In solid mechanics, the ratio of lateral strain to linear (longitudinal) strain is termed as:

Introduction / Context:
In mechanics of materials, small deformations are described using strain components. When a bar is pulled in tension, it elongates in the loading direction and contracts laterally. The proportional relationship between these orthogonal strains defines an important elastic constant used across civil, mechanical, and materials engineering.

Given Data / Assumptions:

• Material is homogeneous, isotropic, and linearly elastic within the small-strain range.
• Lateral strain refers to strain normal to the loading axis; linear (longitudinal) strain is along the loading axis.
• Sign convention: lateral strain is typically negative in tension; the ratio is often reported as a positive magnitude.

Concept / Approach:
The constant that relates lateral strain (epsilon_lateral) to longitudinal strain (epsilon_longitudinal) is called Poisson's ratio, symbol ν (nu). By definition: ν = - (epsilon_lateral / epsilon_longitudinal). The minus sign makes ν positive for most materials under tension because lateral strain is negative while longitudinal strain is positive.

Step-by-Step Solution:
Identify the property asked: ratio of lateral strain to linear strain.Recall the definition: ν = - (ε_lateral / ε_longitudinal).Match with option texts: the only named constant for this ratio is Poisson's ratio.

Verification / Alternative check:
Typical ν values: steel ≈ 0.3, concrete ≈ 0.15–0.2, rubber up to ≈ 0.49. These well-known ranges confirm this identification.

Why Other Options Are Wrong:

• Bulk modulus: volumetric stress/volumetric strain, not lateral/longitudinal ratio.
• Modulus of elasticity (Young's modulus): normal stress/longitudinal strain.
• Shear modulus: shear stress/shear strain.
• Young's modulus (duplicate wording of modulus of elasticity): same as above.

Common Pitfalls:
Confusing ν with E (Young's modulus) because both are elastic constants; mixing the sign convention and forgetting the minus sign in the formal definition.

Final Answer:
Poisson's ratio