Continuum Mechanics provides the theoretical foundations for the mechanics of solids and fluids. In particular, continuum mechanic is used in stress and strength analyses of structures. My research is concerned with the geometric and analytic aspects of the fundamental notions of continuum mechanics such as fluxes, stresses and equilibrium. See the following

• Fluxes on Manifolds – a slideshow and notes
• Fluxes on Fractals and Whitney's Geometric Integration Theory – a slideshow
• Stress Theory on Manifolds – a slideshow
• Generalized Bodies and Maxwell's Stress Energy Tensor – a slideshow 
• The Global Point of View on Stress Theory – a slideshow
• Stress Optimization and Load Capacity of Structures – a  slideshow
• The Octopus's arm as a Continuous Robot – a preprint