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.
Ph.D. (1985) University of Illinois