(sketch is self-made)

So, many solid materials have a so-called “Young modulus E” which describes the mechanical stress that develops inside a material when it is deformed. Basically, when a material is deformed by a deformation ε, then the stress σ is σ = E · ε.

ε is measured as Δx/x, i.e. when you take 1m of steel and deform (stretch) it by 1mm, then ε = 1mm / 1m = 10^-3. The value of E is set for any material, i.e. E(steel) = 200 GPa, or 200 kN/mm². So if you stretch it by a deformation of ε = 10^-3, you get a stress σ = 10⁻³ · 200 GPa = 200 MPa.

A practical application of this would be if you have an elastic wire (a wire made from steel, in this case), and you want to calculate how much force you need to stretch it.

This means that if the steel bar has a cross-section area of A = 1mm², and a length of 1 m, and you stretch it by an additional 1mm, then ε = 10^-3 and to calculate the force F, you multiply σ by A and get F = σ · A = 200 MPa · 1 mm² = 200 N/mm² · 1 mm² = 200 N. This is the force that you have to exert to stretch the wire to this length.

In a follow-up article i intend to show how you calculate how much energy you need to stretch the wire to this length, which is surprisingly simple to do if you know some calculus and the basic rule that dW = F · dx. To sum it up, the result would be W = ∫ F · dx = ½ · F · Δx. For the above example this would be W = ½ · F · Δx = ½ · 200 N · 1 mm = 0.1 J. Which is surprisingly little energy, in my opinion.

Did i calculate this correctly? Can somebody check please?