Simple Stress and Strain MCQ with answer and solution

Concept

Independent elastic constants for isotropic materials

Formula

E = 2G(1 + ν) = 3K(1 - 2ν)

Step-by-step solution

1. For an elastic, isotropic material, four elastic moduli are defined: E (Young's), G (Shear), K (Bulk), and nu (Poisson's ratio). 2. These constants are interconnected by elasticity relations: E = 2G(1+ν) and E = 3K(1-2ν). 3. Specifying any two parameters completely defines the remaining two. 4. Hence, the number of independent elastic constants for an isotropic material is 2. Answer: A

Explanation

A linearly elastic, isotropic material possesses four primary elastic constants (Young's modulus E, Shear modulus G, Bulk modulus K, and Poisson's ratio ν). However, due to interrelationships (e.g., E = 2G(1+ν) and E = 3K(1-2ν)), only two of these constants are mathematically independent.

Why the other options are wrong

B) 3 is incorrect; no standard material symmetry class requires 3 independent constants. C) 4 is the total number of primary constants, but only 2 are independent. D) 6 corresponds to certain crystal lattices, not isotropic solids.

Shortcut

Isotropic = 2 independent constants; Orthotropic = 9; Anisotropic = 21.

Common mistake

Counting all four interconnected elastic constants (E, G, K, ν) as independent.