How to draw a bar as a node

Question

Could anyone tell me how is it possible to add "bars" as a node such as in the image below :

I would like to implement the "dl" segment :

\documentclass{article}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{accents}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\usepackage{geometry}
 \usepackage{caption}
\usepackage{color}



\usepackage{enumitem}
\usepackage{pgf, tikz, adjustbox}
\usetikzlibrary{spy}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns, matrix, positioning}
\usetikzlibrary{arrows.meta,
                patterns.meta
                }

\begin{document}


\begin{figure}[h]
\centering
\begin{tikzpicture}[
         > = Straight Barb,
dot/.style = {circle, fill, inner sep=2.0pt, node contents={}},
every label/.append style = {label distance =2pt, inner sep=1pt, fill=white},
   samples = 101,
    domain = 0:10
                        ]
% axis
\draw[-stealth] (-1.5, 0) -- (11,  0) node[right] {$\underline{e}_x$}; % x-axis
\draw[-stealth] (0, 0) -- ( 0,4.3) node[above] {$\underline{e}_z$}; % y-axis
\foreach \i in {-1,0, ...,10} 
\draw   (\i, 1mm) -- ++ (0,-2mm);
% function
\draw[very thick, blue]    
    plot    ({\x}, {(exp(1-1.3*(\x^2)/32))}) -- (10,0.0468);
\path[pattern={Lines[angle=45,distance={3pt},
               line width=0.2pt]},
               pattern color=blue]
    plot    ({\x}, {(exp(1-1.3*(\x^2)/32))}) |- (0,0) ;
    
% domain
\path   (0,0) node[red,dot,label=below left:$0$] (0,2.7183) node[dot] (10,0) node[red,dot,label=below:$L$];

% Labels
\draw[stealth-stealth, thick, red]    
plot    ({\x}, {(exp(1-1.3*(\x^2)/32)) + 1/2});
\draw [yshift=-0.6cm, stealth-stealth,thick,red](0,0) -- node [fill=white] {$R$} (10,0);
\draw [xshift=-0.5cm, stealth-stealth,thick,red](0,0) -- node [fill=white] {$h$} (0,2.7183);
\node[right,red] at (5,2.0) {$\epsilon$};

\path (4,1.4191) node[dot,red,scale=0.5];
\path (5,0.9845) node[dot,red,scale=0.5];


\end{tikzpicture}
\caption{Allongement le long du domaine}
\end{figure}

\end{document}

Giving :

Thank you for your help,

Answer 1

This is with a "let's do it approx" approach: just move with relative polar coordinates around the points and draw a line through them. You could probably try to move perpendicularly to the plot, but I do not think that the effort will be so much better...

(Note: I just put the changed lines here; your code is not minimal, so I prefer not to repost it). Instead of plotting the node, do the following:

\draw[red, thick]  (4,1.4191) ++(-135:0.2) -- ++(60:0.4);
\draw[red, thick]  (5,0.9845) ++(-135:0.2) -- ++(60:0.4);
\path (4,1.4191) -- node[below, red, sloped, font=\small]{$\mathrm{d}\,l$} (5,0.9845);

you can adjust the angles and length if you want.