Timothy J. Healey

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.