Question

Which of the following options is/are correct?

• A. The stress-strain graph for a nonlinear elastic material is as shown in the figure. 
  
• B. Material properties are independent of position in a homogeneous material.
• C. An isotropic material has infinitely many planes of material symmetry.
• D. The stress-strain graph for a linear elastic material is as shown in the figure. 
  

Hint:

- Nonlinear elastic \(\Rightarrow\) nonlinear curve but identical loading and unloading paths.
- Homogeneous \(\Rightarrow\) properties are independent of position.
- Isotropic \(\Rightarrow\) properties independent of direction, so infinite symmetry planes.
- Linear elastic \(\Rightarrow\) straight line stress-strain with no hysteresis.

Answer 1

The Correct Option is B

Step 1: Check option (A).
A nonlinear elastic material has a nonlinear stress-strain curve, but unloading follows the same path as loading (no hysteresis). The figure shown has different loading and unloading paths, which corresponds to inelastic or plastic behavior, not nonlinear elasticity.
\(\Rightarrow\) (A) is incorrect. 

Step 2: Check option (B).
By definition, a homogeneous material has properties independent of position. Hence material constants are the same at all points in the body.
\(\Rightarrow\) (B) is correct. 

Step 3: Check option (C).
An isotropic material has identical properties in all directions. This implies infinitely many planes of symmetry because the material response does not depend on orientation.
\(\Rightarrow\) (C) is correct. 

Step 4: Check option (D).
A linear elastic material follows Hooke's law: stress is proportional to strain. This gives a straight-line stress-strain curve, and loading and unloading occur along the same line. The figure shown for (D) is correct.
\(\Rightarrow\) (D) is correct. 

\[\boxed{\text{Correct options: (B), (C), (D)}}\]