Example usage

mods, which stands for “mechanics of deformable solids” is a python package that implements various equations from the textbook “Mechanics of Materials” by R.C. Hibbeler (9th edition). My intention with mods is to aid instructors and students alike in teaching (learning) solid mechanics at the undergraduate level. Presently, mods only supports plane stress and strain analyses.

Here, I will demonstrate some functions from mods. mods was made with the engineering student in mind; most functions should be straight forward to use.

Stress Transformation

Suppose we transform an element shown in a) into the element shown by b):

Working this problem out by hand is a little bit laborous, but not too bad:

Using mods, this problem is a breeze. We can easily determine the transformed stresses (in MPa):

from mods.stress_transformation import normal_stress_transform, shear_stress_transform

print(f'Transformed normal stresses (sigma x prime, sigma y prime): {normal_stress_transform(-80, 50, -25, -30)}')
print(f'Transformed shear stress: {shear_stress_transform(-80, 50, -25, -30)}')

Transformed normal stresses (sigma x prime, sigma y prime): (-25.84936490538904, -4.1506350946109585)
Transformed shear stress: -68.79165124598852

Von Mises Failure Envelope

Here’s a fun problem from Hibbeler (9th edition):

The first step is to determine the yield strength of A-36 steel. Luckily, you don’t have to flip through Hibbeler to the back pages of the textbook:

from mods.datasets import get_mechanical_properties_si

mech_props_df = get_mechanical_properties_si()
mech_props_df.iloc[:, [0, 1, 3, 8, 9]]

	Material Family	Material	Density (g/m3)	Tens. Yield Strength (MPa)	Comp. Yield Strength (MPa)
0	Aluminum	2014-T6	2790000	414.0	414.0
1	Wrought Alloys	6061-T6	2710000	255.0	255.0
2	Cast Iron Alloys	Gray ASTM 20	7190000	NaN	NaN
3	Cast Iron Alloys	Malleable ASTM A-197	7280000	NaN	NaN
4	Copper Alloys	Red Brass C83400	8740000	70.0	70.0
5	Copper Alloys	Bronze C86100	8830000	345.0	345.0
6	Magnesium Alloy	[Am 1004-T611]	1830000	152.0	152.0
7	Steel Alloys	Structural A-36	7850000	250.0	250.0
8	Steel Alloys	Structural A992	7850000	345.0	345.0
9	Steel Alloys	Stainless 304	7860000	207.0	207.0
10	Steel Alloys	Tool L2	8160000	703.0	703.0
11	Titanium Alloy	[Tl-6A1-4V1]	4430000	924.0	924.0
12	Concrete	Low Strength	2380000	NaN	NaN
13	Concrete	High Strength	2370000	NaN	NaN
14	Plastic Reinforced	Kevlar 49	1450000	NaN	NaN
15	Plastic Reinforced	30% Glass	1450000	NaN	NaN
16	Wood Select Structural Grade	Douglas Fir	470000	NaN	NaN
17	Wood Select Structural Grade	White Spruce	3600000	NaN	NaN

We can see that the yield strength of A-36 structural steel (in both tension and compression) is 250 MPa. We can use this to plot the Von Mises failure envelope:

from mods.failure import plot_von_mises_failure_envelope

plot_von_mises_failure_envelope(250, 70, -60, 40)

The red dot indicates our stress state. We can see that the dot lies within the failure envelope for A-36 steel, which means our material is not expected to fail at the stress state specified by the problem.