Which of the following statements about isotropic materials is true?
- AThey have different properties in different directions
- BThey require only one elastic constant to describe their behaviour
- CThey have the same elastic properties in all directionsCorrect
- DThey cannot be deformed elastically
Solution
Concept
Elastic properties of isotropic materials
Formula
NONE
Step-by-step solution
1. Isotropic materials exhibit identical physical characteristics in all directions at any given point. 2. The stress-strain relationships remain invariant regardless of the directional orientation of applied forces. 3. Therefore, isotropic materials have the same elastic properties in all directions. Answer: C
Explanation
An isotropic material exhibits identical physical and mechanical properties regardless of the orientation or direction in which they are measured. In contrast, anisotropic materials vary in properties depending on the axis of loading. Therefore, option C accurately defines isotropic material behavior.
Why the other options are wrong
A) Direction-dependent properties are characteristic of anisotropic materials. B) Isotropic materials require two independent elastic constants to describe their elastic behavior. D) Isotropic materials undergo elastic deformation when subjected to loads within their elastic limit.
Shortcut
"Iso" means same: Isotropic materials have identical elastic properties in all directions.
Common mistake
Selecting option B by confusing the definition of isotropic materials with needing only a single elastic constant instead of two independent constants.
Correct answer: C) They have the same elastic properties in all directions