We know metals forms a solid with Metallic Bonding which is the electrostatic forces between the metal cation and the sea of delocalized electrons contributed by the metal cations.
When you bend the metal, the electrostatic forces prevent them from moving away too far out. This is what causes the elasticity of the metal.
But what if I apply a high Positive Voltage to the metal and remove some of the "sea of delocalized electrons"?
Will the elasticity of the metal decrease?
Let's say you take a copper sphere with a radius of 1cm and charge it to a million volts. The self capacitance of a sphere of radius $r$ is:
$$ C = 4\pi\epsilon_0 r $$
so the charge you've added or removed from the sphere is:
$$ Q = CV \approx 1.11 \times 10^{-6} \,\text{C} $$
The number of copper atoms in our sphere is:
$$ N = \tfrac{4}{3}\pi r^3 \,\rho \frac{N_A}{M} $$
where $N_A$ is Avagadro's number and $M$ is the molar mass of copper. If we assume that each copper atom contributes one electron to the conduction band then the charge in the conduction band is $Q=Ne$, and doing the sums gives:
$$ Q \approx 57000 \,\text{C} $$
So even a million volts changes the charge in the conduction band by only about $0.000000002$%.
The point of all this is any change you make by applying an external voltage is so small as to be immeasurable.
