Attempts at the formulation of response laws of many materials regularly encounter microstructural randomness and complexity of several scales. As a result, problems have to be cast in the framework of stochastic (micro)mechanics. This calls for a range of techniques lying at the intersection of mechanics, thermodynamics, materials science and applied/stochastic mathematics. Applications include composite materials, polycrystals, granular media, functionally graded materials and biomaterials. Methods involve classical and non-classical continuum mechanics, stochastic mechanics/dynamics, computational mechanics, random geometry (+ mathematical morphology) and experiments.
Current research:
- Modeling the spatio-temporal mutliscale dynamics of head trauma. This research is based on MRI of human brain, conducted jointly with faculty in the Departments of Bioengineering (Brad Sutton) and Kinesiology (Steve Broglio).
- Continuum thermomechanics in the presence of anomalous (not Fourier-type) heat conduction. See Book 2.
- Continuum (thermo)mechanics of fractal media. Fractal media are ubiquitous in nature, yet fall outside the realm of conventional continuum mechanics. However, they can be brought into the framework of continuum theories via dimensional regularization. See papers [103, 104, 108, ...].
Past/present funding sources
- National Science Foundation
- US Army Corps of Engineers
- Air Force Office of Scientific Research
- San Diego Supercomputer Center
- Office of Naval Research
- American Forest and Paper Association
- US Department of Agriculture
- Canada Foundation for Innovation
- NSERC
- Atmospheric Environment Service Canada
- Canada Centre for Inland Lakes and Waters
- e-Xstream engineering and Ministry of Economy of the Wallonia Region, Belgium