One example of the many discussions which arose is the stabilising or destabilising effect of higher-order terms which is still a hotly debated question. This workshop concentrated on problems of fracture which are at present being approached by specialists other than engineers, although the problems are of concern to the latter group as well. Direct computational modelling is now possible, employing finite elements linked across each element boundary by cohesive forces. Such modelling yields very specific results of great complexity, and efforts are being made by certain pure mathematicians to model systems of this type employing the tools of homogenization. Allowance for the development of microcracks throughout the medium requires the use of functions of bounded variation and introduces a significant new component in the asymptotic analysis.
Current research is directed towards two and three dimensions.
New ideas are needed, and access to guidance from the engineering community about what assumptions may be realistic is one of the by-products of the workshop. R Craster, J R Willis, V Shenoy. Seeds have been sown and the full extent of the benefit will be apparent in a year or two, when contacts established during the programme have had the opportunity to mature into productive collaborations. It is not possible to delineate the full range of possibilities here. Phase transformations .