Elasticity and materials — identify the incorrect statement Which one of the following statements is incorrect regarding material behaviour and terminology (kern distance, viscoelasticity, isotropy/orthotropy)?

Introduction / Context:
Understanding standardized material terminology is fundamental in strength of materials. This question examines the definitions of kern distance, viscoelasticity, isotropy, and orthotropy and asks you to spot the incorrect statement among them.

Given Data / Assumptions:

• Axially loaded members may carry eccentric loads; kern defines the no-tension zone.
• Material classes include elastic, plastic, and viscoelastic; time dependence matters.
• Directional property variation is captured by terms “isotropic” and “orthotropic”.

Concept / Approach:

Compare each statement with standard definitions: the kern distance is the limiting eccentricity from the centroid that still maintains compressive stress over the whole section. Viscoelastic materials exhibit time-dependent stress–strain (creep/relaxation). Isotropy means properties are identical in all directions. Orthotropy means three mutually perpendicular preferred directions with distinct properties (e.g., wood: longitudinal, radial, tangential).

Step-by-Step Evaluation:

Verification / Alternative check:

Engineering handbooks and textbooks consistently define isotropy as directional uniformity (E, ν, G invariant with direction), while anisotropy/orthotropy cover directional variation. Hence (c) is unequivocally wrong.

Why Other Options Are Wrong (as answers):

• (a), (b), (d) are correct statements; choosing them as “incorrect” would be a misinterpretation.
• “All the above” cannot be true since not all statements are incorrect.

Common Pitfalls:

• Confusing isotropic with anisotropic; “iso” means same.
• Overlooking that orthotropy is a specific type of anisotropy with three orthogonal symmetry axes.

Final Answer:

An isotropic material has different mechanical properties in different directions.