utils package

Submodules

utils.abaqus module

utils.abaqus.get_results_from_json(fname: str) → Dict

Read homogenization results from json and return compliance tensors

Parameters:

fname (str) – path to json file

Raises:

ValueError – if json file does not contain all required data

Returns:

dictionary with keys ‘job’, ‘name’, ‘compliance_tensors_M’

Return type:

Dict

utils.abaqus.write_abaqus_inp(lat: Lattice, strut_radii: Iterable, metadata: Dict[str, str], loading: List[Tuple] = [(1, 1, 1.0), (1, 2, 1.0), (1, 3, 1.0), (2, 1, 0.5), (2, 2, 0.5), (2, 3, 0.5)], fname: str | None = None, element_type: str | None = 'B31')

Write abaqus input script for a specific lattice and loading

Parameters:

• lat (Lattice) – Lattice

• loading (List[Tuple]) – list of 3-element tuples where first element is reference point number second is degree of freedom to which displacement is applied and third is the magnitude of displacement

• fname (Optional[str], optional) – name of input script file or stream to write to

• metadata (Dict[str, str]) – dictionary that will be written in header

• lat – Lattice object

• loading – list of 3-element tuples where first element is reference point number, second is degree of freedom to which displacement is applied and third is the magnitude of displacement

• metadata – Extra information to put in the *Header section

• fname – if fname is provided, output is written to file fname. Otherwise, return lines of text. Defaults to None.

utils.abaqus.write_abaqus_inp_nopbc(lat: Lattice, strut_radii: ndarray, metadata: Dict[str, str], fname: str | None = None, element_type: str | None = 'B31', node_sets: Dict[str, Iterable] | None = None, boundary_conditions: Dict[str, Iterable] | None = None)

Write abaqus input script for a specific lattice and loading

utils.abaqus.write_abaqus_inp_normals(lat: Lattice, strut_radii: ndarray, metadata: Dict[str, str], fname: str | None = None, element_type: str | None = 'B31', loading: List[Tuple] = [(1, 1, 1.0), (1, 2, 1.0), (1, 3, 1.0), (2, 1, 0.5), (2, 2, 0.5), (2, 3, 0.5)], mesh_params: Dict[str, float | int] = {'max_length': 1, 'min_div': 3})

Write abaqus input script for a specific lattice and loading

Parameters:

• lat (Lattice) – Lattice

• loading (List[Tuple]) – list of 3-element tuples where first element is reference point number second is degree of freedom to which displacement is applied and third is the magnitude of displacement

• fname (Optional[str], optional) – name of input script file or stream to write to

• metadata (Dict[str, str]) – dictionary that will be written in header

• lat – Lattice object

• loading – list of 3-element tuples where first element is reference point number, second is degree of freedom to which displacement is applied and third is the magnitude of displacement

• metadata – Extra information to put in the *Header section

• fname – if fname is provided, output is written to file fname. Otherwise, return lines of text. Defaults to None.

utils.elasticity_func module

utils.elasticity_func.Mandel_rot_matrix_inplace(Q: ndarray, R: ndarray) → None

Fill the 6x6 rotation matrix for Mandel stress/strain vector

Parameters:

• Q (Union[np.ndarray, Tensor]) – 3x3 rotation matrix

• R (Union[np.ndarray, Tensor]) – 6x6 rotation matrix to be filled

utils.elasticity_func.Mandel_rot_matrix_numpy(Q: ndarray) → ndarray

Generate 6x6 rotation matrix for Mandel stress/strain vector

Parameters:

Q (np.ndarray) – 3x3 rotation matrix

Returns:

6x6 rotation matrix for Mandel stress/strain vector

Return type:

np.ndarray

utils.elasticity_func.Voigt_rot_matrix_strain_inplace(Q: ndarray, R: ndarray) → None

Fill the 6x6 rotation matrix for Voigt strain vector

Parameters:

• Q (Union[np.ndarray, Tensor]) – 3x3 rotation matrix

• R (Union[np.ndarray, Tensor]) – 6x6 rotation matrix to be filled

utils.elasticity_func.Voigt_rot_matrix_strain_numpy(Q: ndarray) → ndarray

Generate 6x6 rotation matrix for Voigt strain vector

Parameters:

Q (np.ndarray) – 3x3 rotation matrix

Returns:

6x6 rotation matrix for Voigt strain vector

Return type:

np.ndarray

utils.elasticity_func.Voigt_rot_matrix_stress_inplace(Q: ndarray, R: ndarray) → None

Fill the 6x6 rotation matrix for Voigt stress vector

Parameters:

• Q (Union[np.ndarray, Tensor]) – 3x3 rotation matrix

• R (Union[np.ndarray, Tensor]) – 6x6 rotation matrix to be filled

utils.elasticity_func.Voigt_rot_matrix_stress_numpy(Q: ndarray) → ndarray

Generate 6x6 rotation matrix for Voigt stress vector

Parameters:

Q (np.ndarray) – 3x3 rotation matrix

Returns:

6x6 rotation matrix for Voigt stress vector

Return type:

np.ndarray

utils.elasticity_func.Youngs_modulus(S: ndarray, d: ndarray) → ndarray

Calculate Young’s modulus in a specific direction

Parameters:

• S (np.ndarray) – Compliance tensor (3,3,3,3)

• d (np.ndarray) – Direction vector (…,3)

Returns:

_description_

Return type:

np.ndarray

utils.elasticity_func.compliance_4th_order_to_Voigt(S: ndarray) → ndarray

Convert 4th order compliance tensor to Voigt notation

Parameters:

S (np.ndarray) – 4th order compliance tensor

Returns:

6x6 Voigt notation compliance matrix

Return type:

np.ndarray

utils.elasticity_func.compliance_Mandel_to_Voigt(S: ndarray) → ndarray

Convert Mandel notation compliance matrix to Voigt notation

Parameters:

S (np.ndarray) – 6x6 Mandel notation compliance matrix

Returns:

6x6 Voigt notation compliance matrix

Return type:

np.ndarray

utils.elasticity_func.compliance_Voigt_to_4th_order(S: ndarray) → ndarray

Convert Voigt notation compliance matrix to 4th order tensor

Parameters:

S (np.ndarray) – 6x6 Voigt notation compliance matrix

Returns:

4th order compliance tensor

Return type:

np.ndarray

utils.elasticity_func.compliance_Voigt_to_Mandel(S: ndarray) → ndarray

Convert Voigt notation compliance matrix to Mandel notation

Parameters:

S (np.ndarray) – 6x6 Voigt notation compliance matrix

Returns:

6x6 Mandel notation compliance matrix

Return type:

np.ndarray

utils.elasticity_func.numpy_Mandel_to_cart_4(C: ndarray) → ndarray

Convert 6x6 Mandel notation tensor to 4th order tensor

Parameters:

C (np.ndarray) – Mandel notation tensor (…,6,6)

Returns:

4th order tensor of shape (…,3,3,3,3)

Return type:

np.ndarray

utils.elasticity_func.numpy_cart_4_to_Mandel(_C: ndarray) → ndarray

Convert 4th order tensor to 6x6 Mandel notation

Parameters:

_C (np.ndarray) – 4th order tensor of shape (…,3,3,3,3)

Returns:

6x6 Mandel notation tensor

Return type:

np.ndarray

utils.elasticity_func.rotate_4th_order(T: ndarray, Q: ndarray) → ndarray

Rotate 4th order tensor to a new coordinate system

Parameters:

• T (np.ndarray) – 3x3 rotation matrix

• Q (np.ndarray) – 4th order tensor

Returns:

Rotated 4th order tensor

Return type:

np.ndarray

utils.elasticity_func.rotate_Voigt_compliance(S: ndarray, R: ndarray) → ndarray

Rotate 6x6 compliance matrix in Voigt notation

Parameters:

• S (np.ndarray) – 6x6 Voigt compliance matrix

• R (np.ndarray) – 3x3 rotation matrix

Returns:

Rotated 6x6 Voigt compliance matrix

Return type:

np.ndarray

utils.elasticity_func.rotate_Voigt_stiffness(C: ndarray, R: ndarray) → ndarray

Rotate 6x6 stiffness matrix in Voigt notation

Parameters:

• C (np.ndarray) – 6x6 Voigt stiffness matrix

• R (np.ndarray) – 3x3 rotation matrix

Returns:

Rotated 6x6 Voigt stiffness matrix

Return type:

np.ndarray

utils.elasticity_func.stiffness_4th_order_to_Voigt(C: ndarray) → ndarray

Convert 4th order stiffness tensor to Voigt notation

Parameters:

C (np.ndarray) – 4th order stiffness tensor

Raises:

ValueError – Wrong shape of C

Returns:

6x6 Voigt notation stiffness matrix

Return type:

np.ndarray

utils.elasticity_func.stiffness_Mandel_to_Voigt(C: ndarray) → ndarray

Convert Mandel notation stiffness matrix to Voigt notation

Parameters:

C (np.ndarray) – 6x6 Mandel notation stiffness matrix

Returns:

6x6 Voigt notation stiffness matrix

Return type:

np.ndarray

utils.elasticity_func.stiffness_Voigt_to_4th_order(C: ndarray) → ndarray

Convert Voigt notation stiffness matrix to 4th order tensor

Parameters:

C (np.ndarray) – 6x6 Voigt notation stiffness matrix

Returns:

4th order stiffness tensor

Return type:

np.ndarray

utils.elasticity_func.stiffness_Voigt_to_Mandel(C: ndarray) → ndarray

Convert Voigt notation stiffness matrix to Mandel notation

Parameters:

C (np.ndarray) – 6x6 Voigt notation stiffness matrix

Returns:

