What is the relationship between stress and strain in a material's elastic range?

In a material’s elastic range, the relationship between stress and strain is direct and proportional, meaning that when stress increases, strain increases proportionally, and vice versa. This behavior is described by Hooke's Law, which states that the stress applied to a material is directly proportional to the strain it produces, provided that the material remains within its elastic limit.

This proportional relationship allows engineers to predict how materials will behave when subjected to forces. The slope of the stress-strain curve in the elastic range is known as the modulus of elasticity or Young's modulus, which quantifies the material's stiffness.

In contrast, the other options reflect different types of relationships that do not apply within the elastic range. For instance, an inversely proportional relationship would suggest that as stress increases, strain decreases, which contradicts the observed behavior of materials within their elastic limits. Similarly, claiming there is no relationship ignores the fundamental principles governing elastic behavior, while a cubic relationship implies a much more complex interaction that does not describe simple elastic behavior.