How to add arrows near the plot path and fill the area under this path?

Question

I'd like to draw a closed plot path filled with pattern and surrounded by arrows:

When I used @Jake's solution to add arrows (Decorate a path with little arrows parallel to it) then the pattern made with the method proposed by @Domenico Camasta vanishes (Modified pattern does not see the pattern color option). The command postaction=decorate causes that the pattern filling the area is not created.

1. What can I do to avoid executing 2-times the \addplot for the same path in the code below?
2. Why removing of enlargelimits=true affects the distance between arrows and the plot path?
3. How to trim both axes at the origin of the coordinate system?

The code is following:

\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage{pgfplots}
\usepackage{tikz}
\pgfplotsset{compat=newest}

\usetikzlibrary{decorations.markings}
\usetikzlibrary{patterns}
\usepgfplotslibrary{fillbetween}

\definecolor{mygreen}{rgb}{0.00000,0.60000,0.00000}

\makeatletter
\pgfdeclarepatternformonly[\LineSpace]{my north east lines}%
    {\pgfqpoint{-1pt}{-1pt}}%
    {\pgfqpoint{\LineSpace}{\LineSpace}}%
    {\pgfqpoint{\LineSpace}{\LineSpace}}%
    {\pgfsetcolor{\tikz@pattern@color}
     \pgfsetlinewidth{0.4pt}
     \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
     \pgfpathlineto{\pgfqpoint{\LineSpace + 0.1pt}{\LineSpace + 0.1pt}}
     \pgfusepath{stroke}
    }
\makeatother

\newdimen\LineSpace
\tikzset{
    line space/.code={\LineSpace=#1},
    line space=9pt
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[%
width=10cm,
height=7cm,
axis on top=true,
axis x line=middle,
axis y line=middle,
xtick=\empty,
ytick=\empty,
extra x ticks={0,0.1},
extra x tick labels={$x_{min}$,$x_{max}$},
extra y ticks={600},
extra y tick labels={$F_{max}$},
extra y tick style={yticklabel style={xshift=0.8ex, anchor=west}},
xlabel={piston position},
ylabel={force},
enlargelimits=true
]
\addplot[
    name path=A,color=blue,solid,forget plot,smooth,
    decoration={
        markings,
        mark=between positions 0.1 and 1 step 3em with {\draw [-latex] (-2mm,0) -- (2mm,0);},
        raise=0.6cm
    },
    postaction=decorate
]
table[row sep=crcr]{%
    0       60\\
    0.005   450\\
    0.025   550\\
    0.1     600\\
} node [above=0.8ex,pos=0.96] {$F_{\rightarrow}(x)$};
\addplot[
    name path=B,color=mygreen,solid,forget plot,smooth,
    decoration={
        markings,
        mark=between positions 0.1 and 1 step 3em with {\draw [-latex] (-2mm,0) -- (2mm,0);},
        raise=0.6cm
    },
    postaction=decorate
]
table[row sep=crcr]{%
    0.1     600\\
    0.095   200\\
    0.065   100\\
    0       60\\
} node [below=1.0ex,pos=0.93] {$F_{\leftarrow}(x)$};
\addplot fill between[of=A and B,
                      split,
                      every segment no 1/.style={pattern=my north east lines,pattern color=gray}
                     ];
\node[fill=white] at (0.05,350) {\textcolor{gray}{dissipated energy}};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

This kind of approximate graph is a nice one to do in Metapost because you have flexibility to draw as you like, without fighting the constraints of a tool designed for plotting functions. I've used the subpath feature to decorate the path with arrows.

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(1);

minf = 13;
maxf = 144; 
minx = 0;
maxx = 233;

path f, xx, yy; 
z0 = (minx,minf);
z1 = (1/30[minx,maxx],14/15[minf,maxf]);
z2 = (maxx,maxf);
z3 = z1 rotatedabout(1/2[z0,z2],180);
f = z0 .. controls z1 .. z2 .. controls z3 .. cycle;

xx = (minx-2,0) -- (maxx+20,0);
yy = (0,-2) -- (0,maxf+20);

for i = -maxx step maxx/34 until maxx:
  draw (left--right) scaled maxx rotated 45 shifted(i,0) withcolor .8 white;
endfor
clip currentpicture to f;

drawoptions(withcolor .5 white);
drawarrow xx; 
drawarrow yy;
draw (up  --down ) scaled 2 shifted (maxx,0);
draw (left--right) scaled 2 shifted (minx,maxf);
drawoptions();

draw subpath(0,1) of f withcolor .67 blue;
draw subpath(1,2) of f withcolor .56 green;

label.bot(btex $x_{\min}$ etex, (minx,0));
label.bot(btex $x_{\max}$ etex, (maxx,0));
label.lft(btex $F_{\max}$ etex, (minx,maxf));

label(btex piston position etex, ((minx+maxx)/2,-20));
label(btex force etex rotated 90, (-20,(minf+maxf)/2));

label(btex $F_{\to}(x)$        etex, point 0.9 of f shifted 12 up)   withcolor .67 blue;
label(btex $F_{\leftarrow}(x)$ etex, point 1.7 of f shifted 14 down) withcolor .56 green;

picture de; de = thelabel(btex dissipated energy etex, center f);
unfill bbox de; draw de withcolor .5 white;

% the arrow decorations
ahangle := 30; ahlength := 3; r=12; 
for a = 2r step 2.55r until arclength f - r:
  drawarrow subpath(arctime a of f, arctime a+r of f) of f 
            shifted 3 unitvector(direction arctime a of f of f rotated 90);
endfor

endfig;
end.