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In this picture, the red curve is an elastic rod that has resistance to bending and extension. I am trying to model the adhesions (contact) between the rod and the substrate (glass): the green dashed lines. We will try to model it as in a spring-like bond. But, I need it in integral form.

From a numerical view, I can write that: \begin{equation} E = \sum_i \frac{1}{2}kz_i^2 \end{equation} where $i$ represent the bond at certain position.

How can I transform this discretization into an integral form that covers all the green parts?

In this picture, at a certain position <span class=$x$ adhesions start to appear" />

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  • $\begingroup$ Do you know what z is as a function of x? If you only have the zs as a discrete set of points there's not much more you can do than some sort of summation. $\endgroup$
    – GrapefruitIsAwesome
    Commented Feb 11, 2022 at 14:35
  • $\begingroup$ How large are the steps $\Delta x$ between subsequent values of $z_i$ ? $\endgroup$
    – fishinear
    Commented Feb 11, 2022 at 14:39

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