Assigning Materials

This examples showcases how material properties can be assigned to geometries in sectionproperties.

First we must import the Material() object.

from sectionproperties.pre import Material

Materials in sectionproperties require the following properties:

• Name [string]

• Elastic modulus [float]

• Poisson’s ratio [float]

• Density (mass per unit volume) [float]

• Yield strength [float]

• Color (see here for a list of named colors) [string]

For example, the following creates a typical steel material, using consistent Newtown and millimetre units:

steel = Material(
    name="Steel",
    elastic_modulus=200e3,  # N/mm^2 (MPa)
    poissons_ratio=0.3,  # unitless
    density=7.85e-6,  # kg/mm^3
    yield_strength=500,  # N/mm^2 (MPa)
    color="grey",
)

The below examples highlight a number of ways materials can be assigned to geometries in sectionproperties.

Assign material to a shapely geometry

The Geometry() constructor takes an optional material argument.

from shapely import Polygon

from sectionproperties.analysis import Section
from sectionproperties.pre import Geometry


# assign steel to a shapely polygon
poly = Polygon([(0, 0), (5, 2), (3, 7), (1, 6)])
geom = Geometry(geom=poly, material=steel)
geom.create_mesh(mesh_sizes=1)
Section(geometry=geom).plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

Assign material to arbitrary geometry

The Geometry.from_points() method also takes an optional material argument.

# create list of points, facets and holes
points = [(0, 0), (10, 5), (15, 15), (5, 10), (6, 6), (9, 7), (7, 9)]
facets = [(0, 1), (1, 2), (2, 3), (3, 0), (4, 5), (5, 6), (6, 4)]
control_points = [(4, 4)]
holes = [(7, 7)]

# create geometry object, specifying material
geom = Geometry.from_points(
    points=points,
    facets=facets,
    control_points=control_points,
    holes=holes,
    material=steel,
)
geom.create_mesh(mesh_sizes=1)
Section(geometry=geom).plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

Assign material to geometry from the section library

All methods in the section library take an optional material argument.

from sectionproperties.pre.library import polygon_hollow_section


geom = polygon_hollow_section(d=200, t=6, n_sides=8, r_in=20, n_r=12, material=steel)
geom.create_mesh(mesh_sizes=10)
Section(geometry=geom).plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

Assigning a material after creating a geometry

A geometry’s material may be altered at any time by simply assigning a new Material to the .material attribute of the Geometry object.

from sectionproperties.pre.library import rectangular_section


# create a rectangular section with the default material
geom = rectangular_section(d=16, b=100)
geom.create_mesh(mesh_sizes=10)
Section(geometry=geom).plot_mesh()

# assign steel to the geometry, remesh and recreate the Section object
geom.material = steel
geom.create_mesh(mesh_sizes=10)
Section(geometry=geom).plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

Assigning materials to CompoundGeometry objects

A CompoundGeometry does not have a .material attribute and therefore, a Material cannot be directly assigned. Since a CompoundGeometry is simply a combination of Geometry objects, the material should be assigned to each individual Geometry object that make up the CompoundGeometry.

# create a timber material
timber = Material(
    name="Timber",
    elastic_modulus=8e3,
    poissons_ratio=0.35,
    density=6.5e-7,
    yield_strength=20,
    color="burlywood",
)

# create individual geometries with material properties applied
beam = rectangular_section(d=35, b=170, material=timber)
plate1 = rectangular_section(d=35, b=16, material=steel)
plate2 = rectangular_section(d=35, b=16, material=steel)

# combine geometries, maintaining assigned materials
geom = (
    beam
    + plate1.align_to(other=beam, on="left")
    + plate2.align_to(other=beam, on="right")
)

# mesh and plot
geom.create_mesh(mesh_sizes=[20, 10, 10])
Section(geometry=geom).plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

Materials can also be changed after the fact by looping through the Geometry objects contained with the CompoundGeometry object.

# create CompoundGeometry without materials
rect1 = rectangular_section(d=10, b=10)
rect2 = rectangular_section(d=20, b=20).align_to(other=rect1, on="right")
geom = rect1 + rect2
geom.create_mesh(mesh_sizes=[1])
Section(geometry=geom).plot_mesh()

# create list of materials
mat_list = [steel, timber]

# loop through Geometry objects in CompoundGeometry to change materials
for geometry, mat in zip(geom.geoms, mat_list):
    geometry.material = mat

# remesh and recreate Section object
geom.create_mesh(mesh_sizes=[1])
Section(geometry=geom).plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

For more information, see Assigning Material Properties.