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Q.

The elastic behaviour of material for linear stress and linear strain, is shown in the figure.
The energy density for a linear strain of 5 × 10^–4 is ............. kJ/m³. Assume that material is elastic up to the linear strain of 5 × 10^–4.

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answer is 25.

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Detailed Solution

$\begin{array}{l} Y = \frac{stress}{strain} = \frac{60}{3 \times 10^{- 10}} = 20 \times 10^{10} \\ Energy density = \frac{1}{2} stress \times strain \\ = \frac{1}{2} (strain)^{2} Y = \frac{1}{2} {(5 \times 10^{- 4})}^{2} \times 20 \times 10^{10} \\ = 25 \times 10^{2} \times 10 = 25 \frac{kJ}{m^{3}} \end{array}$

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The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 × 10–4 is ............. kJ/m3. Assume that material is elastic up to the linear strain of 5 × 10–4.