Volumetric stiffness definition:\nA body is subjected to equal direct stresses in three mutually perpendicular directions (hydrostatic state). The ratio of direct stress to the corresponding volumetric strain is called:

Introduction / Context:
When a material experiences uniform pressure from all directions, it changes volume without shape distortion. The proportionality constant relating pressure (direct stress) to volumetric strain defines the material’s resistance to uniform compression.

Given Data / Assumptions:

• Hydrostatic (triaxial) state: σx = σy = σz.
• Small strains and linear elasticity.

Concept / Approach:
Bulk modulus K is defined as K = hydrostatic stress / volumetric strain. It complements Young’s modulus (uniaxial response) and shear modulus (distortional response without volume change).

Step-by-Step Solution:

Verification / Alternative check:
Thermodynamics and wave-propagation relations (e.g., speed of sound in solids) also rely on K, further confirming its definition for volumetric response.

Why Other Options Are Wrong:

• Young’s modulus relates axial stress to axial strain.
• Modulus of rigidity (G) relates shear stress to shear strain.
• Poisson’s ratio is the negative ratio of lateral to axial strain in uniaxial loading.

Common Pitfalls:
Confusing K with E due to both being “stiffness” measures; forgetting that K governs volume change, not shape distortion.

Final Answer:
bulk modulus