# Deformation of solids

> CIE A-Level Physics · CIE 9702
> Source: https://www.owlsprep.com/study/cie-9702-u6-overview/
> Weight: n/a

This unit explores how solid materials deform under applied forces, linking experimental observations to key material properties that underpin engineering design and applied physics applications.

**Prerequisites:** [Forces and Newton's laws of motion](https://www.owlsprep.com/study/cie-9702-u3-forces/); [Work, energy and power](https://www.owlsprep.com/study/cie-9702-u5-work-energy/)

## Learning objectives

- Distinguish between elastic and plastic deformation of solid materials
- Calculate stress, strain and Young modulus from experimental deformation data
- Interpret force-extension and stress-strain graphs for different classes of materials
- Calculate strain energy and relate it to work done deforming a solid material

## Unit at a glance

This unit progresses from basic definitions of deformation parameters to interpreting how different materials behave under load, ending with calculation of energy stored during deformation. The learning arc builds sequentially: we start with core quantities to quantify deformation, then move to graphical representations of behaviour, distinguish between permanent and temporary deformation, and finally connect deformation to energy storage.

Work through the following sub-topics in order to build your understanding:
- [Stress, strain and Young modulus](https://www.owlsprep.com/study/cie-9702-u6-stress-strain-and-young-modulus/) — Learn core definitions and experimental methods to calculate stress, strain and Young modulus.
- [Force-extension and stress-strain graphs](https://www.owlsprep.com/study/cie-9702-u6-force-extension-and-stress-strain/) — Interpret key features of deformation graphs for brittle, ductile and polymeric materials.
- [Elastic and plastic deformation](https://www.owlsprep.com/study/cie-9702-u6-elastic-and-plastic-deformation/) — Distinguish between temporary and permanent deformation, and learn key concepts like yield point.
- [Strain energy](https://www.owlsprep.com/study/cie-9702-u6-strain-energy/) — Calculate energy stored in a deformed solid using formulas and graphical methods.

## Common pitfalls

- **Wrong:** Confusing extension with total length when calculating strain or Young modulus
  - Why it fails: Strain depends only on the change in length from the original undeformed state
  - Correct: Always use $ΔL$ (extension) divided by original length $L_0$ to calculate strain
- **Wrong:** Assuming all materials follow Hooke's law up to their breaking point
  - Why it fails: Hooke's law only applies in the proportional elastic region for most materials, and many materials never follow it
  - Correct: Only apply Hooke's law for deformation within the proportional limit of a Hookean material

## Cheatsheet

| Quantity/Concept | Formula / Key Definition |
| --- | --- |
| Tensile Stress | $\sigma = \frac{F}{A}$, where $F$ = applied force, $A$ = cross-sectional area |
| Tensile Strain | $\varepsilon = \frac{\Delta L}{L_0}$, where $ΔL$ = extension, $L_0$ = original length |
| Young Modulus | $E = \frac{\sigma}{\varepsilon} = \frac{FL_0}{A\Delta L}$, a constant for a given material |
| Hooke's Law | $F = k\Delta L$, applies up to the proportional limit |
| Strain Energy (Hookean) | $U = \frac{1}{2}F\Delta L = \frac{1}{2}k(\Delta L)^2$ |

## What's next

Begin with the first sub-topic to master core definitions of stress, strain and Young modulus, which form the foundation for all other concepts in this unit. Work through each sub-topic in order to build up your understanding of material deformation step by step. Once you have completed all sub-topics in this unit, you can progress to the next unit introducing core properties of waves.

- [Stress, strain and Young modulus](https://www.owlsprep.com/study/cie-9702-u6-stress-strain-and-young-modulus/)
- [Next Unit: Waves](https://www.owlsprep.com/study/cie-9702-u7-overview/)
- [Force-extension and stress-strain graphs](https://www.owlsprep.com/study/cie-9702-u6-force-extension-and-stress-strain/)

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