def test_ref(self):
forwards = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
backward = finite_strain.DeformationGradientTensor( self.ubi0, self.ub )
for i in range(5):
m = i * 0.5
ef = forwards.finite_strain_ref( m )
eb = backward.finite_strain_lab( -m )
self.assertTrue( np.allclose( ef, -eb ) )
def test_lab(self):
forwards = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
backward = finite_strain.DeformationGradientTensor( self.ubi0, self.ub )
for i in range(5):
m = i * 0.5
ef = forwards.finite_strain_lab( m )
# this is a bit misleading - negative m puts you in the other frame
eb = backward.finite_strain_ref( -m )
self.assertTrue( np.allclose( ef, -eb ) )
def setUp(self):
# longer along the x-axis in the lab
# this is the a axis in the reference
self.ubi = np.array([[0,1,0],[-1.1,0,0],[0,0,1]],float)
self.ubi0 = np.eye(3)
self.ub0 = np.linalg.inv(self.ubi0)
self.dgt = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
def test_strain_ref(self):
from xfab.tools import ubi_to_u_and_eps
dzero_cell = indexing.ubitocellpars( self.ubi0 )
u, eps_xfab_ref_e6 = ubi_to_u_and_eps( self.ubi, dzero_cell )
dgt = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
eps_new = dgt.finite_strain_ref( m=0.5 )
self.assertTrue( np.allclose( dgt.U, u ) )
self.assertTrue( np.allclose( dgt.U, self.u ) )
self.assertTrue( np.allclose( finite_strain.symm_to_e6(eps_new), eps_xfab_ref_e6 ) )
self.assertTrue( np.allclose( finite_strain.e6_to_symm(eps_xfab_ref_e6), eps_new ) )
def test_strain_lab(self):
from xfab.tools import ubi_to_u_and_eps
dzero_cell = indexing.ubitocellpars( self.ubi0 )
u, eps_xfab_ref_e6 = ubi_to_u_and_eps( self.ubi, dzero_cell )
emat = finite_strain.e6_to_symm( eps_xfab_ref_e6 )
Exfab = np.dot(np.dot( u, emat), u.T )
dgt = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
eps_new = dgt.finite_strain_lab( m=0.5 )
self.assertTrue( np.allclose( dgt.U, u ) )
self.assertTrue( np.allclose( dgt.U, self.u ) )
self.assertTrue( np.allclose( eps_new, Exfab ) )
def test_svd(self):
dgt = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
u,s,vt = dgt.SVD
fcalc = np.dot( np.dot( u, np.diag(s)) , vt )
self.assertTrue( np.allclose( fcalc, dgt.F ) )
def test_polar(self):
dgt = finite_strain.DeformationGradientTensor( self.ubi, self.ub0 )
v,r,s = dgt.VRS
self.assertTrue( np.allclose( np.dot( v, r), dgt.F ) )
self.assertTrue( np.allclose( np.dot( r, s), dgt.F ) )