🧵 Mat(erial)

Mat

../_images/mat.png
class fibermat.mat.Mat(*args, **kwargs)

A class inherited from pandas.DataFrame to describe a fibrous material made up of a set of random fibers.

It defines:

  • the geometry of the straight fibers.

  • the initial configuration (positions and orientations).

  • the material properties.

Parameters

nint, optional

Number of fibers. Default is 0.

lengthfloat, optional

Fiber length (mm). Default is 25 mm.

widthfloat, optional

Fiber width (mm). Default is 1 mm.

thicknessfloat, optional

Fiber thickness (mm). Default is 1 mm.

sizefloat, optional

Box dimensions (mm). Default is 50 mm.

thetafloat, optional

In plane angle (rad). Default is π rad.

psifloat, optional

Out-of-plane angle (rad). Default is 0 rad.

shearfloat, optional

Shear modulus (MPa). Default is 1 MPa.

tensilefloat, optional

Tensile modulus (MPa). Default is ∞ MPa.

seedint, optional

Random seed for reproducibility. Default is 0.

Other Parameters

kwargs :

Additional keyword arguments ignored by the function.

Note

The constructor calls init() method if the object is instantiated with parameters. Otherwise, initialization is performed with the pandas.DataFrame constructor.

Use:
>>> # Generate a set of fibers
>>> mat = Mat(100)
>>> mat
       l    b    h          x          y          z         u         v    w    G    E
0   25.0  1.0  1.0   2.440675   8.890827 -24.338157  0.289366  0.957218 -0.0  1.0  inf
1   25.0  1.0  1.0  10.759468 -11.499601 -24.178519  0.651721  0.758459  0.0  1.0  inf
2   25.0  1.0  1.0   5.138169  11.759701 -23.967450  0.865730 -0.500512 -0.0  1.0  inf
3   25.0  1.0  1.0   2.244159  23.109427 -23.766064  0.252040 -0.967717  0.0  1.0  inf
4   25.0  1.0  1.0  -3.817260 -12.562343 -23.716864  0.957840 -0.287303  0.0  1.0  inf
..   ...  ...  ...        ...        ...        ...       ...       ...  ...  ...  ...
95  25.0  1.0  1.0 -15.840432  -0.477060  23.096819  0.128503  0.991709 -0.0  1.0  inf
96  25.0  1.0  1.0   4.325647 -13.629269  23.645974  0.898537 -0.438898 -0.0  1.0  inf
97  25.0  1.0  1.0 -23.994623 -12.282176  23.874757  0.900374 -0.435117 -0.0  1.0  inf
98  25.0  1.0  1.0  16.447001 -22.098542  24.091469  0.051275 -0.998685 -0.0  1.0  inf
99  25.0  1.0  1.0 -24.765226  -3.279169  24.516947  0.549633 -0.835406  0.0  1.0  inf

[100 rows x 11 columns]

Data

  • indexpandas.Index

    Fiber label. Each label refers to a unique fiber.

  • Fiber dimensions:
    • lpandas.Series

      Fiber length (mm). By default, 25 mm long fibers are used.

    • bpandas.Series

      Fiber width (mm). By default, 1 mm wide fibers are used.

    • hpandas.Series

      Fiber thickness (mm). By default, 1 mm thick fibers are used.

  • Fiber position:
    • xpandas.Series

      X-coordinate (mm). By default, positions are randomly distributed with a uniform distribution between the positions X: [-25 mm ; 25 mm].

    • ypandas.Series

      Y-coordinate (mm). By default, positions are randomly distributed with a uniform distribution between the positions Y: [-25 mm ; 25 mm].

    • zpandas.Series

      Z-coordinate (mm). By default, positions are randomly distributed with a uniform distribution between the positions Z: [-25 mm ; 25 mm].

  • Fiber orientation:
    • upandas.Series

      X-component. By default, orientations are randomly distributed with a uniform distribution in the half-unit circle θ: [-π / 2, π / 2].

    • vpandas.Series

      Y-component. By default, orientations are randomly distributed with a uniform distribution in the half-unit circle θ: [-π / 2, π / 2].

