def stresses(ε_x, ε_z, A):
r"""Calculate the membrane and vertical shear stresses for the given
horizontal and shear strain rates and fluidity"""
I = Identity(2)
tr = trace(ε_x)
ε_e = sqrt((inner(ε_x, ε_x) + inner(ε_z, ε_z) + tr**2) / 2)
μ = 0.5 * A**(-1 / n) * ε_e**(1 / n - 1)
return 2 * μ * (ε_x + tr * I), 2 * μ * ε_z
def M(ε, A):
r"""Calculate the membrane stress for a given strain rate and
fluidity"""
I = Identity(2)
tr_ε = trace(ε)
ε_e = sqrt((inner(ε, ε) + tr_ε**2) / 2)
μ = 0.5 * A**(-1 / n) * ε_e**(1 / n - 1)
return 2 * μ * (ε + tr_ε * I)
def M(ε, B):
I = Identity(2)
tr_ε = trace(ε)
ε_e = sqrt((inner(ε, ε) + tr_ε**2) / 2)
μ = 0.5 * B * ε_e**(1 / n - 1)
return 2 * μ * (ε + tr_ε * I)