System Requirements for Viewing

INSTRUCTOR: Professor Martin Ostoja-Starzewski

Course Length: 5.5 Hours

Purpose and Background

This course examines an array of methods developed over the past few decades. Knowledge of these methods is needed in 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

• Stochastic/fractal geometries of microstructures and lattice models (periodicity vs. randomness, rigidity,  dynamics, and optimality)
• Meso-scale bounds for random (non)linear (in)elastic media, and size of representative volume element (RVE)
• Scalar/tensor random/fractal fields and stochastic finite elements (SFE)
• Mechanics of fractal media
• Classical (Cauchy) versus generalized (micro-polar or nonlocal) models
• Formation of fractal patterns at elastic-inelastic transitions

Intended Audience

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