Distinguished University Research Professor, Joint/Mathematics
Continuum Physics and Nonlinear Analysis

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.

Selected publications:

1. Nonlinear Problems of Elasticity, 2nd edn., Springer, 2005.
2. (with W. Lacarbonara) Forced radial motions of nonlinearly viscoelastic shells, J. Elasticity 96 (2009) 155-190.
3. The shuddering pendulum, J. Nonlinear Science 21 (2011) 595--638.
4. (with S. Ulusoy) The asymptotics of heavily burdened viscoelastic rods, Quart. Appl. Math. 70 (2012) 437--467.
5. (with D. Bourne) The Taylor-Couette problem for flow in a deformable cylinder, J. Dynamics Diff. Eqns. 27 (2015) 457--480.
6. (with A. B. Stepanov) Radially symmetric motions of nonlinearly viscoelastic bodies under live loads, Archive for Rational Mech. Anal. 226 (2017) 1209--1247.

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