Past OxMOS Workshop/Meeting/Lecture

27 April 2011
14:00
Abstract

We consider the problem of cavitation in nonlinear elasticity, or the formation of macroscopic cavities in elastic materials from microscopic defects, when subjected to large tension at the boundary.

The main goal is to determine the optimal locations where the body prefers the cavities to open, the preferred number of cavities, their optimal sizes, and their optimal shapes. To this aim it is necessary to analyze the elastic energy of an incompressible deformation creating multiple cavities, in a way that accounts for the interaction between the cavitation singularities. Based on the quantitative version of the isoperimetric inequality, as well as on new explicit constructions of incompressible deformations creating cavities of different shapes and sizes, we provide energy estimates showing that, for certain loading conditions, there are only the following possibilities:

  • only one cavity is created, and if the loading is isotropic then it is created at the centre
  • multiple cavities are created, they are spherical, and the singularities are well separated
  • there are multiple cavities, but they act as a single spherical cavity, they are considerably distorted, and the distance between the cavitation singularities must be of the same order as the size of the initial defects contained in the domain.

In the latter case, the formation of thin structures between the cavities is observed, reminiscent of the initiation of ductile fracture by void coalesence.

This is joint work with Sylvia Serfaty (LJLL, Univ. Paris VI).

  • OxMOS Workshop/Meeting/Lecture
6 January 2010
09:00
to
8 January 2010
13:00
Speaker names are listed below.
Abstract
Speakers include: * David Abrahams (Manchester, UK); * Stuart Antman (Maryland, USA); * Martine Ben Amar (Ecole Normale Supérieure, France); * Mary Boyce (MIT, USA); * John Hutchinson (Harvard, USA); * Nadia Lapusta (Caltech, USA); * John Maddocks (Lausanne, Switzerland); * Stefan Mueller (Bonn, Germany); * Christoph Ortner (Oxford, UK); * Ares Rosakis (Caltech, USA); * Hanus Seiner (Academy of Sciences, Czech Republic); * Eran Sharon (Hebrew University, Israel); * Lev Truskinovsky (Lab de Mécanique des Solids, France); * John Willis (Cambridge, UK).
  • OxMOS Workshop/Meeting/Lecture
7 December 2009
09:00
to
8 December 2009
17:00
Speaker names are listed below.
Abstract
Speakers include: * Graeme Ackland (School of Physics and Astronomy, Edinburgh) * Andrea Braides (Rome II) * Thierry Bodineau (École Normale Supérieure, Paris) * Matthew Dobson (Minneapolis) * Laurent Dupuy (CEA, Saclay) * Ryan Elliott (Minneapolis) * Roman Kotecky (Warwick) * Carlos Mora-Corral (BCAM, Bilbao) * Stefano Olla (CEREMADE, Paris-Dauphine) * Bernd Schmidt (TU Munich) * Lev Truskinovsky (École Polytechnique, Palaiseau) * Min Zhou (Georgia Tech, Atlanta)
  • OxMOS Workshop/Meeting/Lecture
3 June 2009
09:00
to
18:00
M. Ortiz, M. Luskin, F.Legoll, O. Pierre-Louis, A.Raoult
Abstract
Macroscopic properties of solids are inherently connected to their micro- and nano-scale details. For example, the microstructure and defect distribution influence the elastic and plastic properties of a crystal while the details of a defect are determined by its elastic far-field. The goal of multi-scale modelling is to understand such connections between microscopic and macroscopic material behaviour. This workshop brings together researchers working on different aspects of multi-scale modelling of solids: mathematical modelling, analysis, numerical computations, and engineering applications.
  • OxMOS Workshop/Meeting/Lecture

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