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\dateposted{2025-11-05}
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\title{Recent advances in finite fracture mechanics---a tribute to
Dominique Leguillon's scientific achievements}

\alttitle{Progr\`{e}s r\'{e}cents en m\'{e}canique finie de la rupture ---
un hommage \`{a} l'\oe{}uvre scientifique de Dominique Leguillon}

\author{\firstname{Jean-Baptiste} \lastname{Leblond}}
\email{jbl@lmm.jussieu.fr}

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On the scene of contemporaneous French fracture mechanics, Dominique
Leguillon stands as a singular and most remarkable character. Indeed,
after the completion of his PhD thesis undertaken and pursued at the
Laboratoire de Mod\'{e}lisation en M\'{e}canique of Universit\'{e}
Pierre et Marie Curie (Paris VI) (now part of Sorbonne Universit\'{e}),
he was appointed as Ing\'{e}nieur de Recherches in the CNRS (Centre
National de la Recherche Scientifique). His already heavy task, which
he managed to perform alone, consisted in the organization and
maintenance of the ensemble and network of computers of the Laboratoire
de Mod\'{e}lisation en M\'{e}canique. But he would not limit his
activities to such aspects and undertook scientific cooperations with
various researchers, and notably our illustrious colleague Evariste
Sanchez-Palencia. With him, he dedicated numerous and fruitful efforts
to various important issues in mechanics of deformable solids, such as
periodic homogenization, matched asymptotic expansions, and occurrence
of singularities. The popularity and impact of these studies allowed
him to successfully apply for a post of Directeur de Recherches at the
CNRS. This highly improbable passage from a position of engineer in
charge of computers to one of researcher is exceptional enough in the
CNRS to deserve a very special mention. 

But it was in the 2000's that Dominique's career and scientific
reputation really started to take off. In order to explain the nature
of his essential contribution, it is first necessary to provide some
elements of context. 

The aim of the classical theory of fracture mechanics is to study and
predict propagation of cracks in materials. It is of utmost practical
importance, and serves as a basis to avoid crack-induced failure of
various mechanical objects and structures. But in spite of its very
numerous and important successes, it is still prone to notable
shortcomings. For instance, it permits to predict crack propagation
from some small pre-existing crack, but not in a sound structure devoid
of any pre-crack. Even more critically, it fails to predict crack
initiation from a notch root, in spite of the frequent occurrence of
such a situation, notably in welded joints. 

The essential contribution of Dominique, which no longer owed anything
to anyone else, was to overcome these limitations by proposing an
extended theory, nowadays known as ``finite fracture mechanics''. This
new approach of this type of problems requires the definition of some
``double'' or ``coupled'' criterion, involving two necessary conditions
for crack propagation, one on the opening stress before propagation,
the other on the energy-release-rate. The new theory is termed
\textit{finite} fracture mechanics because it does not split crack
propagation into infinitesimal steps, each governed by the double
criterion, but into steps that may be finite, over some distance
determined by the criterion.

Dominique's proposal immediately drew attention from numerous
researchers in the field at various places in the world, and met with
very important success; experimenters active in France, Europe,
Isra\"{e}l and the USA, embarked on the experimental verification of
this proposal and its practical applications. Dominique collaborated
with them and accompanied them in his typically friendly way, thus
weaving a large web of international cooperations.

These features permit to state that Dominique's new theory of finite
fracture mechanics stands as one of the major additions brought to
fracture mechanics in the last few decades. 

Having retired, Dominique changed almost nothing in his working habits,
and went on coming to his research institution every day, pursuing the
development of his ideas with his colleagues and friends. However,
having reached the age of 75 in full command of his intellectual means,
and although nothing permitted to foresee such an event, Dominique
suddenly succumbed to a heart attack while he was walking in the
street. He leaves an immense emptiness behind him, but also appealing
scientific perspectives, because his ideas, being so simple, elegant
and straightforwardly applicable to problems of both scientific and
technical nature, can still motivate numerous and importants
developments; so true it is that fracture mechanics cannot possibly be
content with predicting and depicting the propagation of cracks while
forgetting about their initiation.  

For those who had the privilege of knowing Dominique, he will remain an
exceptional colleague and friend. The aim of this special issue of
\textit{Comptes-Rendus M\'{e}canique} dedicated to him is to fittingly
honor his memory, by showing how his ideas still give rise and
stimulate diverse and interesting works.

\vspace*{2pc}

\hspace*{7cm}
\begin{xxminipage}
Jean-Baptiste Leblond\frnewline
Emeritus Professor\frnewline 
Sorbonne Universit\'e\frnewline
Member of the French Academy of Sciences\frnewline
France\frnewline
\textemail{jbl@lmm.jussieu.fr}
\end{xxminipage}

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