Young's Modulus

An elastic modulus is always defined as the stress divided by the strain. A large modulus means that the material is hard to deform. Young's modulus, Y, is defined for a stress that causes a change in length $\Delta$L/L. Stress is plotted versus strain in the curve below.

In the straight line region, the slope is Y, Young's modulus. A typical value: Y = 2.0$\cdot$10¹¹ N/m² for steel Above and below that region, the material is no longer elastic. The elastic limit is the point beyond which the material will not return to its original shape. Here we will always work in the region where the modulus is constant.

For tensile/compressional stress, Young's modulus is:

where F is the force, and A is the cross-sectional area of the object that the force is applied to.