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fem_class.py
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fem_class.py
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import taichi as ti
import meshtaichi_patcher as mp
import numpy as np
@ti.data_oriented
class LoadModel:
def __init__(self,
filename,
v_norm=1
):
# load_mesh
model_type = filename.split('.')[-1]
if model_type == "node":
self.mesh_rawdata = mp.load_mesh_rawdata(filename)
self.mesh = mp.load_mesh(self.mesh_rawdata, relations=["CV", "VV", "CE", "EV", "FV", "FC", "FE"])
self.mesh.verts.place({
'x': ti.math.vec3,
'v': ti.math.vec3,
'pf': ti.math.vec3,
'f': ti.math.vec3,
'fe': ti.math.vec3,
'ox': ti.math.vec3
})
self.mesh.verts.x.from_numpy(self.mesh.get_position_as_numpy())
self.mesh.verts.ox.from_numpy(self.mesh.get_position_as_numpy())
self.mesh.verts.v.fill(0.0)
self.mesh.verts.pf.fill(0.0)
self.mesh.verts.f.fill(0.0)
self.mesh.verts.fe.fill(0.0)
self.indices = ti.field(ti.u32, shape=len(self.mesh.cells) * 4 * 3)
self.init_tet_indices()
else:
self.mesh_rawdata = mp.load_mesh_rawdata(filename)
self.mesh = mp.load_mesh(self.mesh_rawdata, relations=["FV"])
self.mesh.verts.place({'x': ti.math.vec3,
'ox': ti.math.vec3,
'rx': ti.math.vec3})
self.mesh.verts.x.from_numpy(self.mesh.get_position_as_numpy())
self.mesh.verts.ox.from_numpy(self.mesh.get_position_as_numpy())
self.mesh.verts.rx.from_numpy(self.mesh.get_position_as_numpy())
self.indices = ti.field(ti.i32, shape=len(self.mesh.faces) * 3)
self.init_surf_indices()
x_np = self.mesh.verts.rx.to_numpy()[:, 1]
line_min = np.where(x_np == x_np.min(0))[0]
line_max = np.where(x_np == x_np.max(0))[0]
self.min_len = len(line_min)
self.max_len = len(line_max)
self.line0 = ti.ndarray(dtype=ti.i32, shape=self.min_len)
self.line1 = ti.ndarray(dtype=ti.i32, shape=self.max_len)
self.line0 = line_min
self.line1 = line_max
self.v_norm = v_norm
self.vert_num = len(self.mesh.verts)
self.center = ti.Vector.field(3, ti.f32, shape=1)
self.I = ti.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]], ti.i32)
self.norm_volume_equipment()
@ti.kernel
def norm_volume_equipment(self):
if self.v_norm != 0:
for vert in self.mesh.verts:
vert.x *= self.v_norm
vert.ox *= self.v_norm
@ti.kernel
def init_surf_indices(self):
for f in self.mesh.faces:
for j in ti.static(range(3)):
self.indices[f.id * 3 + j] = f.verts[j].id
@ti.kernel
def init_tet_indices(self):
for c in self.mesh.cells:
ind = [[0, 2, 1], [0, 3, 2], [0, 1, 3], [1, 2, 3]]
for i in ti.static(range(4)):
for j in ti.static(range(3)):
self.indices[(c.id * 4 + i) * 3 + j] = c.verts[ind[i][j]].id
@ti.kernel
def cal_barycenter(self):
self.center[0].fill(0)
for i in self.mesh.verts.x:
self.center[0] += self.mesh.verts.x[i]
self.center[0] /= self.vert_num
@ti.data_oriented
class Implicit(LoadModel):
