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# Timothy J. Healey

Professor

### Departments/Programs

- Mathematics

### Graduate Fields

- Applied Mathematics
- Mathematics
- Theoretical and Applied Mechanics

## Research

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.

## Courses

## 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.
- Material symmetry and chirality in nonlinearly elastic rods, Math. Mech. Solids 7 (2002), 405–420.
- Global continuation in displacement problems of nonlinear elastostatics via the Leray-Schauder degree, Arch. Rat. Mech. Anal. 152 (2000), 273–282.
- Global continuation in nonlinear elasticity (with H. Simpson), Arch. Rat. Mech. Anal. 143 (1998), 1–28.
- Preservation of nodal structure on global bifurcating solution branches of elliptic equations with symmetry (with H. Kielhöfer), JDE 106 (1993), 70-89