def F1(w):
u = w["disp"]
p = w["press"]
F = grad(u) + identity(u)
J = det(F)
Finv = inv(F)
return p * J * transpose(Finv) + mu * F
def A12(w):
u = w["disp"]
F = zeros_like(grad(u))
for i in range(3):
F[i, i] += 1.
F += grad(u)
J = det(F)
Finv = inv(F)
return J * transpose(Finv)
def F1(w):
u = w["disp"]
p = w["press"]
F = zeros_like(grad(u))
for i in range(3):
F[i, i] += 1.
F += grad(u)
J = det(F)
Finv = inv(F)
return p * J * transpose(Finv) + mu * F
def A11(w):
u = w["disp"]
p = w["press"]
eye = identity(u)
F = grad(u) + eye
J = det(F)
Finv = inv(F)
L = (p * J * np.einsum("lk...,ji...->ijkl...", Finv, Finv)
- p * J * np.einsum("jk...,li...->ijkl...", Finv, Finv)
+ mu * np.einsum("ik...,jl...->ijkl...", eye, eye))
return L
def A11(w):
u = w["disp"]
p = w["press"]
F = zeros_like(grad(u))
eye = zeros_like(grad(u))
for i in range(3):
F[i, i] += 1.
eye[i, i] += 1.
F += grad(u)
J = det(F)
Finv= inv(F)
L = (p * J * einsum("lk...,ji...->ijkl...", Finv, Finv)
- p * J * einsum("jk...,li...->ijkl...", Finv, Finv)
+ mu * einsum("ik...,jl...->ijkl...", eye, eye))
return L
def A12(w):
u = w["disp"]
F = grad(u) + identity(u)
J = det(F)
Finv = inv(F)
return J * transpose(Finv)
def deformation_gradient(w):
dudX = grad(w["displacement"])
F = dudX + identity(dudX)
return F, inv(F)
