Nonlinear Problems of Solid Mechanics

ISR-affiliated Professor Stuart Antman (Math) received a one-year, $123K NSF grant for Nonlinear Problems of Solid Mechanics. The investigator gives careful mathematical treatments of a variety of dynamical and steady-state nonlinear problems for deformable rods, shells, and three-dimensional solid bodies, possibly in contact with moving fluids, variable temperature fields, and electromagnetic fields. The bodies are composed of nonlinearly elastic, plastic, viscoplastic, or magneto-(visco-)elastic materials. The goals of these studies are to discover new nonlinear effects and new kinds of instabilities, determine thresholds in constitutive equations separating qualitatively different responses, determine general classes of constitutive equations that are both physically and mathematically natural, determine how existence, regularity, and well-posedness depend on material behavior, contribute to the theory of shocks and dissipative mechanisms in solids, and develop new methods of nonlinear analysis and of effective computation for problems of solid mechanics.