Modulus of Elasticity is defined as which of the following?

• A. Stress divided by Strain in the elastic region; also a measure of stiffness
• B. The onset of plastic deformation
• C. The maximum stress before failing
• D. The ratio of energy to volume

Answer: (A)

Modulus of Elasticity, or Young's modulus, is a measure of stiffness that describes how resistant a material is to elastic (reversible) deformation. In the linear elastic portion of the stress–strain curve, stress and strain are proportional, following Hooke’s law: sigma = E * epsilon. This means the ratio of stress to strain is constant for small deformations, and that constant is the modulus of elasticity. It tells you how steep the curve is in that elastic region: a larger E means a stiffer material that deforms less under a given load.

This concept differs from the onset of plastic deformation (yield point), which marks when the material stops obeying the linear relation and permanent deformation begins; and from the maximum stress before failure (ultimate tensile strength), which is about strength at fracture under load. It also isn’t simply the energy per volume stored, which relates to strain energy density rather than stiffness.