This symposium pertains to the study of mathematical methods in problems of nonlinear elasticity, continuum mechanics, and structural mechanics and is motivated by the many contributions of Timothy Healey in this area. Healey pioneered the use of group-theoretic methods in global bifurcation problems with symmetry. Along with Henry Simpson, he developed a nonlinear Fredholm degree to prove the existence of global solution continua in nonlinear elasticity. Along with many co-workers, his approach based on symmetry and global bifurcation/continuation has illuminated the behavior of a wide-variety of physical systems, including rod structures, lipid-bilayer vesicles, phase transitions, wrinkling in thin sheets, creasing in soft solids, and brittle fracture. Recently he has established new existence theorems for thin, nonlinearly elastic shells undergoing large membrane strains.
Background
Solutions to today’s important technological problems will often involve the use of advanced materials and structures in extreme environments. These demanding applications dictate that scientists and engineers develop a deep mathematical understanding of the global solution-sets for the relevant boundary value problems in nonlinear solid mechanics.
Issues
There are many open issues in this field, that straddle physics, mechanics, materials science, and applied mathematics. Encompassed are a diverse set of topics, such as the careful mathematical modeling of important phenomena at appropriate length and time scales; rigorous analysis of the resulting mathematical problems to learn as much as possible in the analytical setting; and efficient and robust computational analysis and simulation to learn what cannot be obtained from analysis alone.
Objective and Topics
The objective of the symposium is to bring together the different communities who work on the various aspects—experimental, mathematical modeling, and numerical simulations—of problems in the nonlinear elastic deformation of materials and structures. We plan to include scientists from the mechanics, physics and applied mathematics communities who study these problems at different length (from continuum to atomistic) and time (from geological to ballistic) scales.
Topics of interest will include rod and thin structures theories, wrinkling and buckling problems, active materials and phase transformations, and fracture mechanics. Discussion will focus on the characterization of global bifurcation/continuation of solutions to these problems and their interpretation and application. Works presenting experimental, analytical, and numerical tools for the facilitation of such studies, such as high-speed digital image correlation, Fredholm degree theory, group-theoretic methods, and robust high-performance computational methodologies, are also welcome.
Broadly, the symposium will endeavour to look back at the great milestones achieved over the preceding decades, and to look forward toward the developing ideas for solving the challenging problems of tomorrow.
The symposium is supported by the following organizations