Plenary Lecture

Hamiltonian Formalisms Applied to Continuum Mechanics Potential Use for Fracture Mechanics


Professor Naman Recho
ERMESS/ EPF-Ecoles d'Ingenieurs, Sceaux and
LaMI, University Blaise Pascal, Clermont II

Abstract: The first part of this paper deals with several Hamiltonian formalisms in elasticity. We first present briefly the formalisms of Zhong and Bui, (Bui, [1]; Zhong, [2]), which resolve respectively the two-end problem and the Cauchy problem in elasticity. Then we propose a new Hamiltonian formalism, which resolves simultaneously the two problems mentioned above and it shows the link between the two formalisms. The potential use for fracture mechanics purposes is then mentioned. In fact, when traditional theories in fracture mechanics are used, asymptotic analyses are often carried out by using high-order differential equations governing the stress field near the crack tip. The solution of the high-order differential equations becomes difficult when one deals with anisotropic or multiplayer media etc. The key of our idea is to introduce the Hamiltonian system, usually studied in rational mechanics, into continuum mechanics also, one can obtain a system of first-order differential equations, instead of the high-order differential equation. This method is very efficient and quite simple to obtain solution of the governing equations of this class of problems. It allows dealing with large range of problems, which may be difficult to resolve by using traditional methods.
By using this approach, we have resolved various problems. Some of them have been solved previously and some not yet. We see that the present method is particularly efficient for resolving multi-material problems. So the multi-material problem can be resolved as a single material problem through the construction of a transfer matrix.
We believe that a large domain can be found in applying this new approach into fracture mechanics.

Brief Biography of the Speaker:
Naman Recho is a Professor at the University Blaise Pascal in Clermont Ferrand, France, he is also head of ERMESS- Research laboratory (Equipe de Recherche en Mecanique et Securite des Structures) at EPF Engineering school in Sceaux, France.
He has worked extensively with conceptual and applied aspects of fracture mechanics, with welded offshore structures and reliability analysis of cracked structures. He also teaches at Centre des Hautes Etudes de la Construction, Paris, and is guest Professor at Hefei University of Technology in China.
Professor Naman Recho was educated at the French University of Pierre and Marie Curie in Paris. He graduated in this university as Doctor Engineer in 1980 and "Docteur d'Etat Es-Sciences Physiques" in 1987. He is full Professor since 1988. He is delegate (Delegation CNRS) at National Centre of Scientific Research in Paris 2005-2007 and has written three textbooks within Fracture Mechanics and Fatigue Analysis.
In the recent 10 years, he directed more than 15 theses dealing with fracture mechanics and fatigue design of welded joints and participated into several research programs with industries.



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