Short Course: Mechanics of Random and Fractal Materials and Structures

Professor Martin Ostoja StarzewskiMechanics of Random and Fractal Materials and Structures

Martin Ostoja-Starzewski

Department of Mechanical Science and Engineering,

Institute for Condensed Matter Theory and Beckman Institute

University of Illinois at Urbana-Champaign

Sunday, August 4, 2013 from 9:00 a.m. - 5:00 p.m. with Breaks

208 Armadillo Room

Cost: $250, pay for through Registration


Course Objective

This course gives exposition of an array of methods developed over the past few decades, and necessary for reading the literature and doing research on mechanics of random and/or fractal material microstructures. This is the grand theme of contemporary mechanics of materials, including geomechanics and biomechanics. Various coupled field phenomena or flow in porous media, besides (non)linear, (in)elastic responses can also be handled by techniques presented here.

Course Outline (6 hours)

1. Stochastic/fractal geometries of microstructures and lattice models (periodicity vs. randomness, rigidity, dynamics, and optimality)

2. Meso-scale bounds for random (non)linear (in)elastic media, and size of representative volume element (RVE)

3. Scalar/tensor random/fractal fields and stochastic finite elements (SFE)

4. Mechanics of fractal media

5. Classical (Cauchy) versus generalized (micro-polar or nonlocal) models

6. Formation of fractal patterns at elastic-inelastic transitions

Course Notes: to be distributed

Reference Text (not required): Microstructural Randomness and Scaling in Mechanics of Materials, M. Ostoja-Starzewski, CRC Press (2008)

M. Ostoja-Starzewski, J. Li, H. Joumaa and P.N. Demmie, “From fractal media to continuum mechanics,” ZAMM 93, 1-29, 2013.

Who Will Benefit

Researchers in (thermo)mechanics of (and transport phenomena in) heterogeneous random and/or fractal materials and stochastic multiscale problems

Instructor’s Bio

Professor  Martin Ostoja-Starzewski’s research interests are primarily in mechanics and transport phenomena in random/fractal media, hyperbolic thermo-elasticity, micro-polar theories, and biomechanics. He published 140+ journal papers and two books: Microstructural Randomness and Scaling in Mechanics of Materials, CRC Modern Mechanics and Mathematics Series (2008), and Thermo-elasticity with Finite Wave Speeds, Oxford Mathematical Monographs, Oxford University Press (2009). He also (co-)edited 10 books/journal special issues and co-organized numerous meetings. He is/was on the editorial boards of Journal of Thermal Stresses, Probabilistic Engineering Mechanics, Actual Problems of Aviation and Aerospace Systems, ASME Journal of Applied Mechanics, International Journal of Damage Mechanics, and Archive of Applied Mechanics, Acta Mechanica. Also, he is Co-Editor of the CRC Modern Mechanics and Mathematics Series, and Chair Managing Editor of Mathematics and Mechanics of Complex Systems, ( He is a Fellow of ASME, AAM, WIF, and an Assoc. Fellow of AIAA.