def __init__(self, filename, v_norm=1, replace_direction=0, replace_alpha=0):
super().__init__(filename)
self.de_list = []
self.v_norm = v_norm
self.replace_direction = replace_direction
self.replace_alpha = replace_alpha
self.rota_mat = ti.Matrix.field(3, 3, dtype=ti.f32, shape=1)
self.dt = 1.0
self.gravity = ti.Vector([0.0, -9.8, 0.0])
self.e = 7e6 # 杨氏模量
self.nu = 0.1 # 泊松系数
self.mu = self.e / (2 * (1 + self.nu))
self.la = self.e * self.nu / ((1 + self.nu) * (1 - 2 * self.nu))
self.density = 5e5
self.eta = 2 # 粘滞阻尼系数
self.E1 = 2.5
self.E2 = 1.5
self.cell_num = len(self.mesh.cells)
self.V = ti.field(dtype=ti.f32, shape=())
self.Dm = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num) # Dm
self.W = ti.field(ti.f32, shape=self.cell_num) # 四面体体积
self.B = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num) # Dm逆
self.m = ti.field(ti.f32, shape=self.vert_num) # 点的质量
self.F = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num)
self.F_old = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num)
self.E = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num)
self.b = ti.Vector.field(3, dtype=ti.f32, shape=self.vert_num)
self.r0 = ti.Vector.field(3, dtype=ti.f32, shape=self.vert_num)
self.p0 = ti.Vector.field(3, dtype=ti.f32, shape=self.vert_num)
self.dot_ans = ti.field(ti.f32, shape=())
self.r_2_scalar = ti.field(ti.f32, shape=())
self.mul_ans = ti.Vector.field(3, dtype=ti.f32, shape=self.vert_num)
self.norm_volume()
self.fem_pre_cal()
if self.replace_alpha:
self.replace(self.replace_direction, self.replace_alpha)
@ti.kernel
def reset(self):
for vert in self.mesh.verts:
vert.x = vert.ox
self.mesh.verts.v.fill(0.0)
self.mesh.verts.f.fill(0.0)
self.mesh.verts.fe.fill(0.0)
@ti.kernel
def norm_volume(self):
for cell in self.mesh.cells:
v = ti.Matrix.zero(ti.f32, 3, 3)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
v[j, i] = self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
self.V[None] += -(1.0 / 6.0) * v.determinant()
if self.v_norm != 0:
for vert in self.mesh.verts:
vert.x *= 1000 / self.V[None] * self.v_norm
vert.ox *= 1000 / self.V[None] * self.v_norm
@ti.kernel
def replace(self, direction: ti.i32, alpha: ti.f32):
if direction == 0:
self.rota_mat[0] = ([[1, 0, 0],
[0, ti.cos(alpha), ti.sin(alpha)],
[0, -ti.sin(alpha), ti.cos(alpha)]
])
elif direction == 1:
self.rota_mat[0] = ([[ti.cos(alpha), 0, -ti.sin(alpha)],
[0, 1, 0],
[ti.sin(alpha), 0, ti.cos(alpha)],
])
else:
self.rota_mat[0] = ([[ti.cos(alpha), ti.sin(alpha), 0],
[-ti.sin(alpha), ti.cos(alpha), 0],
[0, 0, 1]
])
for vert in self.mesh.verts.ox:
Tox = self.mesh.verts.ox[vert] @ self.rota_mat[0]
Tx = self.mesh.verts.x[vert] @ self.rota_mat[0]
self.mesh.verts.ox[vert] = Tox
self.mesh.verts.x[vert] = Tx
@ti.kernel
def fem_pre_cal(self):
for cell in self.mesh.cells:
for i in ti.static(range(3)):