    • wpandas.Series

      Z-component. By default, orientations are in the plane, so the Z-component is 0.

  • Material properties:
    • Gpandas.Series

      Shear modulus (MPa). By default, shear modulus is 1 MPa.

    • Epandas.Series

      Tensile modulus (MPa). By default, tensile modulus is infinite, which corresponds to fibers that are infinitely rigid in tension and bending.

Attributes

attrs :

Global attributes of DataFrame.

Methods

init() :

Generate a set of random straight fibers.

check() :

Check that a Mat object is defined correctly.

property attrs
Global attributes of DataFrame:
  • nint

    Number of fibers. By default, it is empty (n = 0).

  • sizefloat

    Box dimensions (mm). By default, the domain is a 50 mm square cube.

check()

Check that a Mat object is defined correctly.

This method is called when a Mat object is initialized.

Raises

KeyError

If any keys are missing from the columns of Mat object.

AttributeError

If any attributes are missing from the dictionary attrs.

IndexError
If row indices are incorrectly defined:

  • Row indices are not unique in [0, …, n-1] where n is the number of fibers.

  • Fiber labels are not sorted.

ValueError
If any of the following conditions are not met:

  • Dimensions are not positive.

  • Positions are not within a box of size specified in attrs.

  • Orientation vectors do not have unit lengths.

  • Material properties are not positive.

Returns

bool

Indicates whether the object can be instantiated as Mat.

Tip

  • If self is None, it returns an empty Mat object.

  • If a “skip_check” flag is True in attrs, the check is passed.

static init(n=0, length=25.0, width=1.0, thickness=1.0, size=50.0, theta=3.141592653589793, psi=0.0, shear=1.0, tensile=inf, seed=0, **kwargs)

Generate a set of random straight fibers.

Parameters

nint, optional

Number of fibers. Default is 0.

lengthfloat, optional

Fiber length (mm). Default is 25 mm.

widthfloat, optional

Fiber width (mm). Default is 1 mm.

thicknessfloat, optional

Fiber thickness (mm). Default is 1 mm.

sizefloat, optional

Box dimensions (mm). Default is 50 mm.

thetafloat, optional

In plane angle (rad). Default is π rad.

psifloat, optional

Out-of-plane angle (rad). Default is 0 rad.

shearfloat, optional

Shear modulus (MPa). Default is 1 MPa.

tensilefloat, optional

Tensile modulus (MPa). Default is ∞ MPa.

seedint, optional

Random seed for reproducibility. Default is 0.

Returns

matpandas.DataFrame

Initialized Mat object.

Other Parameters

kwargs :

Additional keyword arguments ignored by the function.

Example

from fibermat import *

# Generate a set of fibers
mat = Mat(100)

# Check data
Mat.check(mat)  # or `mat.check()`
# -> returns True if correct, otherwise it raises an error.

# Get fiber data
dimensions = mat[[*"lbh"]]  # size: (n x 3)
positions = mat[[*"xyz"]]  # size: (n x 3)
orientations = mat[[*"uvw"]]  # size: (n x 3)

# Figure
fig, ax = plt.subplots(subplot_kw=dict(projection='3d', aspect='equal',
                                       xlabel="X", ylabel="Y", zlabel="Z"))
ax.view_init(azim=45, elev=30, roll=0)
if len(mat):
    # Draw fibers
    for i in tqdm(range(len(mat)), desc="Draw fibers"):
        # Get fiber data
        fiber = mat.iloc[i]
        # Calculate fiber end points
        A = fiber[[*"xyz"]].values - 0.5 * fiber.l * fiber[[*"uvw"]].values
        B = fiber[[*"xyz"]].values + 0.5 * fiber.l * fiber[[*"uvw"]].values
        plt.plot(*np.c_[A, B])
    # Set drawing box dimensions
    ax.set_xlim(-0.5 * mat.attrs["size"], 0.5 * mat.attrs["size"])
    ax.set_ylim(-0.5 * mat.attrs["size"], 0.5 * mat.attrs["size"])
plt.show()
../_images/mat.png