What law states that stress is directly proportional to strain within a proportionality limit?

Stress being directly proportional to strain within a proportionality limit is defined by Hooke's Law. This principle is fundamental in the field of mechanics of materials and governs how materials behave elastically when subjected to stress. In essence, Hooke's Law states that the amount of deformation (strain) in an elastic material is directly proportional to the applied stress, as long as the material is deformed within its elastic limit.

This relationship can be mathematically expressed as σ = Eε, where σ represents stress, ε represents strain, and E represents the modulus of elasticity (or Young's Modulus). This means that as stress increases, strain increases at a constant rate until the material reaches its yield point, beyond which it may undergo plastic deformation.

The other concepts mentioned, while related to material science, address different aspects. Young's Modulus is a measure of the stiffness of a material and is directly related to Hooke's Law, but it does not itself define the relationship. Poisson's Ratio describes how a material expands or contracts laterally when stretched or compressed, which is not about the direct proportionality between stress and strain. Elasticity Theory encompasses more than just the simple linear relationship, exploring how materials return to their original shape after deformation and dealing