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Host: Isaac Newton Institute for Mathematical Sciences
Homepage: http://www.newton.cam.ac.uk/programs/smmw01.html
Organizers: K Bhattacharya (Caltech), P Suquet (Marseille), JR Willis (Cambridge)
Description:
The Summer School and Concentration will kick-off the programme Mathematical Developments in Solid Mechanics and Materials Science. The recent years have
seen much advance in the mathematical aspects of materials science and solid mechanics. Materials science and solid mechanics have posed interesting questions in
mathematics and in turn mathematical analysis has brought new insights in these areas. The key issue is how the microscopic structure of a solid material influences its
macroscopic response to stimuli like stress and magnetic field, and conversely how the application of macroscopic loads influences the microstructure. In particular,
phase transformations, damage and fracture may occur, creating structures at various length scales which can evolve with macroscopic stimulus. The challenge, both
for mathematics and physical modelling, is to comprehend relationships between models at different length scales. This has led already to well-developed theories in
static or equilibrium situations. Length scales can be linked using the theory of ``homogenization'' when the scales are widely separated, and the formation of
microstructure can be addressed using a class of variational problems that do not admit classical solutions, but only those which are highly oscillatory. Mathematical
tools for describing microstructure have been developed and these have been used to study the link between microstructure and macroscopic properties. Yet
challenges remain, and these have inspired different approaches. Much of this development has been at the continuum level and linking it to the atomistic length scales
is a continuing theme. Some phenomena may be unstable, at least at the microscopic level, and, even if stable, may admit multiple equilibria. Therefore, the study of
the kinetics of the processes is a key requirement, making demands for modelling, for computation and for the analysis of partial differential equations. In particular,
the (possibly hierarchical) development of large-scale patterns is an important challenge
Speakers: G Allaire (Paris VI), M Finnis (Belfast), S Müller (MPI, Leipzig), E Van der Giessen (Delft)
Mail Address:
Professor JR Willis DAMTP Silver Street Cambridge CB3 9EW
Date received: January 20, 1999, revised August 28, 1999
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