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SUMMARY:The variational approach to fracture: formulation\, general proper
 ties and examples
DTSTART:20180309T121500
DTEND:20180309T131500
DTSTAMP:20261001T230350Z
UID:ea65b27bfe29fa85c16f17b65f694eb62dd761e1664f089b16f14df2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Dr Jean-Jacques Marigo\, Ecole Polytechnique\, Palaiseau
 \, Île-de-France\, France\nAbstract : The lecture is devoted to gradient 
 damage models which allow us to describe all the process of degradation of
  a body including the nucleation of cracks and their propagation. The cons
 truction of such model follows the variational approach to fracture [2] an
 d proceeds into two stages: (1)\ndefinition of the energy\; (2) formulatio
 n of the damage evolution problem. The total energy of the body is defined
  in terms of the state variables which are the displacement field and the 
 damage field in the case of quasi-brittle materials [5]\, whereas they con
 tain also the plastic strain field in the case of ductile materials [1]. T
 hat energy contains in particular gradient damage terms in order to avoid 
 too strong damage localizations. The formulation of the damage evolution p
 roblem then based on the concepts of irreversibility\, stability and energ
 y balance\, as well inquasi-static as in dynamic [4]. That allows us to co
 nstruct homogeneous as well as localized damage solutions in a closed form
  and to illustrate the concepts of loss of stability\, of scale effects\, 
 of damage localization\, and of structural failure. Moreover\, the variati
 onal formulation leads to a natural numerical method based on an alternate
  minimization algorithm. Several numerical examples will illustrate the ab
 ility of this approach to account for all the process of fracture includin
 g a 3D thermal shock problem where the crack evolution is very complex [3]
 .\n\nReferences\n[1] R. Alessi\, J.-J. Marigo\, and S. Vidoli. Gradient da
 mage models coupled with plasticity: variational formulation and main prop
 erties. Mechanics of Materials\, 80:351–367\, 2015.\n[2] B. Bourdin\, G.
  A. Francfort\, and J.-J. Marigo. The variational approach to fracture. J.
  Elasticity\, 91(1–3):5–148\, 2008.\n[3] B. Bourdin\, J.-J. Marigo\, C
 . Maurini\, and P. Sicsic. Morphogenesis and propagation of complex cracks
  induced by thermal shocks. Phys. Rev. Lett.\, 112(1):014301\, 2014.\n[4] 
 T. Li\, J. J. Marigo\, D. Guilbaud\, and S. Potapov. Numerical investigati
 on of dynamic brittle fracture via gradient damage models. Advanced Modeli
 ng and Simulation in Engineering Sciences\, DOI: 10.1186/s40323-016-0080-x
 :3–26\, 2016.\n[5] K. Pham\, H. Amor\, J.-J. Marigo\, and C. Maurini. Gr
 adient damage models and their use to approximate brittle fracture. Intern
 ational Journal of Damage Mechanics\, 20(4):618–652\, 2011\n\nBio : Jean
 -Jacques Marigo obtained his PhD in Mechanics from the University Pierre a
 nd Marie Curie (Paris\, France). He is currently a full-time professor in 
 the mechanics department at the Ecole Polytechnique (Palaiseau\, Île-de-F
 rance\, France). He has received the Prix Paul Doistau-Emile Blutet in 200
 2 from the l'Académie des Sciences (France) and the Tullio Levi Civita In
 ternational Prize in Mechanics and Applied Mathematics in 2011 by the Tull
 io Levi Civita Foundation (Italy). Since 2009\, Prof. Marigo is an associa
 ted editor of the Journal of Elasticity.
LOCATION:GC B3 30 https://plan.epfl.ch/?room=GCB330
STATUS:CONFIRMED
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