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- probabilistic aspects of fracture
- extreme value statistics
- applied differential geometry.
Sample Project: Application of Function Space Integration in Modeling of Brittle Fracture
The field of statistical fracture mechanics, to which most of Dr. Kunin's research belongs, is rapidly growing as a result of increased engineers' interest in modern composite materials-- light, strong, and high temperature resistant, but often dangerously brittle. Conventional fracture mechanics models proved to have reached their limits of applicability when dealing with such materials as carbon-carbon and ceramic composites, and a search for new fracture models with probabilistic features is gaining popularity in the fracture research community.
The Crack Diffusion Theory (CDT), developed by Dr. Kunin and his co-authors, addresses the evaluation of probability distributions of critical (i.e., failure causing) loads, crack lengths, etc. The commonly observed randomness and tortuosity of crack paths are taken into account by introducing the set, W, of virtual crack paths and, then, averaging over W the various probabilities associated with the formation of a particular crack. This makes the language of function space integration (over W equipped with an appropriate measure m) a natural one. Fractographic information about fracture surfaces (in particular, their fractal dimension) influences the choice of W and m. Another source of stochastization in CDT is the fluctuation of a material's strength on a microscale; it is reflected in a random field of specific fracture energy and affects the form of the functional integrand. Besides non-traditional formalism, CDT introduces unorthodox parameters characterizing material's resistance to fracture and suggests methodologies of their evaluation.
The study of the functional integrals, which appear in CDT, by both analytical (e.g., asymptotic), as well as numerical (e.g., Monte Carlo) methods is a challenging undertaking.
- “Application of Double-Poisson Process in Brittle Fracture” (with I. Savin), International Journal of Pure and Applied Mathematics, V. 72, No. 4, 2011.
- "Optimal Chaos Control and Discretization Algorithms", International Journal of Engineering Science, 44, No. 1-2 (2006), 59-66 (with G. Chernykh and I. Kunin).
- "Extreme value type distributions with bounded support", International Journal of Pure and Applied Mathematics, 12, No. 4 (2004), 499-513.
- "Lorenz-type controlled pendulum", International Journal of Engineering Science, 41 (2003), 433-448 (with I. Kunin and G. Chernykh).
- "Evaluation of Statistical Fracture Toughness Parameters on the Basis of Crack Arrest Experiment," Probabilistic Engineering Mechanics, 13 (1998), 139--146 (with R. S. Dearth).
- "Modeling of Brittle Fracture Based on the Ensemble Averaging Concept," Engineering Fracture Mechanics, 58 (1997), 437--457 (with A. Chudnovsky and M. Gorelik).
- "A Stochastic Model for Slow Crack Growth in Brittle Materials," Applied Mechanics Reviews, 47 (1994), 175--183.
- "On Representation of Fracture Profiles by Fractional Integrals of Wiener Process," Journal of Applied Physics, 70 (1991), 7651--53 (with M. Gorelik).
- Ph.D. (math) University of Illinois at Chicago, 1992.
- M.S. (math) Yale University, 1991.
- B.S. (math and mechanics) Leningrad University, 1977.
- At UAH since 1992.