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Gilles Francfort

The Mysterious Role of Stability in Solids with Defects
 

Abstract

Adjudicating the correct model for the behavior of solid continua in the presence of defects is no easy task.  In this respect as in many others, solid mechanics lags way behind its more popular and attractive sibling, fluid mechanics.  In this talk, I propose to describe the ambiguity created by the onset and growth of material defects in solids.  Then, I will suggest a notion of structural stability that may help to secure meaningful evolutions. I will illustrate how such a notion leads us from the good to the bad, and then to the ugly when going from plasticity to fracture, and then to damage.  The only conclusion to be drawn is that much of the mystery remains.