def disp_def_cst(u, coords=(x, y, z), h_vec=(1, 1, 1)):
"""
Compute strain measures for C-CST elasticity, as defined
in [CST]_.
Parameters
----------
u : Matrix (3, 1), list
Displacement vector function to apply the micropolar operator.
coords : Tuple (3), optional
Coordinates for the new reference system. This is an optional
parameter it takes (x, y, z) as default.
h_vec : Tuple (3), optional
Scale coefficients for the new coordinate system. It takes
(1, 1, 1), as default.
Returns
-------
strain : Matrix (3, 3)
Strain tensor.
curvature : Matrix (3, 3)
Curvature tensor.
"""
strain = sym_grad(u, coords, h_vec)
curvature = S(1) / 4 * curl(curl(u, coords, h_vec), coords, h_vec)
return strain, dual_tensor(curvature)
def disp_def_micropolar(u, phi, coords=(x, y, z), h_vec=(1, 1, 1)):
"""
Compute strain measures for micropolar elasticity, as defined
in [NOW]_.
Parameters
----------
u : Matrix (3, 1), list
Displacement vector function to apply the micropolar operator.
phi : Matrix (3, 1), list
Microrrotation (pseudo)-vector function to apply the
micropolar operator.
coords : Tuple (3), optional
Coordinates for the new reference system. This is an optional
parameter it takes (x, y, z) as default.
h_vec : Tuple (3), optional
Scale coefficients for the new coordinate system. It takes
(1, 1, 1), as default.
Returns
-------
strain : Matrix (3, 3)
Strain tensor.
curvature : Matrix (3, 3)
Curvature tensor.
"""
strain = grad_vec(u, coords, h_vec) - dual_tensor(phi)
curvature = grad_vec(phi, coords, h_vec)
return strain, curvature
def test_dual_vector():
tensor = Matrix([[0, 3, -2], [-3, 0, 1], [2, -1, 0]])
vector = Matrix([1, 2, 3])
assert dual_vector(tensor) == vector
assert dual_tensor(vector) == tensor