Stochastic Modeling

Download Mechanics of Random and Multiscale Microstructures by Dominique Jeulin, Martin Ostoja-Starzewski PDF

By Dominique Jeulin, Martin Ostoja-Starzewski

This publication reports fresh theoretical, computational and experimental advancements in mechanics of random and multiscale strong fabrics. the purpose is to supply instruments for greater knowing and prediction of the consequences of stochastic (non-periodic) microstructures on fabrics’ mesoscopic and macroscopic houses. specific subject matters contain a overview of experimental ideas for the microstructure description, a survey of key equipment of likelihood thought utilized to the outline and illustration of microstructures by means of random modes, static and dynamic elasticity and non-linear difficulties in random media through variational ideas, stochastic wave propagation, Monte Carlo simulation of random non-stop and discrete media, fracture data versions, and computational micromechanics.

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For a given model, the functional Tis obtained: • by theoretical calculation • by estimation on simulations of the random structure, or on samples of the real structures. In the latter case, it is possible to estimate the parameters from the "experimental" T , and to test the validity of assumptions. The estimation of the functional T(K) is easily performed from the implementation of the basic operations of mathematical morphology, namely erosions or dilations. "i T(K) (K being variable) obtained for a given model are coherent (which is not the case of any prior analytical model, as often used in the literature).

Munk, K. Watson and F. 'iCn (1979), Sound 'I'ransmiss·ion through a Fluctuating Ocean, Cambridge Univ. Press, Cambridge. [14]1. ;;iuk and M. ) (1998), Micromechanics of random media II- Special issue of Int. J. Solids Struct. 35(19). [15] M. Ostoja-Starzemki and I. ) (1994), Micromechanics of Random Media- Special Issue of Appl. Mech. Rev. 47, (1, Part 2). C. B. , 21, 287-305. Statistical Continuum Mechanics 31 [17] S. Torquato (1991), Random heterogeneous media: microstructure and improved hounds on effective properties, Appl.

We show how the well known Foldy-Twersky integral equation is derived. In Section 5 we showed how to derive statistical equations for the mean pressure and the coherence ftmction when we limited our coru;ideration to small sound-speed fluctuations and forward scattering. Explicit expressions were obtained for an initial plane wave and a finite source. Finally in Section 6 we considered a problem in which backscattering was important. The problem was one-dimensional and the sotmd speed fluctuations were small.

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