September - December 1999

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

Workshop on

**Models of Fracture
**

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.