Materials mechanics – definition: What is the ratio of lateral strain to axial strain for a homogeneous, isotropic material called?

Introduction / Context:
When a prismatic bar is pulled in tension, it elongates in the loading direction and simultaneously contracts in the directions perpendicular to the load. The quantitative link between these two strains is fundamental in strength of materials and helps predict 3D deformation from 1D loading. The name assigned to this ratio is frequently used in civil, mechanical, and materials engineering design.

Given Data / Assumptions:

• Material is homogeneous and isotropic so properties are the same in all directions.
• Deformation is within the elastic range so linear relations apply.
• Axial strain means strain along the load; lateral strain means strain perpendicular to the load.

Concept / Approach:
The property that links the lateral contraction to the axial extension is called Poisson's ratio, commonly denoted by the symbol nu. It is defined as the negative of the ratio of lateral strain to axial strain, but as a magnitude it is often quoted as a positive number between about 0.15 and 0.50 for common engineering materials. It works together with Young's modulus to determine elastic deformation in three dimensions.

Step-by-Step Solution:
Identify the strains: axial strain = change in length / original length.Lateral strain = change in lateral dimension / original lateral dimension.Use the definition: Poisson's ratio = (lateral strain) / (axial strain) with a minus sign by sign convention.Match the term: the described ratio corresponds to Poisson's ratio.

Verification / Alternative check:
Typical values: steel about 0.30, concrete about 0.15 to 0.20 (short-term), rubber near 0.5. These known ranges confirm the interpretation of the ratio connecting transverse and axial strains.

Why Other Options Are Wrong:

• Hooke's ratio: not a standard term; Hooke's law relates stress and strain via modulus.
• Plastic ratio: plasticity refers to permanent deformation, not the elastic strain ratio.
• Yield ratio: relates strengths, not strains.
• Modulus ratio: used in composite analysis (e.g., n = Es/Ec), unrelated to lateral/axial strain ratio.

Common Pitfalls:
Confusing Poisson's ratio with Young's modulus; forgetting the sign convention (lateral strain is negative in tension), even though the reported value is a positive magnitude.

Final Answer:
Poisson's ratio