6x6 Mandel notation stiffness matrix

Return type:

np.ndarray

utils.elasticity_func.strain_to_Voigt_inplace(e: ndarray, x: ndarray) → None

Fill Voigt notation vector from 2nd order strain tensor

Parameters:

• e (Union[np.ndarray, Tensor]) – 2nd order strain tensor

• x (Union[np.ndarray, Tensor]) – Voigt strain vector

utils.elasticity_func.strain_to_Voigt_numpy(e: ndarray) → ndarray

Convert 2nd order strain tensor to Voigt notation

Parameters:

e (np.ndarray) – 2nd order strain tensor

Returns:

Voigt strain vector

Return type:

np.ndarray

utils.elasticity_func.stress_to_Voigt_inplace(s: ndarray, x: ndarray) → None

Fill Voigt notation vector from 2nd order stress tensor

Parameters:

• s (Union[np.ndarray, Tensor]) – 2nd order stress tensor

• x (Union[np.ndarray, Tensor]) – Voigt stress vector

utils.elasticity_func.stress_to_Voigt_numpy(s: ndarray) → ndarray

Convert 2nd order stress tensor to Voigt notation

Parameters:

s (np.ndarray) – 2nd order stress tensor

Returns:

Voigt stress vector

Return type:

np.ndarray

utils.elasticity_func.tens_2d_to_Mandel_inplace(s: ndarray, x: ndarray) → None

Fill Mandel vector from 2nd order tensor

Parameters:

• s (Union[np.ndarray, Tensor]) – 2nd order tensor

• x (Union[np.ndarray, Tensor]) – Mandel vector

utils.elasticity_func.tens_2d_to_Mandel_numpy(s: ndarray) → ndarray

Convert 2nd order tensor to Mandel vector

Parameters:

s (np.ndarray) – 2nd order tensor

Returns:

Mandel vector

Return type:

np.ndarray

utils.plotting module

utils.plotting.plotly_scaling_surf(C: ndarray, rel_dens: Iterable[float], title: str = '', fig: Figure | None = None, subplot: dict | None = None, resolution: int = 100j) → Figure

Plot the surface of scaling exponent for a given stiffness tensor

Parameters:

• C (np.ndarray) – stacked compliance tensors [n_rel_dens, 3,3,3,3]

• rel_dens (Iterable[float]) – corresponding relative densities

• title (str, optional) – title for plot. Defaults to ‘’.

• fig (Optional[dict], go.Figure) – can pass an existing figure. Defaults to None.

• subplot (Optional[dict], optional) – subplot arguments. Expect keys [‘index’,’ncol’]. Defaults to None.

Returns:

plotly figure

Return type:

go.Figure

utils.plotting.plotly_tensor_projection(C: ndarray, point_func: Callable | None = None, title: str = '', fig: Figure | None = None, subplot: dict | None = None, clim: Tuple[float, float] | None = None, resolution: complex = 100j) → Figure

Plot a projection of 4-th order tensor using plotly

Parameters:

• C (np.ndarray) – 4-th order tensor of shape (3,3,3,3) or (1,3,3,3,3)

• point_func (Optional[Callable]) – function to apply point-wise to projections.

• title (str, optional) – plot title

• fig (Optional[go.Figure]) – existing figure. If None, a new figure is created.

• subplot (Optional[dict]) – dictionary with keys [‘index’,’ncol’] to pick the subplot

• clim (Optional[Tuple[float, float]]) – limits of color scale

• resolution (complex, optional) – resolution of grid on the sphere given as complex number. Defaults to 100j.

Returns:

Resulting plotly figure

Return type:

go.Figure

utils.plotting.plotly_unit_cell_3d(lat: Lattice, repr: Literal['cropped', 'fundamental'] = 'cropped', coords: Literal['reduced', 'transformed'] = 'reduced', show_node_numbers: bool = False, fig: Figure | None = None, subplot: dict | None = None, highlight_nodes: Iterable | None = None, highlight_edges: Iterable | None = None, show_uc_box: bool = False) → Figure

Plot unit cell in 3D using plotly

Parameters:

• lat (Lattice) – Unit cell to plot

• repr (Literal["cropped", "fundamental"], optional) – Representation of edges. Defaults to ‘cropped’.

• coords (Literal["reduced", "transformed"], optional) – Coordinate system to use. Defaults to ‘reduced’.

• show_node_numbers (bool, optional) – Whether to show node numbers. Defaults to False.

• fig (Optional[go.Figure], optional) – Existing plotly figure. Defaults to None.

• subplot (Optional[dict], optional) – Subplot information. Should contain keys ‘index’ and ‘ncols’. Defaults to None.

• highlight_nodes (Optional[Iterable], optional) – List of node numbers that should be highlighted. Defaults to None.

• highlight_edges (Optional[Iterable], optional) – List of edges that should be highlighted. Defaults to None.

• show_uc_box (bool, optional) – Whether to show unit cell bounding box. Defaults to False.

Returns:

Resulting plotly figure

Return type:

go.Figure