Martin Ostoja-Starzewski | El investigador Martin Ostoja-Starzewski, de la University of Illinois at Urbana-Champaign (EEUU), ofrecerá la conferencia inaugural del Programa de Doctorado en Ingeniería Mecánica y de Organización Industrialde la Universidad de Sevilla.
La ponencia titulada 'Randomness in Continuum Mechanics' se impartirá el martes 22 de noviembre de 10.30 a 13.00 horas en el Salón de Grados de la Escuela Técnica Superior de Ingeniería (ETSI).
Lecture 1: Randomness in Continuum Mechanics: Elastic Materials. Microstructural randomness is present in just about all solid materials. When dominant (macroscopic) length scales are large relative to microscales, one can safely work within classical, deterministic solid mechanics. However, when the separation of scales does not hold, various concepts of continuum mechanics need to be re-examined and new methods developed. In this lecture we review random media models as a basis of stochastic mechanics, and then focus on scaling from a Statistical Volume Element (SVE) to a Representative Volume Element (RVE) in elastic materials. Starting from the Hill-Mandel homogeneity condition, without assuming any spatial periodicity, the trend to RVE is given in terms of hierarchies of mesoscale bounds and, very concisely, through a scaling function.
Lecture 2: Randomness in Continuum Mechanics: Inelastic Materials. The methodology outlined in the first lecture forms a systematic basis for setting up of tensor random fields of material properties as well as stochastic finite element methods. The scaling from SVE to RVE is then generalized to various other types of material behavior: nonlinear elasticity, elasto-plasticity, rigid plasticity, viscoelasticity (in time or frequency domains), Darcy permeability, and thermoelasticity. The strategy can also be extended to homogenization of random media by micropolar (Cosserat) rather than by classical (Cauchy) continua. Overall, we arrive at a comparison of SVE-to-RVE scaling trends for different types of random microstructures. | 
