The strain energy stored per unit volume in a material under stress can be calculated using the following formula:

$U = \frac{1}{2} \sigma \epsilon$

where $\sigma$ is the stress and $\epsilon$ is the strain.

For an elastic material, stress is proportional to strain (Hooke's law), and the constant of proportionality is the Young's modulus (Y). So we can write:

$\sigma = Y \epsilon$

Substituting this into the energy density equation we get:

$U = \frac{1}{2} Y \epsilon^2$

The strain given in the problem is 0.04%, which needs to be converted to a decimal for use in this formula. Therefore, $\epsilon = 0.04/100 = 0.0004$.

Substituting the values into the equation gives:

$U = \frac{1}{2} \times 7.0 \times 10^{10} N/m^2 \times (0.0004)^2 = 5600 ~J/m^3$