def test_equivalence(self):
young = 1000.0;
poisson = 0.3;
iso_mat = Material.create_isotropic(3, 1.0, young, poisson);
ortho_mat = Material.create_orthotropic(1.0,
np.ones(3)*young,
np.ones(6)*poisson,
np.ones(3)*(0.5*young/(1+poisson)));
self.assert_symmetry(ortho_mat.material_tensor, 3);
self.assertEqual(iso_mat.dim, ortho_mat.dim);
self.assertEqual(iso_mat.density, ortho_mat.density);
self.assert_array_almost_equal(iso_mat.material_tensor,
ortho_mat.material_tensor);
def test_isotropic_material(self):
young = 1000.0
poisson = 0.3
mat = Material.create_isotropic(3, 1.0, young, poisson)
self.assertEqual(3, mat.dim)
self.assertEqual(1.0, mat.density)
self.assert_symmetry(mat.material_tensor, mat.dim)
strain = np.array([
[1.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
])
stress = mat.strain_to_stress(strain)
self.assertAlmostEqual(
young * (1 - poisson) / (1 + poisson) / (1 - 2 * poisson),
stress[0, 0])
self.assertAlmostEqual(
young * poisson / (1 + poisson) / (1 - 2 * poisson), stress[1,
1])
self.assertAlmostEqual(
young * poisson / (1 + poisson) / (1 - 2 * poisson), stress[2,
2])
self.assertAlmostEqual(0.0, stress[0, 1])
self.assertAlmostEqual(0.0, stress[1, 0])
self.assertAlmostEqual(0.0, stress[0, 2])
self.assertAlmostEqual(0.0, stress[2, 0])
self.assertAlmostEqual(0.0, stress[1, 2])
self.assertAlmostEqual(0.0, stress[2, 1])
def test_isotropic_material(self):
young = 1000.0;
poisson = 0.3;
mat = Material.create_isotropic(3, 1.0, young, poisson);
self.assertEqual(3, mat.dim);
self.assertEqual(1.0, mat.density);
self.assert_symmetry(mat.material_tensor, mat.dim);
strain = np.array([
[1.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0], ]);
stress = mat.strain_to_stress(strain);
self.assertAlmostEqual(young * (1-poisson)/(1+poisson)/(1-2*poisson),
stress[0, 0]);
self.assertAlmostEqual(young * poisson /(1+poisson)/(1-2*poisson),
stress[1, 1]);
self.assertAlmostEqual(young * poisson /(1+poisson)/(1-2*poisson),
stress[2, 2]);
self.assertAlmostEqual(0.0, stress[0, 1]);
self.assertAlmostEqual(0.0, stress[1, 0]);
self.assertAlmostEqual(0.0, stress[0, 2]);
self.assertAlmostEqual(0.0, stress[2, 0]);
self.assertAlmostEqual(0.0, stress[1, 2]);
self.assertAlmostEqual(0.0, stress[2, 1]);
def single_triangle_2D_setup(self):
vertices = np.array([
[0.0, 0.0],
[1.0, 0.0],
[0.0, 1.0],
])
faces = np.array([[0, 1, 2]])
mesh = form_mesh(vertices, faces)
material = Material.create_isotropic(2, 1.0, 1.0, 0.0)
assembler = Assembler(mesh, material)
return assembler
def single_triangle_2D_setup(self):
vertices = np.array([
[0.0, 0.0],
[1.0, 0.0],
[0.0, 1.0],
]);
faces = np.array([
[0, 1, 2]
]);
mesh = form_mesh(vertices, faces);
material = Material.create_isotropic(2, 1.0, 1.0, 0.0);
assembler = Assembler(mesh, material);
return assembler;
def test_isotropic_material_2D(self):
young = 1000.0;
poisson = 0.3;
mat = Material.create_isotropic(2, 1.0, young, poisson);
self.assertEqual(2, mat.dim);
self.assertEqual(1.0, mat.density);
self.assert_symmetry(mat.material_tensor, mat.dim);
strain = np.array([ [1.0, 0.0], [0.0, 0.0] ]);
stress = mat.strain_to_stress(strain);
self.assertAlmostEqual(strain[0,0],
stress[0,0]/young - poisson*stress[1,1]/young );
self.assertAlmostEqual(strain[1,1],
stress[1,1]/young - poisson*stress[0,0]/young );
self.assertAlmostEqual(strain[0, 1],
stress[0,1] * (1+poisson) / young);
