Question

Mathematically,strain energy =.....................?

Answer 1

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. ... Regarding young's modulus E, the strain energy formula is given as, U = σ2 / 2E × V.

Answer 2

Mathematically, energy = $\[ = F\delta /2\]$

Explanation:

• The energy stored in a body due to deformation is called strain energy.
• It is denoted by $U$.
• The strain energy per unit volume is called strain energy density.
• The system under strain returns to its original shape when the applied force is removed.
• It is represented by the formula

       $\[U = F\delta /2\]$

      Here, $\[F=\]$ force applied and $\[\delta= \]$ compression

• If stress $\[\sigma \]$ is proportional to strain $\[\varepsilon \]$, then the strain energy formula becomes

       $\[U = \frac{1}{2}V\sigma \varepsilon \]$

      Here, $V=$ Volume of the body, $\[\sigma= \]$ stress, $\[\varepsilon= \]$ strain

• The strain energy formula regarding Young's Modulus $E$ is given as:

       $\[U = \frac{{{\sigma ^2}}}{{2E \times V}}\]$

      Here, $\[\sigma =\]$ stress, $E=$ Young's Modulus, $V=$ Volume of the body

• An example of strain energy can be a rod on which an external force is applied that it bents.
• This rod is now in a deformed state and the energy stored in this case in the rod is called strain energy.
• It is equal to the work done on the rod.

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