Which of the following statements reflects the principle of Hooke's Law?

The principle of Hooke's Law states that the deformation or strain of an elastic material is directly proportional to the applied stress, provided that the material's elastic limit is not exceeded. This means that if you apply more stress to a material within its elastic range, it will deform more, establishing a linear relationship between stress (force per unit area) and strain (deformation per unit length).

In practical terms, this relationship can be quantitatively expressed by the equation:

[

\sigma = E \cdot \epsilon

]

where (\sigma) is the stress, (E) is the modulus of elasticity (a material constant), and (\epsilon) is the strain. The direct proportionality highlights that doubling the stress will lead to a proportional increase in strain, reflecting the material's elastic behavior under load.

The other statements suggest relationships that deviate from this direct proportionality, leading to incorrect interpretations of how stress and strain relate according to Hooke’s Law. Hooke’s Law is foundational in understanding the mechanics of materials and is crucial in numerous engineering applications, especially when dealing with load-bearing structures and components.