What is defined as the proportion of volumetric stress related to the volumetric strain of a material?

The correct answer is the Bulk Modulus of Elasticity, which specifically describes the relationship between volumetric stress applied to a material and the resulting volumetric strain that occurs in that material.

When pressure is applied uniformly to an object, the Bulk Modulus quantifies how much the volume of that object decreases in response to that pressure. Mathematically, it is defined as the ratio of the change in pressure (stress) to the fractional change in volume (strain). This concept is critical in understanding the behavior of materials under compressive stresses, especially in fluids and solids that experience uniform load conditions, such as in geotechnical engineering.

In contrast, Young's Modulus measures the relationship between tensile stress (force per area) and tensile strain (deformation) in a material along one dimension, while Shear Modulus focuses on shear stress related to shear strain. The Elastic Limit refers to the maximum stress that a material can withstand without permanent deformation but does not specifically address the volumetric relationship defined by the Bulk Modulus. Therefore, the Bulk Modulus is the correct term associated with volumetric changes in a material due to applied stress, highlighting its significance in material science and engineering applications.