Define volumetric strain: it is the ratio of which quantities for a deforming body?

Introduction / Context:
Strain measures quantify deformation and are central to elasticity, plasticity, and design checks. Volumetric strain is especially important in hydrostatic loading and bulk modulus calculations.

Given Data / Assumptions:

• Small deformation (engineering strain) regime.
• Volume changes from V to V + ΔV under load.
• Uniform material properties for definition purposes.

Concept / Approach:
Volumetric strain ε_v characterises dilatation or compression and is defined as:
epsilon_v = ΔV / VThis is analogous to linear strain ε = ΔL / L but extended to three dimensions.

Step-by-Step Solution:

Verification / Alternative check:
The bulk modulus K relates pressure p to volumetric strain: p = K * ε_vfor small elastic deformations, confirming the definition.

Why Other Options Are Wrong:
Thickness-based ratios refer to linear or lateral strain, not volumetric.Original volume to change in volume is the reciprocal and not the standard definition.Change in length/original length defines linear strain, not volumetric.

Common Pitfalls:
Confusing volumetric and linear strains; neglecting that volumetric strain can be nonzero even when linear strains sum to zero in anisotropic cases.

Final Answer:

Change in volume to the original volume