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The American Institute of Aeronautics and Astronautics (AIAA)

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    Course Overview

    Stochastic Mechanics of Materials and Structures


    This course presents an array of methods to study mechanics of spatially random material microstructures involving several scales. The course begins with lectures on random geometry and stochastic processes and fields, including spatial point processes, mathematical morphology, geodesics, ergodicity, and entropy. Subsequent topics include: periodic versus disordered truss- and beam-type lattices, and a construction of corresponding classical and non-classical (Cosserat, non-local, strain-gradient, chiral …) continua; introduction to statistical continuum theories, including thermomechanics of random media; scaling to Representative Volume Element (RVE) in conductivity, linear or finite (thermo)elasticity, elasto-plasticity, permeability, and coupled field phenomena; methods for problems below the RVE (i.e., those lacking the separation of scales) via micromechanically-based stochastic finite elements; tensor random fields, effects of microscale material randomness on waves and wavefronts (e.g. shocks) in linear and non-linear elastic/dissipative media; introduction to stochastic damage mechanics; elements of fractional calculus and fractals.


    Key Topics

    • To develop familiarity with a wide array of methods in mechanics of spatially random materials and structures, specifically:
    • Introduction to stochastic geometric models of microstructures
    • Scalar and tensor random fields; fractal and Hurst effects
    • Scale-dependent homogenization of random elastic/inelastic materials
    • Stochastic (micro)mechanics as a basis for stochastic finite elements (SFE)
    • Waves in random media


    Who Should Attend

    Researchers in (thermo)mechanics, dynamics and transport phenomena in spatially random materials and structures. These include research scientists in solid and structural mechanics, graduate students and postdocs, faculty.


    General Course Information

    • Type of Course: Instructor-Led Short Course
    • Course Level: Advanced
    • Course Length: 2 days
    • AIAA CEU's available: yes