# what to use for mass in a 2D FEM simulation

I am trying to find the energy of a wave travelling through a solid material in a 2D Finite Element Method (FEM) - Simulation.

As a general approach I would try to use $E_{kin}=\frac{1}{2}mv^2$ at the highest particle velocity $v$, as this would be the point, where all the energy in the wave is kinetic and potential energy should be zero. So I would know the energy of the wave

But what would I use for mass? Since it is a 2D simulation, I image that, as the third dimension is infinitely small, there is no mass. Now I remember seeing in a paper once (sorry, I don't know the source anymore), that people used density $\rho$ instead of mass in their 2D FEM simulations.

My questions have 2 parts:

• Is using density instead of mass justifiable? If not, what other approach could someone point me to?
• The units would not match up anymore. So if it was ok to use density how would I use it.
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Density is mass per unit "something". In a string that means $kgm^{-1}$ on a plane it's $kgm^{-2}$ and in three dimensions it's $kgm^{-3}$. In your simulation you are only concerned with the behaviour in the two dimensions, you are effectively working in 3D with one unit of finite element thick.