Strain measures: The ratio of the change in volume to the original volume of a body under load is called what?

Introduction / Context:Different strain measures quantify deformation in various directions and modes. Recognising which definition applies avoids errors in bulk modulus or multi-axial stress calculations.

Given Data / Assumptions:

• Small-strain (engineering strain) regime.
• Volume change ΔV relative to original volume V.
• Isotropic or anisotropic loading does not change the definition itself.

Concept / Approach:Volumetric strain ε_v is defined as ε_v = ΔV / V. Linear (axial) strain is ΔL / L; lateral strain is transverse strain associated with Poisson effects; Poisson’s ratio ν = −(lateral strain)/(linear strain) in uniaxial loading.

Step-by-Step Solution:

Verification / Alternative check:Bulk modulus K uses ε_v: p = K * ε_v for hydrostatic loading (small strains), reinforcing the definition.

Why Other Options Are Wrong:Linear and lateral strains are one-dimensional measures; Poisson’s ratio is a material constant relating them, not a strain itself.

Common Pitfalls:Confusing Poisson’s ratio (dimensionless constant) with a strain measure; mixing linear and volumetric changes.

Final Answer:

Volumetric strain