for j in ti.static(range(3)):
self.Dm[cell.id][j, i] = \
self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
self.B[cell.id] = self.Dm[cell.id].inverse() # Dm逆
self.W[cell.id] = -(1.0 / 6.0) * self.Dm[cell.id].determinant() # 四面体体积
for i in ti.static(range(4)):
self.m[cell.verts[i].id] += 0.25 * self.density * self.W[cell.id] # 把体元质量均分到四个顶点
@ti.kernel
def fem_get_force_sim_Co_rotated(self): # 实时力计算
for vert in self.mesh.verts:
vert.fe += self.gravity * self.m[vert.id]
vert.f = vert.fe
vert.pf = vert.f # pf是外力
# if vert.fe[0] != 0 or vert.fe[1] != 0 or vert.fe[2] != 0:
# print(vert.fe)
for cell in self.mesh.cells:
Ds = ti.Matrix.zero(ti.f32, 3, 3)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
Ds[j, i] \
= self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
self.F[cell.id] = Ds @ self.B[cell.id]
U, sig, V = self.ssvd(self.F[cell.id])
P = 2 * self.mu * (self.F[cell.id] - U @ V.transpose())
H = -self.W[cell.id] * P @ self.B[cell.id].transpose()
for i in ti.static(range(3)):
fi = ti.Vector([H[0, i], H[1, i], H[2, i]])
self.mesh.verts.f[cell.verts[i].id] += fi
self.mesh.verts.f[cell.verts[3].id] += -fi
@ti.kernel
def fem_get_force_Kelvin(self): # 实时力计算
for vert in self.mesh.verts:
vert.f = self.gravity * self.m[vert.id] + vert.fe
# if vert.fe[0] != 0 or vert.fe[1] != 0 or vert.fe[2] != 0:
# print(vert.fe)
for cell in self.mesh.cells:
Ds = ti.Matrix.zero(ti.f32, 3, 3)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
Ds[j, i] \
= self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
self.F[cell.id] = Ds @ self.B[cell.id]
U, sig, V = self.ssvd(self.F[cell.id])
sigma = 1 / 2 * (self.F[cell.id].transpose() @ self.F[cell.id] - self.I)
sigma_old = 1 / 2 * (self.F_old[cell.id].transpose() @ self.F_old[cell.id] - self.I)
# delta_epsilon = sigma - sigma_old
# sigma_c = self.eta * delta_epsilon / self.dt
sigma_c = self.E1 ** 2 * sigma / (self.E1 + self.E2) * (
1 - ti.exp((self.E1 - self.E2) * self.dt / self.eta))
P = 2 * self.mu * (self.F[cell.id] - U @ V.transpose()) + \
self.la * ((U @ V.transpose()).transpose() @ self.F[cell.id] - self.I).trace() * (U @ V.transpose())
P += sigma_c
H = -self.W[cell.id] * P @ self.B[cell.id].transpose()
for i in ti.static(range(3)):
fi = ti.Vector([H[0, i], H[1, i], H[2, i]])
self.mesh.verts.f[cell.verts[i].id] += fi
self.mesh.verts.f[cell.verts[3].id] += -fi
self.F_old[cell.id] = self.F[cell.id]
@ti.kernel
def fem_get_force_Neo_Hookean(self): # 实时力计算
for vert in self.mesh.verts:
vert.f = self.gravity * self.m[vert.id] + vert.fe
for cell in self.mesh.cells:
Ds = ti.Matrix.zero(ti.f32, 3, 3)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
Ds[j, i] \
= self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
self.F[cell.id] = Ds @ self.B[cell.id]
J = self.F[cell.id].determinant()
logJ = ti.log(J)
F_inv_tran = self.F[cell.id].inverse().transpose()
