The GATE Grind

GATE 2024 AE – Question 25

Structures · Strength of materials: Strain energy, Castigliano's principles, three-dimensional Hooke's law, plane stress and strain, Euler buckling · 1 mark · Multiple select

Which of the following options is/are correct?

(A) The stress-strain graph for a nonlinear elastic material is as shown in the figure [Figure: a curve for loading and a different curve for unloading, which returns to a non-zero strain at zero stress].

(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 [Figure: a single straight line, followed in both loading and unloading].

Diagram for GATE 2024 AE question 25
  1. The stress-strain graph for a nonlinear elastic material is as shown in the figure (loading and unloading follow different curves)
  2. Material properties are independent of position in a homogeneous material
  3. An isotropic material has infinitely many planes of material symmetry
  4. The stress-strain graph for a linear elastic material is as shown in the figure (a single straight line for loading and unloading)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (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 (a single straight line for loading and unloading)

Explanation

A homogeneous material has the same properties at all points (B), and an isotropic material has the same properties in all directions, so every plane is a plane of symmetry (C). A linear elastic material follows one straight line in loading and unloading (D). In (A) the unloading path is different and ends at a permanent strain, which is plastic behaviour, not elastic.