import gstaichi as ti
import genesis as gs
from .elasto_plastic import ElastoPlastic
[docs]
@ti.data_oriented
class Snow(ElastoPlastic):
"""
The snow material class for MPM.
Note
----
Snow is a special type of ElastoPlastic that get's harder when compressed.
It doesn't support von Mises yield criterion.
Parameters
----------
E: float, optional
Young's modulus. Default is 1e6.
nu: float, optional
Poisson ratio. Default is 0.2.
rho: float, optional
Density (kg/m^3). Default is 1000.
lam: float, optional
The first Lame's parameter. Default is None, computed by E and nu.
mu: float, optional
The second Lame's parameter. Default is None, computed by E and nu.
sampler: str, optional
Particle sampler ('pbs', 'regular', 'random'). Note that 'pbs' is only supported on Linux for now. Defaults to
'random'.
yield_lower: float, optional
Lower bound of yield condition. Default is 2.5e-2.
yield_higher: float, optional
Upper bound of yield condition. Default is 4.5e-3.
"""
def __init__(
self,
E=1e6, # Young's modulus
nu=0.2, # Poisson's ratio
rho=1000.0, # density (kg/m^3)
lam=None,
mu=None,
sampler="random",
yield_lower=2.5e-2,
yield_higher=4.5e-3,
):
super().__init__(
E=E,
nu=nu,
rho=rho,
lam=lam,
mu=mu,
sampler=sampler,
yield_lower=yield_lower,
yield_higher=yield_higher,
use_von_mises=False,
)
[docs]
@ti.func
def update_F_S_Jp(self, J, F_tmp, U, S, V, Jp):
S_new = ti.Matrix.zero(gs.ti_float, 3, 3)
Jp_new = Jp
for d in ti.static(range(3)):
S_new[d, d] = min(max(S[d, d], 1 - self._yield_lower), 1 + self._yield_higher)
Jp_new *= S[d, d] / S_new[d, d]
F_new = U @ S_new @ V.transpose()
return F_new, S_new, Jp_new
[docs]
@ti.func
def update_stress(self, U, S, V, F_tmp, F_new, J, Jp, actu, m_dir):
# Hardening coefficient: material harder when compressed
h = ti.exp(10 * (1.0 - Jp))
mu, lam = self._mu * h, self._lam * h
r = U @ V.transpose()
stress = 2 * mu * (F_new - r) @ F_new.transpose() + ti.Matrix.identity(gs.ti_float, 3) * lam * J * (J - 1)
return stress
