Skip to main content

Faculty Profile

faculty photo

224 Kimball
Cornell University
Ithaca, NY 14853

Phone: 607/255-3738

Timothy J. Healey

Professor

B.S. 1976 (Missouri)

M.S. 1978 (Illinois)

Ph.D. 1985 (Illinois)

Professional Biography

The grandson of immigrants, Tim Healey was the first in his extended family to attend the university. With the full support of an Evans Scholarship, he studied mathematics and civil engineering at the University of Missouri where he was awarded the B.S. degree in 1976. He obtained an M.S. from the University of Illinois in 1978 and then worked for two years as a licensed structural engineer in Los Angeles. He returned to Illinois to pursue his doctoral studies in 1980. After receiving his Ph.D. in 1984, he spent one year as a visiting professor in the Department of Mathematics at the University of Maryland. He joined the Department of Theoretical & Applied Mechanics at Cornell in 1985. He is a member of the Editorial Boards of the SIAM Journal of Mathematical Analysis , the Journal of Elasticity, the Zeitschrift für angewandte Mathematik und Physik (ZAMP) and Discrete and Continuous Dynamics/Systems B. He has held visiting positions at the Ecole Polytechnique Federal de Lausanne, the University of Minnesota and the University of Sydney. He won a Dean's Prize for Excellence in Teaching in 1993 and a College of Engineering Teaching Award in 1996. He has chaired the Department of Theoretical and Applied Mechanics from 2000 to the present.

Research Interests

I work at the interface between the mechanics of nonlinearly elastic structures and solids, partial differential equations,nonlinear analysis and bifurcation theory. 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. My work ranges from the abstract - e.g., developing a generalized nonlinear Fredholm degree obtaining the existence of solutions “in the large” in 3-D nonlinear elasticity – to the more concrete – e.g., modeling the helical microstructure of things like DNA in elastic rod models. I am particularly interested in the role of constitutive hypotheses (modeling) within general classes of problems exhibiting instability and bifurcation phenomena. Indeed experiments on real materials often involve bifurcations from some homogeneous state to more exotic ones, e.g., the onset of super-coiling in DNA, the stress-induced formation of microstructure in shape-memory alloys, etc. We employ rigorous methods of nonlinear analysis to predict the onset, global post-critical formation and stability of patterns in the “exotic” secondary states. This interplay between constitutive hypotheses, nonlinear analysis and also computation, in comparison with the physical phenomena, enables not only the calibration of predictive models but also the potential for classifying materials according to mathematical constitutive hypotheses.

Current Project:
NSF, Applied Mathematics, DMS 0707715 "Multiphase Problems of Nonlinear Elasticity"

Recent Courses:
TAM 718 Topics in Bifurcation Theory
TAM 752 Nonlinear Elasticy
TAM 6110 Methods of Applied Math II (Spring 2009)
TAM 3100 Introduction to Applied Math I (Summer 2009)

 

Selected Publications

  • T.J. Healey & H. Kielhöfer, "Preservation of Nodal Structure on Global Bifurcating Solution Branches of Elliptic Equations with Symmetry", Journal of Differential Equations, vol. 106, no. 1, (1993), p. 70.
  • T.J. Healey, H. Kielhöfer & C.A. Stuart, "Global branches of positive weak solutions of semilinear elliptic problems over nonsmooth domains", Royal Society of Edinburgh, 124A, (1994), p. 371.
  • J.C. Wohlever & T.J. Healey, "A group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell", Comput. Meth. Appl. Mech. Engr., vol. 122, (1995), p. 315.
  • T.J. Healey & P. Rosakis, "Unbounded Branches of Globally Injective Solutions in the Forced Displacement Problem of Nonlinear Elasticity", J. Elasticity, vol. 49, (1997), p. 65.
  • T.J. Healey & H. Simpson, "Global Continuation in Nonlinear Elasticity", Arch. Rational Mech. Anal., vol. 143, (1998), p. 1.
  • A. Vainchtein, T.J. Healey, P. Rosakis & L. Truskinovsky, "The Role of the Spinodal Region in One-Dimensional Models of Phase Transformations", Physica D, vol. 115, (1998), p. 29.
  • A. Vainchtein, T.J. Healey & P. Rosakis, "Bifurcation and Metastability in a New One-Dimensional Model for Martensitic Phase Transitions", Comput. Meth. Appl. Mech. Engr., vol. 170, (1999), p. 407.
  • T.J. Healey & H. Kielhöfer, "Global Continuation via Higher-Gradient Regularization and Singular Limits in Forced One-Dimensional Phase Transitions", SIAM J. Math. Anal., vol. 31, (2000), p. 1307.
  • T.J. Healey, "Global Continuation in Displacement Problems of Nonlinear Elastostatics via the Leray-Schauder Degree", Arch. Rational Mech. Anal., vol. 152, (2000), p. 273.
  • G. Domokos & T.J. Healey, "Hidden Symmetry of Global Solutions in Twisted Elastic Rings", J. Nonlinear Science, vol. 11, (2001), p. 47.
  • Material Symmetry and Chirality in Nonlinearly Elastic Rods, Math. Mech. Solids 7 (2002) 405-420. PDF
  • K. MacEwen & T.S. Healey, A Simple Approach to the 1:1 Resonance Bifurcation in Follower-Load Problems, Nonlinear Dynamics 32 (2003) 143-159.
  • T.S. Healey & E. Montes, Global Bifurcation in Nonlinear Elasticity with an Application to Barrelling States of Cylindrical Columns, J. Elasticity 71 (2003) 33-58.
  • T.J. Healey & P. Mehta, Straightforward Computation of Spatial Equilibria of Geometrically Exact Cosserat Rods, Int., J. Bifurcation Chaos 15 (2005) p. 949. 
  • G. Domokos & T.J. Healey, Multiple Helical Perversions of Finite Intrinsically Curved Rods, Int., J. Bifurcation Chaos 15 (2005) p. 871.
  • T.J. Healey & P. Mehta, On 2D Steady Solutions of the Planar Couette Flow Problem, Physics of Fluids 17 (2005) (094108) p.1.
  • T.J. Healey, H. Kielhöfer & S. Krömer, Bifurcation with a Two-Dimensional Kernel, J. Diff. Eq. 220 (2006) p. 234.
  • A Mareno & T.J. Healey, Global Continuation in Second-Gradient Nonlinear Elasticity, SIAM Math. Anal. 38 (2006) p. 103.
  • M. Lilli, T.J. Healey, H. Kielhöfer, Singular Perturbation as a Selection for Young-Measure Solutions, SIAM Math. Anal. 39 (2007) p. 195.
  • T.J. Healey & U. Miller, Two-Phase Equilibria in the Anti-Plane Shear of an Elastic Solid with Interfacial Effects via Global Bifurcation, Proc Roy. Soc. A, 463 (2007) p. 1117.
  • L. Deseri & T.J. Healey, Variational Derivation for Higher Spatial-Gradient Van der Waals Fluids: Equilibria and Bifurcation, to appear Note di Matematica (2007).