Timothy J. Healey

Professor and Chair of Theoretical & Applied Mechanics (T&AM) and Member of the Field of Mathematics

Web Site www.tam.cornell.edu/Healey.html Contact Information Office:  212 Kimball Hall Phone:  (607) 255-3738 Fax:  (607) 255-2011 Email:  tjh10@cornell.edu

Education

Ph.D. (1985) University of Illinois

Research Area: Nonlinear elasticity, nonlinear analysis, partial differential equations

I work at the interface between nonlinear analysis of pde’s — mostly elliptic systems — and the mechanics of elastic structures and solid continua. Nonlinear (finite) elasticity is the central model of continuum solid mechanics. It has a vast range of applications, including flexible engineering structures, biological structures — both macroscopic and molecular, and materials like elastomers and shape-memory alloys — everything from fighter jets to lingerie! Although the beginnings of the subject date back to Cauchy, the current state of existence theory is quite poor; properly formulated problems of the subject are often out of the range of present day mathematics. In other words there are many open problems.

My work ranges from the abstract — e.g., developing a generalized nonlinear Fredholm degree to obtain solutions “in the large” in 3-D nonlinear elasticity — to the more concrete — e.g., modeling the helical microstructure of DNA in elastic rod models. Most recently I have become quite interested in the analysis of elastic surfaces in models inspired by “biological membranes.”

Selected Publications

Global continuation in nonlinear elasticity (with H. Simpson), Arch. Rat. Mech. Anal. 143 (1998), 1–28.

Global continuation in displacement problems of nonlinear elastostatics via the Leray-Schauder degree, Arch. Rat. Mech. Anal. 152 (2000), 273–282.

Global continuation via higher-gradient regularization and singular limits in forced one-dimensional phase transitions (with H. Kielhöfer), SIAM J. Math. Anal. 31 (2000), 1307.

Material symmetry and chirality in nonlinearly elastic rods, Math. Mech. Solids 7 (2002), 405–420.

Global bifurcation in nonlinear elasticity with an application to barrelling states of cylindrical columns (with E. Montes), J. Elasticity 71 (2003), 33–58.

Bifurcation with a two-dimensional kernel (with S. Krömer and H. Kielhöfer), J. Diff. Eq. 220 (2006), 234–258.

Two-phase equilibria in the anti-plane shear of an elastic solid with interfacial effects via global bifurcation (with U. Miller), Proceeding of the Royal Society A 463 (2007), 1117–1134.

Last modified: October 31, 2006