (
self._just_touching_gap.size * self._grid_spacing**2)
failed, pressure, gap, total_displacement, contact_nodes = rey(
self._just_touching_gap, self.conv_func, self._adhesion_model,
self._tol, self._max_it, target_mean_gap, target_mean_pressure)
self._results = {
'loads_z':
pressure,
'total_displacement_z':
total_displacement,
'interference':
np.mean((slippy.asnumpy(self._just_touching_gap) +
slippy.asnumpy(total_displacement))[slippy.asnumpy(
pressure > 0)]),
'converged':
not failed,
'gap':
gap,
'contact_nodes':
contact_nodes
}
if add_to_cache:
self.add_to_cache(self._results['interference'], target_load,
pressure, failed)
def results(self):
if self._results is None:
print("No results found in height opt func")
if slippy.CUDA:
xp = cp
else:
xp = np
if self.im_mats and 'surface_1_displacement' not in self._results:
# need to put the loads into an np array of right shape
# find the full displacements (and convert to np array)
# find disp on surface 1 and surface 2
surf_1 = self._model.surface_1
surf_2 = self._model.surface_2
span = tuple([
s * (2 - pa) for s, pa in zip(self._just_touching_gap.shape,
self._periodic_axes)
])
# noinspection PyUnresolvedReferences
im1 = surf_1.material.influence_matrix(
span=span,
grid_spacing=[surf_1.grid_spacing] * 2,
components=['zz'])['zz']
# noinspection PyUnresolvedReferences
im2 = surf_2.material.influence_matrix(
span=span,
grid_spacing=[surf_1.grid_spacing] * 2,
components=['zz'])['zz']
if 'domain' in self._results and 'loads_in_domain' in self._results:
full_loads = xp.zeros(self._just_touching_gap.shape)
full_loads[
self._results['domain']] = self._results['loads_in_domain']
full_disp = slippy.asnumpy(
self.conv_func(self._results['loads_in_domain'],
ignore_domain=True))
full_loads = slippy.asnumpy(full_loads)
elif 'loads_z' in self._results:
full_loads = slippy.asnumpy(self._results['loads_z'])
full_disp = slippy.asnumpy(
self._results['total_displacement_z'])
else:
raise ValueError("Results not properly set")
conv_func_1 = plan_convolve(full_loads,
im1,
None,
circular=self._periodic_axes)
conv_func_2 = plan_convolve(full_loads,
im2,
None,
circular=self._periodic_axes)
disp_1 = conv_func_1(full_loads)
disp_2 = conv_func_2(full_loads)
if slippy.CUDA:
disp_1, disp_2 = xp.asnumpy(disp_1), xp.asnumpy(disp_2)
full_loads = xp.asnumpy(full_loads)
total_load = float(np.sum(full_loads) * self._grid_spacing**2)
if 'contact_nodes' in self._results:
contact_nodes = self._results['contact_nodes']
else:
contact_nodes = full_loads > 0
if 'gap' in self._results:
gap = self._results['gap']
else:
gap = self._just_touching_gap - self._results[
'interference'] + full_disp
results = {
'loads_z': full_loads,
'total_displacement_z': full_disp,
'surface_1_displacement_z': disp_1,
'surface_2_displacement_z': disp_2,
'contact_nodes': contact_nodes,
'total_normal_load': total_load,
'interference': self._results['interference'],
'gap': gap
}
return results
else:
return self._results
def __init__(self,
just_touching_gap: np.ndarray,
model: _ContactModelABC,
adhesion_model: _AdhesionModelABC,
initial_contact_nodes: np.ndarray,
max_it: int,
rtol: float,
material_options: typing.Union[typing.Sequence[dict], dict],
max_set_load: float,
rtol_outer: float = 0,
max_it_outer: int = 0,
use_cache: bool = True,
cache_loads=True,
periodic_axes: typing.Tuple[bool] = (False, False)):
if slippy.CUDA:
xp = cp
cache_loads = False
else:
xp = np
self._grid_spacing = model.surface_1.grid_spacing
self._just_touching_gap = np.asarray(just_touching_gap)
self._model = model
self._adhesion_model = adhesion_model
self.initial_contact_nodes = initial_contact_nodes
self._max_it = max_it
self._tol = rtol
self._max_it_outer = max_it_outer
self._tol_outer = rtol_outer
self._material_options = material_options
self._original_set_load = max_set_load
self._set_load = float(max_set_load)
self._periodic_axes = periodic_axes
self.cache_heights = [0.0]
self.cache_total_load = [0.0]
self.cache_surface_loads = [xp.zeros(just_touching_gap.shape)]
self.it = 0
self.use_cache = use_cache
self.use_loads_cache = cache_loads
surf_1 = model.surface_1
surf_2 = model.surface_2
self.im_mats = False
self.conv_func: ConvolutionFunction = None
self.cache_max = False
self.last_call_failed = False
self._last_converged_loads = None
if isinstance(surf_1.material, _IMMaterial) and isinstance(
surf_2.material, _IMMaterial):
self.im_mats = True
self._zero_frequency_zero = (
surf_1.material.zero_frequency_value == 0
and surf_2.material.zero_frequency_value == 0)
span = tuple([
s * (2 - pa)
for s, pa in zip(just_touching_gap.shape, periodic_axes)
])
max_pressure = min(
[surf_1.material.max_load, surf_2.material.max_load])
self.max_pressure = max_pressure
im1 = surf_1.material.influence_matrix(
components=['zz'],
grid_spacing=[surf_1.grid_spacing] * 2,
span=span)['zz']
im2 = surf_2.material.influence_matrix(
components=['zz'],
grid_spacing=[surf_1.grid_spacing] * 2,
span=span)['zz']
total_im = im1 + im2
self.total_im = xp.asarray(total_im)
self.contact_nodes = initial_contact_nodes
if use_cache and max_pressure != np.inf:
max_loads = max_pressure * xp.ones(just_touching_gap.shape)
self.cache_total_load.append(max_pressure *
just_touching_gap.size *
surf_1.grid_spacing**2)
max_elastic_disp = self.conv_func(max_loads)
self.cache_heights.append(
xp.max(max_elastic_disp + xp.asarray(just_touching_gap)))
if cache_loads:
self.cache_surface_loads.append(slippy.asnumpy(max_loads))
else:
self.contact_nodes = initial_contact_nodes