P = self.mu * (self.F[cell.id] - F_inv_tran) + self.la * logJ * F_inv_tran
H = -self.W[cell.id] * P @ self.B[cell.id].transpose()
for i in ti.static(range(3)):
fi = ti.Vector([H[0, i], H[1, i], H[2, i]])
self.mesh.verts.f[cell.verts[i].id] += fi
self.mesh.verts.f[cell.verts[3].id] += -fi
@ti.kernel
def fem_get_force_STVK(self): # 实时力计算
for vert in self.mesh.verts:
vert.f = self.gravity * self.m[vert.id] + vert.fe
for cell in self.mesh.cells:
Ds = ti.Matrix.zero(ti.f32, 3, 3)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
Ds[j, i] \
= self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
self.F[cell.id] = Ds @ self.B[cell.id]
self.E[cell.id] = 0.5 * (self.F[cell.id].transpose() @ self.F[cell.id] - self.I)
P = self.F[cell.id] @ (2 * self.mu * self.E[cell.id] + self.la * self.E[cell.id].trace() * self.I)
H = -self.W[cell.id] * P @ self.B[cell.id].transpose()
for i in ti.static(range(3)):
fi = ti.Vector([H[0, i], H[1, i], H[2, i]])
self.mesh.verts.f[cell.verts[i].id] += fi
self.mesh.verts.f[cell.verts[3].id] += -fi
@ti.kernel
def fem_get_b(self):
for vert in self.mesh.verts:
self.b[vert.id] = self.m[vert.id] * vert.v + self.dt * vert.f
@ti.kernel
def mat_mul_sim_Co_rotated(self, ret: ti.template(), vel: ti.template()):
for vert in self.mesh.verts:
ret[vert.id] = vel[vert.id] * self.m[vert.id]
for cell in self.mesh.cells:
verts = cell.verts
W_c = self.W[cell.id]
B_c = self.B[cell.id]
for u in ti.static(range(4)):
for d in (range(3)):
dD = ti.Matrix.zero(ti.f32, 3, 3)
if u == 3:
for j in ti.static(range(3)):
dD[d, j] = -1
else:
dD[d, u] = 1
dF = dD @ B_c
dP = 2.0 * self.mu * dF
dH = -W_c * dP @ B_c.transpose()
for i in ti.static(range(3)):
for j in ti.static(range(3)):
tmp = (vel[verts[i].id][j] - vel[verts[3].id][j])
ret[verts[u].id][d] += -self.dt ** 2 * dH[j, i] * tmp
@ti.kernel
def mat_mul_Kelvin(self, ret: ti.template(), vel: ti.template()):
for vert in self.mesh.verts:
ret[vert.id] = vel[vert.id] * self.m[vert.id]
for cell in self.mesh.cells:
verts = cell.verts
W_c = self.W[cell.id]
B_c = self.B[cell.id]
for u in ti.static(range(4)):
for d in (range(3)):
dD = ti.Matrix.zero(ti.f32, 3, 3)
if u == 3:
for j in ti.static(range(3)):
dD[d, j] = -1
else:
dD[d, u] = 1
dF = dD @ B_c
sigma = 1 / 2 * (dF.transpose() @ self.F[cell.id]) + 1 / 2 * (self.F[cell.id].transpose() @ dF)
U, sig, V = self.ssvd(dF)
dP = 2 * self.mu * (dF - U @ V.transpose()) + \
self.la * ((U @ V.transpose()).transpose() @ self.F[cell.id] - self.I).trace()
sigma_c = self.E1 ** 2 / (self.E1 + self.E2) * (
1 - ti.exp((self.E1 - self.E2) * self.dt / self.eta))
sigma *= sigma_c
dP += sigma
dH = -W_c * dP @ B_c.transpose()
for i in ti.static(range(3)):
for j in ti.static(range(3)):
tmp = (vel[verts[u].id][d] - vel[verts[3].id][d])
ret[verts[u].id][d] += -self.dt ** 2 * dH[j, i] * tmp
