Material properties under deformation The ratio of lateral strain to linear (longitudinal) strain for an axially loaded specimen is called:

Introduction / Context:
When a bar is stretched axially, it becomes longer in the loading direction and thinner in the lateral directions. The coupling between these strains is captured by a fundamental material constant widely used in stress analysis and finite element modeling.

Given Data / Assumptions:

• Homogeneous, isotropic, linear elastic material.
• Small strains so linear relations apply.

Concept / Approach:
Poisson’s ratio, denoted by ν (nu), is defined as ν = |lateral strain| / |longitudinal strain| (signs differ but magnitude is used in many definitions). It ties together axial and transverse deformations and appears in relationships among E (modulus of elasticity), G (modulus of rigidity), and K (bulk modulus).

Step-by-Step Solution:
Under uniaxial stress, longitudinal strain ε_l = σ / E.Transverse (lateral) strain ε_t = -ν * σ / E.Therefore |ε_t| / |ε_l| = ν, which is Poisson’s ratio.

Verification / Alternative check:
Use constitutive relation: E = 2 G (1 + ν) and K = E / [3 (1 - 2 ν)], confirming ν’s central role.

Why Other Options Are Wrong:
Modulus of elasticity measures stiffness in tension/compression; modulus of rigidity pertains to shear; bulk modulus to volumetric stiffness; thermal expansion coefficient links strain to temperature, not axial-lateral coupling.

Common Pitfalls:
Ignoring negative sign for lateral strain (contraction under tension); assuming ν is constant for all states (it is material dependent, may vary with plasticity).

Final Answer:
Poisson's ratio