Timothy J. Healey
523 Malott Hall
Ph.D. (1985) University of Illinois
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.
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