The elastic potential energy stored in a strained body is the energy per unit volume stored due to deformation. It is given by the formula:
\[ U = \frac{1}{2} \sigma \epsilon, \]
where:
For the total elastic potential energy stored in the body, the energy per unit volume is multiplied by the total volume of the body \( V \). Thus, the total elastic potential energy \( U_{\text{total}} \) is:
\[ U_{\text{total}} = \frac{1}{2} \sigma \epsilon V. \]
Key Observations:
Hence, the elastic potential energy of a strained body is:
\[ \frac{1}{2} \, \text{stress} \times \text{strain} \times \text{volume}. \]