import gstaichi as ti
import genesis as gs
from .base import Base
[docs]
@ti.data_oriented
class Elastic(Base):
"""
The elastic material class for MPM.
Note
----
Elastic objects is softened by multiplying the default E by 0.3.
Reference for the default values of `E` and `nu`:
https://github.com/taichi-dev/taichi_elements/blob/d19678869a28b09a32ef415b162e35dc929b792d/engine/mpm_solver.py#L201
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
'pbs' on supported platforms, 'random' otherwise.
model: str, optional
Stress model ('corotation', 'neohooken'). Default is 'corotation'.
"""
def __init__(
self,
E=3e5,
nu=0.2,
rho=1000.0,
lam=None,
mu=None,
sampler=None,
model="corotation",
):
if sampler is None:
sampler = "pbs" if gs.platform == "Linux" else "random"
super().__init__(E, nu, rho, lam, mu, sampler)
if model == "corotation":
self.update_stress = self.update_stress_corotation
elif model == "neohooken":
self.update_stress = self.update_stress_neohooken
else:
gs.raise_exception(f"Unrecognized constitutive model: {model}")
self._model = model
[docs]
@ti.func
def update_F_S_Jp(self, J, F_tmp, U, S, V, Jp):
F_new = F_tmp
S_new = S
Jp_new = Jp
return F_new, S_new, Jp_new
[docs]
@ti.func
def update_stress_corotation(self, U, S, V, F_tmp, F_new, J, Jp, actu, m_dir):
stress = 2 * self._mu * (F_new - U @ V.transpose()) @ F_new.transpose() + ti.Matrix.identity(
gs.ti_float, 3
) * self._lam * J * (J - 1)
return stress
[docs]
@ti.func
def update_stress_neohooken(self, U, S, V, F_tmp, F_new, J, Jp, actu, m_dir):
stress = self._mu * (F_tmp @ F_tmp.transpose()) + ti.Matrix.identity(gs.ti_float, 3) * (
self._lam * ti.log(J) - self._mu
)
return stress
@property
def model(self):
"""Stress model ('corotation', 'neohooken')"""
return self._model
