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 C(T):
return E / (1 + nu) * (T + nu / (1 - nu) * eye(trace(T), 2))
def C(T):
"""Linear-elastic stress-strain relationship."""
return 2. * Mu * T + Lambda * eye(trace(T), T.shape[0])