GATE 2025 ME – Question 58

Mechanics of Materials · Energy methods · 2 marks · Numerical answer

An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given below. The strain energy density is ________ MJ m$^{-3}$ (rounded off to 2 decimal places).

A $\sigma$-$\varepsilon$ plot made of two straight segments. The first runs from the origin to the point (0.01, 100 MPa), and the second continues to (0.015, 120 MPa).

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Correct answer: 1.04 to 1.06

Explanation

The strain energy density is the area under the curve. The first triangle is $\frac{1}{2} \times 0.01 \times 100 = 0.5$ MJ/m$^3$. The second part is a trapezoid of width $0.005$ and average height $\frac{100 + 120}{2} = 110$ MPa, which is $0.55$ MJ/m$^3$. The total is $1.05$ MJ/m$^3$.