Distinguished University Professor, Joint/Mathematics
Continuum Physics and Nonlinear Analysis
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, USA.
Professor Antman studies a variety of dynamical and steady-state nonlinear problems for rods, shells, and three-dimensional solid bodies. The bodies are composed of nonlinearly elastic, viscoelastic, plastic, viscoplastic, or magnetoelastic materials. In each case, properly invariant, geometrically exact theories encompassing general nonlinear constitutive equations are used. In some cases, the solids interact with fluids. The goals of these studies are to discover new nonlinear effects, determine thresholds in constitutive equations separating qualitatively different responses, treat control problems involving "smart" materials, examine important kinds of instabilities, 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.
(with T.I. Seidman) Quasilinear Hyperbolic-Parabolic Equations of Nonlinear Viscoelasticity, Journal of Differential Equations, 124 (1996), 132-185.
(with M. Lanza de Cristoforis) Peculiar Instabilities due to the Clamping of Shearable Rods, International Journal of Nonlinear Mechanics, 32 (1997), 31-54.
Convergence Properties of Hierarchies of Dynamical Theories of Rods and Shells, Zeitschrift fuer Angewandte Mathematik und Physik, 48 (1997), 874-884.
(with R.S. Marlow and C.P. Vlahacos) The Complicated Dynamics of Heavy Rigid Bodies Attached to Light Deformable Rods, Quarterly of Applied Mathematics, 56 (1998), 431_460.
(with L.S. Srubshchik) Asymptotic Analysis of the Eversion of Nonlinearly Elastic Shells, Journal of Elasticity, 50 (1998), 129-179.