@ti.kernel
def mat_mul_STVK(self, ret: ti.template(), vel: ti.template()):
for vert in self.mesh.verts:
ret[vert.id] = vel[vert.id] * self.m[vert.id]
for cell in self.mesh.cells:
verts = cell.verts
W_c = self.W[cell.id]
B_c = self.B[cell.id]
E_c = self.E[cell.id]
F_c = self.F[cell.id]
for u in ti.static(range(4)):
for d in (range(3)):
dD = ti.Matrix.zero(ti.f32, 3, 3)
if u == 3:
for j in ti.static(range(3)):
dD[d, j] = -1
else:
dD[d, u] = 1
dF = dD @ B_c
dE = 0.5 * (dF.transpose() @ F_c + F_c.transpose() @ dF)
dP = dF @ (2 * self.mu * E_c + self.la * E_c.trace() * self.I) + F_c @ (
2 * self.mu * dE + self.la * dE.trace() * self.I)
dH = -W_c * dP @ B_c.transpose()
for i in ti.static(range(3)):
for j in ti.static(range(3)):
tmp = (vel[verts[i].id][j] - vel[verts[3].id][j])
ret[verts[u].id][d] += -self.dt ** 2 * dH[j, i] * tmp
@ti.kernel
def mat_mul_sim_Neo_Hookean(self, ret: ti.template(), vel: ti.template()):
for vert in self.mesh.verts:
ret[vert.id] = vel[vert.id] * self.m[vert.id]
for cell in self.mesh.cells:
verts = cell.verts
W_c = self.W[cell.id]
B_c = self.B[cell.id]
F = self.F[cell.id]
J = F.determinant()
logJ = ti.log(J)
F_inv_tran = F.inverse().transpose()
for u in ti.static(range(4)):
for d in (range(3)):
dD = ti.Matrix.zero(ti.f32, 3, 3)
if u == 3:
for j in ti.static(range(3)):
dD[d, j] = -1
else:
dD[d, u] = 1
dF = dD @ B_c
term = (F.inverse() @ dF).trace() * F_inv_tran
FDFF = F_inv_tran @ dF.transpose() @ F_inv_tran
dP = self.mu * dF + (self.mu - self.la * logJ) * FDFF + self.la * term
dH = -W_c * dP @ B_c.transpose()
for i in ti.static(range(3)):
for j in ti.static(range(3)):
tmp = (vel[verts[i].id][j] - vel[verts[3].id][j])
ret[verts[i].id][j] += -self.dt ** 2 * dH[d, u] * tmp
def cg(self, n_iter, epsilon):
# self.mat_mul_STVK(self.mul_ans, self.mesh.verts.v)
self.mat_mul_sim_Co_rotated(self.mul_ans, self.mesh.verts.v)
# self.mat_mul_sim_Neo_Hookean(self.mul_ans, self.mesh.verts.v)
# self.mat_mul_Kelvin(self.mul_ans, self.mesh.verts.v)
self.add(self.r0, self.b, -1, self.mul_ans)
self.p0.copy_from(self.r0)
r_2 = self.dot(self.r0, self.r0)
r_2_init = r_2
r_2_new = r_2
for _ in ti.static(range(n_iter)):
# self.mat_mul_STVK(self.mul_ans, self.p0)
# self.mat_mul_sim_Neo_Hookean(self.mul_ans, self.p0)
self.mat_mul_sim_Co_rotated(self.mul_ans, self.p0)
# self.mat_mul_Kelvin(self.mul_ans, self.p0)
dot_ans = self.dot(self.p0, self.mul_ans)
alpha = r_2_new / (dot_ans + epsilon)
self.add(self.mesh.verts.v, self.mesh.verts.v, alpha, self.p0)
self.add(self.r0, self.r0, -alpha, self.mul_ans)
r_2 = r_2_new
r_2_new = self.dot(self.r0, self.r0)
if r_2_new <= r_2_init * epsilon ** 2:
break
beta = r_2_new / r_2
self.add(self.p0, self.r0, beta, self.p0)
self.add(self.mesh.verts.x, self.mesh.verts.x, self.dt, self.mesh.verts.v)
@ti.kernel
