What are the 'Non-linear' characteristics of a wave spring as it approaches its 'Solid Height'?

As a wave spring approaches its solid height $L_s = n \times t$, the load-deflection curve deviates from the linear $P = kf$. This is due to 'wave flattening' where the contact area between waves increases, effectively shortening the active beam length. The spring rate $k$ increases exponentially. Designers must account for this 'stop' mechanism. If the system requires a hard stop, the spring must be designed such that the working load is reached before $80\%$ deflection. Exceeding this causes excessive stress $\sigma$ and can lead to 'coining' of the material, where the wave peaks are permanently flattened.