Hooke's Law is primarily used to define which property of a material?

Hooke's Law is a fundamental principle in material science that defines the relationship between stress and strain within the limits of elasticity of a material. It states that the force or tension applied to an elastic material is directly proportional to the amount of deformation (strain) produced, as long as the material's elastic limit is not exceeded. This relationship characterizes the elastic properties of the material, allowing engineers and scientists to predict how a material will behave under different loading conditions.

In the context of the options provided, elastic properties specifically refer to a material's ability to return to its original shape after the applied load is removed. This is crucial for various engineering applications, ensuring that materials can withstand forces without permanently deforming. An understanding of Hooke's Law assists in determining how materials will perform in real-world scenarios, particularly in structural engineering and mechanical components.

The other options, while related to material properties, do not align with the direct implications of Hooke's Law. Toughness relates to a material's ability to absorb energy and deform plastically without fracturing, plasticity concerns the permanent deformation of a material under stress, and ductility involves a material's capacity to undergo significant plastic deformation before rupture. None of these are defined by the linear stress-strain relationship