12.8: Strain and Elastic Modulus
The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear strain, respectively. The greater the stress, the greater the strain; however, the relationship between strain and stress is not necessarily linear.
Only when the stress acting on a body is sufficiently low is the deformation caused by it directly proportional to the stress value. The proportionality constant in this relation is called the elastic modulus. As strain is dimensionless, the physical unit of elastic modulus is the same as stress (pascal). When a body is characterized by a large value of elastic modulus, the effect of stress is small. On the other hand, a small elastic modulus means that stress produces large strain and a noticeable deformation. For example, stress applied on a rubber band produces a larger strain (deformation) than the same stress applied on a steel band with the same dimensions, because the elastic modulus for rubber is two orders of magnitude smaller than the elastic modulus for steel. The elastic modulus for tensile stress is called the Young's modulus; for bulk stress, it is called the bulk modulus; and for shear stress, it is called the shear modulus.
Table 1. Approximate Elastic Moduli for Selected Materials
| Material | Young's modulus (1010 Pa) |
Bulk modulus (1010 Pa) |
Shear modulus (1010 Pa) |
| Aluminum | 7.0 | 7.5 | 2.5 |
| Bone (tension) | 1.6 | 0.8 | 8.0 |
| Brass | 9.0 | 6.0 | 3.5 |
| Brick | 1.5 | ||
| Copper | 11.0 | 14.0 | 4.4 |
| Crown glass | 6.0 | 5.0 | 2.5 |
| Granite | 4.5 | 4.5 | 2.0 |
| Hardwood | 1.5 | 1.0 | |
| Iron | 21.0 | 16.0 | 7.7 |
| Lead | 1.6 | 4.1 | 0.6 |
| Marble | 6.0 | 7.0 | 2.0 |
| Nickel | 21.0 | 17.0 | 7.8 |
| Polystyrene | 3.0 | ||
| Silk | 6.0 | ||
| Steel | 20.0 | 16.0 | 7.5 |
This text is adapted from Openstax, University Physics Volume 1, Section 12.3: Stress, Strain, and Elastic Modulus.
