biblatex has the built-in standard macro shorthandintro that can do this.
In the .bib file one will then add the shorthand field and give the short citation name there, like this
@article{jd14,
author = {Doe, J. and Smith, J. and Bar, F.},
title = {Some title},
journal = {Some journal},
year = {2014},
shorthand = {JD14},
}
The only thing that remains to be done is to make sure this macro is only called when it is appropriate. While there are some styles that already use shorthandintro, the plain authoryear and authortitle styles do not.
We well see how one can modify the authoryear so it uses the shorthand intro.
The default cite macro for authoryear can be found in authoryear.cbx.
The main citation part that is used if no shorthand is present can be out-sourced into a new macro longcite
\newbibmacro*{longcite}{%
\ifthenelse{\ifnameundef{labelname}\OR\iffieldundef{labelyear}}
{\usebibmacro{cite:label}%
\setunit{\addspace}}
{\printnames{labelname}%
\setunit{\nameyeardelim}}%
\usebibmacro{cite:labelyear+extrayear}}
Then the actual cite macro is changed to print a long citation and shorthand introduction at first cite (obviously the introduction is only printed if a shorthand is actually present) and the shorthand or long (normal) citation on subsequent citations.
\renewbibmacro*{cite}{%
\ifciteseen
{\iffieldundef{shorthand}
{\usebibmacro{longcite}}
{\usebibmacro{cite:shorthand}}}
{\usebibmacro{longcite}
\usebibmacro{shorthandintro}}}
In order to be able to use the \ifciteseen test, we will have to enable the citetracker (for example via citetracker=true).
Other citation styles use different cite macros and the modifications will have to be different then, also this modification does not currently work with \textcite.
MWE
\documentclass[british,a4paper]{article}
\usepackage{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{csquotes}
\usepackage{filecontents}
\usepackage[backend=biber,style=authoryear,citetracker=true]{biblatex}
\begin{filecontents*}{\jobname.bib}
@article{jd14,
author = {Doe, J. and Smith, J. and Bar, F.},
title = {Some Title},
journal = {Some Journal},
year = {2014},
shorthand = {JD14},
}
@article{jd13,
author = {Doe, J. and Smith, J. and Bar, F.},
title = {No shorthand here},
journal = {Some Other Journal},
year = {2013},
}
\end{filecontents*}
\addbibresource{\jobname.bib}
\newbibmacro*{longcite}{%
\ifthenelse{\ifnameundef{labelname}\OR\iffieldundef{labelyear}}
{\usebibmacro{cite:label}%
\setunit{\addspace}}
{\printnames{labelname}%
\setunit{\nameyeardelim}}%
\usebibmacro{cite:labelyear+extrayear}}
\renewbibmacro*{cite}{%
\ifciteseen
{\iffieldundef{shorthand}
{\usebibmacro{longcite}}
{\usebibmacro{cite:shorthand}}}
{\usebibmacro{longcite}
\usebibmacro{shorthandintro}}}
\begin{document}
\cite{jd14} again \cite{jd14} and one more time \cite{jd14}.
Just for comparison \cite{jd13}.
\printbibliography
\end{document}

If you prefer "hereafter <key>" to "henceforth cited as <key>", just add
\DefineBibliographyStrings{english}{citedas = {hereafter}}
to the preamble.
If you like Václav Pavlík's solution with natbib's cite-alias function, you'll be delighted to hear that biblatex's natbibcompatibility mode (just pass natbib=true to the load-time options) also offers these features with (as far as I know) exactly the same syntax.
biblatex? Do you usebiblatex? If so what style do you use? If not, what style would you like to use (just a simple author-year style by the looks of it)? – moewe Sep 30 '14 at 17:34biblatexandalphabeticstyle. Just check page 83-88 in the manual to see the various citation commands provided. – umarcor Sep 30 '14 at 19:02biblatexis out of the question, but I'll add a solution anyway. (Just an aside though: If you use thesvjour3template, you probably ought to adhere to the bib/citation style of that template.) – moewe Oct 01 '14 at 05:29