def add(self, ans: ti.template(), a: ti.template(), k: ti.f32, x3: ti.template()):
for i in ans:
ans[i] = a[i] + k * x3[i]
@ti.kernel
def dot(self, x1: ti.template(), x2: ti.template()) -> ti.f32:
ans = 0.0
for i in x1:
ans += x1[i].dot(x2[i])
return ans
@ti.kernel
def boundary_condition(self):
bounds = ti.Vector([0.2, 0.1, 0.2])
for vert in self.mesh.verts:
for i in ti.static(range(3)):
if vert.x[i] < -bounds[i]:
vert.x[i] = -bounds[i]
if vert.v[i] < 0.0:
vert.v[i] = 0.0
if vert.x[i] > bounds[i]:
vert.x[i] = bounds[i]
if vert.v[i] > 0.0:
vert.v[i] = 0.0
if vert.x[1] + bounds[1] < 0.002 and (vert.v[0] != 0 or vert.v[2] != 0):
vert.v[0] *= 0.1
vert.v[2] *= 0.1
@ti.kernel
def decay(self):
# for vert in self.mesh.verts:
# for i in range(3):
# if vert.v[i] <= 1e-4 and ti.math.length(vert.f) <= 0.1:
# vert.v[i] = 0
self.mesh.verts.fe.fill(0)
@ti.kernel
def Viscoelasticity(self):
for vert in self.mesh.verts:
decay = vert.f - vert.pf # decay是外力+内力-外力，即为纯内力
vert.f -= 0.8 * decay # 外力+内力-0.8*内力，即点力=外力+0.2*内力
# E1 = 0.1
# E2 = 0.1
# N = 0.9
# for vert in self.mesh.verts:
# f = vert.f - vert.pf
# decay = E1*f + E1**2*f/(E1+E2)*(1-ti.exp(-(E1+E2)*self.dt/N))
# print(decay)
# vert.f -= decay
def call_F(self):
de = self.F.to_numpy()
de_sum = np.sum(de) / len(de)
self.de_list.append(de_sum)
def substep(self, step):
for i in range(step):
self.fem_get_force_sim_Co_rotated()
self.Viscoelasticity()
# self.fem_get_force_Kelvin()
# self.fem_get_force_STVK()
# self.fem_get_force_Neo_Hookean()
self.fem_get_b()
self.cg(5, 1e-5)
self.boundary_condition()
self.decay()
self.call_F()
@ti.func
def ssvd(self, fai):
U, sig, V = ti.svd(fai)
if U.determinant() < 0:
for i in ti.static(range(3)):
U[i, 2] *= -1
sig[2, 2] = -sig[2, 2]
if V.determinant() < 0:
for i in ti.static(range(3)):
V[i, 2] *= -1
sig[2, 2] = -sig[2, 2]
return U, sig, V
# @ti.data_oriented
# class Explicit(LoadModel): # This class only for tetrahedron
# def __init__(self, filename, v_norm=1):
# super().__init__(filename)
# self.v_norm = v_norm
#
# self.dt = 7e-4
# self.gravity = ti.Vector([0.0, -9.8, 0.0])
# self.e = 2e6 # 杨氏模量
# self.nu = 0.1 # 泊松系数
# self.mu = self.e / (2 * (1 + self.nu))
# self.la = self.e * self.nu / ((1 + self.nu) * (1 - 2 * self.nu))
# self.density = 1e5
#
# self.cell_num = len(self.mesh.cells)
# self.V = ti.field(dtype=ti.f32, shape=())
# self.Dm = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num) # Dm
# self.W = ti.field(ti.f32, shape=self.cell_num) # 四面体体积
# self.B = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num) # Dm逆
# self.m = ti.field(ti.f32, shape=self.vert_num) # 点的质量
# self.F = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num)
# self.E = ti.Matrix.field(3, 3, ti.f32, shape=self.cell_num)
#
# self.norm_volume()
# self.fem_pre_cal()
#
# @ti.kernel
# def reset(self):
# for vert in self.mesh.verts:
# vert.x = vert.ox
# self.mesh.verts.v.fill(0.0)
# self.mesh.verts.f.fill(0.0)
#
# @ti.kernel
# def norm_volume(self):
# for cell in self.mesh.cells:
# v = ti.Matrix.zero(ti.f32, 3, 3)
# for i in ti.static(range(3)):
# for j in ti.static(range(3)):
# v[j, i] = self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
# self.V[None] += -(1.0 / 6.0) * v.determinant()
# if self.v_norm == 1:
# for vert in self.mesh.verts:
# vert.x *= 1000 / self.V[None]
# vert.ox *= 1000 / self.V[None]
#
# @ti.kernel
# def fem_pre_cal(self): # fem参数预计算
# self.V[None] = 0
# for cell in self.mesh.cells:
# for i in ti.static(range(3)):
# for j in ti.static(range(3)):
# self.Dm[cell.id][j, i] \
# = self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
# self.B[cell.id] = self.Dm[cell.id].inverse()
# self.W[cell.id] = -(1.0 / 6.0) * self.Dm[cell.id].determinant()
# self.V[None] += self.W[cell.id]
# for i in ti.static(range(4)):
# self.m[cell.verts[i].id] += 0.25 * self.density * self.W[cell.id] # 把体元质量均分到四个顶点
#
# @ti.kernel
# def fem_get_force(self): # 实时力计算
# for vert in self.mesh.verts:
# vert.f = self.gravity * self.m[vert.id]
# for cell in self.mesh.cells:
# Ds = ti.Matrix.zero(ti.f32, 3, 3)
# for i in ti.static(range(3)):
# for j in ti.static(range(3)):
# Ds[j, i] \
# = self.mesh.verts.x[cell.verts[i].id][j] - self.mesh.verts.x[cell.verts[3].id][j]
# self.F[cell.id] = Ds @ self.B[cell.id]
# self.E[cell.id] = 0.5 * (self.F[cell.id].transpose() @ self.F[cell.id] - self.I)
# U, sig, V = self.ssvd(self.F[cell.id])
# P = 2 * self.mu * (self.F[cell.id] - U @ V.transpose())
# # P = self.F[cell.id] @ (2 * self.mu * self.E[cell.id] + self.la * self.E[cell.id].trace() * self.I)
# H = -self.W[cell.id] * P @ self.B[cell.id].transpose()
# for i in ti.static(range(3)):
# fi = ti.Vector([H[0, i], H[1, i], H[2, i]])
# self.mesh.verts.f[cell.verts[i].id] += fi
# self.mesh.verts.f[cell.verts[3].id] += -fi
#
# @ti.func
# def ssvd(self, fai):
# U, sig, V = ti.svd(fai)
# if U.determinant() < 0:
# for i in ti.static(range(3)):
# U[i, 2] *= -1
# sig[2, 2] = -sig[2, 2]
# if V.determinant() < 0:
# for i in ti.static(range(3)):
# V[i, 2] *= -1
# sig[2, 2] = -sig[2, 2]
# return U, sig, V
#
# @ti.kernel
# def explicit_time_integral(self):
# for vert in self.mesh.verts:
# vert.v += self.dt * vert.f / self.m[vert.id] * 0.0000125
# vert.x += vert.v * self.dt
#
# @ti.kernel
# def boundary_condition(self):
# bounds = ti.Vector([1.0, 0.1, 1.0])
# for vert in self.mesh.verts:
# for i in ti.static(range(3)):
# if vert.x[i] < -bounds[i]:
# vert.x[i] = -bounds[i]
# if vert.v[i] < 0.0:
# vert.v[i] = 0.0
# if vert.x[i] > bounds[i]:
# vert.x[i] = bounds[i]
# if vert.v[i] > 0.0:
# vert.v[i] = 0.0
#
# def substep(self, step):
# for i in range(step):
# self.fem_get_force()
# self.explicit_time_integral()
# self.boundary_condition()