What is referred to as the proportional limit of a material?

The proportional limit of a material is defined as the point on the stress-strain curve where the stress and strain are linearly related. This means that up to this point, the material will deform elastically and return to its original shape once the load is removed. The relationship between stress (force per unit area) and strain (deformation per unit length) is linear, and this linearity is described by Hooke's Law.

Beyond the proportional limit, the material may still deform under stress, but the relationship between stress and strain is no longer linear, and the material begins to exhibit plastic behavior. This distinction is crucial in structural engineering, as it informs engineers about the limits of elastic behavior and the onset of permanent deformations that can affect the performance and safety of structures.

The other choices describe different material behaviors: the onset of yield, ultimate strength, and concept of no stress, but they do not specifically define the proportional limit which is characterized by linear elasticity.