Isaac Newton Institute for Mathematical Sciences

Mathematical Developments in Solid Mechanics and Materials Science

September - December 1999

Organisers: K Bhattacharaya (Pasadena), P Suquet (Marseille), JR Willis (Cambridge)

Workshop on

Models of Fracture

1-12 November 1999

Current Programme List of Participants

This Workshop forms a part of the programme Mathematical Developments in Solid Mechanics and Materials Science. The topic of fracture has long been of concern for structural engineering, although significant advances have been made by mathematicians, materials scientists and physicists. Over the last few years, physicists interested in nonlinear phenomena have returned to problems of crack propagation, and to the study of model problems in which cracks develop from the breaking of bonds. Also, it is now possible to model the entire development of a crack, in a finite-element model of a continuum, even with inelastic effects (that is, plasticity) allowed for. Damage mechanics is well developed at the phenomenological level, and can also be built into codes that predict fracture. The admission of any model for microscopic processes introduces a length scale, and size effects may emerge. These are of practical importance as well as theoretical interest. Mathematical theory based on variational methods is developing, at least for cracks in elastic media. However, many problems remain: there is no adequate theory for the stability of a propagating crack, even in the framework of linear elasticity, at the present time. Interactions between macro- and micro-cracks require better modelling. The development of (approximate) fractal structure has so far not been modelled mechanistically. Some hint of the influence of underlying lattice structure has been demonstrated (it may apparently prevent steady-state propagation at low speed) but this is not fully worked out. It is intended to allow issues such as these to be aired, by all interested parties. These will be motivated by concern for structural engineering, materials, seismology, and of course the underlying mathematics.

The formal timetable of the workshop is kept deliberately light, so that participants can spend a high proportion of their time actively considering, discussing and perhaps solving outstanding problems. Additional talks and/or discussion sessions can be arranged during the Workshop according to participants' wishes.

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