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American Institute of Aeronautics and Astronautics

    Course Outline

    Course Outline

    Stochastic Mechanics of Materials and Structures


    1. Planar and Spatial Random Processes and Models of Material Microstructures

      [point processes, directional data, random line fields, random tessellations (models of polycrystal, granular, porous media,…), elements of mathematical morphology]

    2. Elements of Random Processes and Fields

      [types of random fields (Markov/Gibbs, evolutionary versus stationary, anisotropic, ergodic, tensor,…), classes of correlation functions, maximum entropy method]

    3. Lattice Models

      [periodic versus non-periodic (central-force, beam…) models and generalized continuum models, rigidity, randomness, dynamics, and optimality]

    4. Statistical Continuum Methods and Bounds for Transport and Elastic Properties

      [statistical hierarchy of functions, non-local effect, homogenization method, percolation problems, maximum entropy approach]

    5. Mesoscale Bounds for Random Media

      [Hill condition, separation of scales and Representative Volume Element (RVE), hierarchies of mesoscale bounds in (non)linear elastic and/or inelastic microstructures]

    6. Random Field Models and Stochastic Finite Elements (SFE)

      [mechanics restrictions imposed on tensor-valued random fields, SFE, random plastic media, damage and fracture in random microstructures]

    7. Advanced Stochastic Solid Mechanics

      [introduction to stochastic ordinary and stochastic partial differential equations, introduction to fractional calculus and fractals]