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Timothy James Healey

Professor
Mathematics
Malott Hall, Room 523

Research Interests

Applied analysis and partial differential equations, mathematical continuum mechanics

I work at the interface between nonlinear analysis of pde's/calculus of variations and the mechanics of materials and elastic structures.  Nonlinear (finite-deformation) 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.  Although the beginnings of the subject date back to Cauchy, the current state of existence theory is generally poor; there are many open problems. 

The two main goals of my work are to establish rigorous existence results and to uncover new phenomena.  The work involves a symbiotic interplay between three key ingredients:  careful mechanics-based modeling, mathematical analysis, and efficient computation.  It ranges from the abstract to the more concrete.

Research Group Members

Selected Publications

Injectivity and self-contact in second-gradient nonlinear elasticity (with A. Palmer), Calc. Var. 56 (2017) no. 114, DOI 10.1007/s00526-017-1212-y.
 
Symmetry-Breaking Global Bifurcation in a Surface Continuum Phase-Field Model for Lipid Bilayer Vesicles (with S. Dharmavaram), SIAM J. Math. Anal., 49 (2017) no. 2, 1027–1059.
 
Direct computation of two-phase icosahedral equilibria of lipid bilayer vesicles (with Q. Li and S. Zhao), Comput. Methods Appl. Mech. Engrg. 314 (2017), 164–179.
 
Stability boundaries for wrinkling in highly stretched elastic sheets (with Q. Li) Journal of the Mechanics and Physics of Solids 97, (2016) 260-274.
 

Injective weak solutions in second-gradient nonlinear elasticity (with S. Krömer), ESAIM: COCV 15 (2009), 863–871.

Education

Ph.D. (1985) University of Illinois

Websites

Research Group Members

Graduate Students