Shear Modulus, Bulk Modulus and Poisson's Ratio

Name: Shear Modulus, Bulk Modulus and Poisson's Ratio
Author: StemPy Lab

A solid can be stretched, but it can also be sheared and squeezed, and a stretched wire also gets thinner. In this course we find the shear modulus and the bulk modulus, we see why a liquid has no shear modulus, we find how much water is compressed in the deep sea, and we use Poisson's ratio to connect the three moduli.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Shear modulus
A sideways force along a face shears a block: its sides tilt through an angle $\theta \approx \dfrac{\Delta x}{h}$ . The shear modulus, or modulus of rigidity, is $G = \dfrac{F/A}{\theta}$ , in pascal. For metals $G$ is about a third of $Y$ . Liquids and gases have no shear modulus: under a steady sideways stress they flow.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Bulk modulus and compressibility
A pressure on all sides changes a body's volume. The bulk modulus is $B = -\dfrac{p}{\Delta V/V}$ , in pascal; its reciprocal is the compressibility. Solids and liquids have large bulk moduli (water $2.2\ \text{GPa}$ , steel $160\ \text{GPa}$ ); a gas at a steady temperature has $B = p$ , so gases are easy to squeeze.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Poisson's ratio and the relations between the moduli
A stretched rod gets thinner. Poisson's ratio is the lateral strain over the longitudinal strain, $\sigma = \dfrac{\Delta d/d}{\Delta L/L}$ ; it lies between $0$ and $0.5$ , about $0.3$ for metals and $0.5$ for rubber. The moduli are linked: $Y = 2G(1 + \sigma)$ and $Y = 3B(1 - 2\sigma)$ , and a stretched rod's volume changes by $\varepsilon(1 - 2\sigma)$ .
1 simulation2 practice questions1 Python program4 problems1 note
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Shear Modulus, Bulk Modulus and Poisson's Ratio: Practice Paper

20 questions · 50 min

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Shear Modulus, Bulk Modulus and Poisson's Ratio

Course outline (3 lessons)

Shear modulus

Bulk modulus and compressibility

Poisson's ratio and the relations between the moduli

Test Your Learning

Your teacher

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