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 a(u, v, w):
F, iF = deformation_gradient(w)
DF = grad(u)
dF = grad(v)
dFiF = mul(dF, iF)
DFiF = mul(DF, iF)
tr_DFiF_dFiF = ddot(transpose(dFiF), DFiF)
lnJ = np.log(det(F))
return (mu * ddot(DF, dF) - (lmbda * lnJ - mu) * tr_DFiF_dFiF +
lmbda * trace(dFiF) * trace(DFiF))
def A12(w):
u = w["disp"]
F = grad(u) + identity(u)
J = det(F)
Finv = inv(F)
return J * transpose(Finv)
def L(v, w):
F, iF = deformation_gradient(w)
dF = grad(v)
lnJ = np.log(det(F))
return mu * ddot(F, dF) + (lmbda * lnJ - mu) * ddot(transpose(iF), dF)