By Dominique Jeulin, Martin Ostoja-Starzewski
This e-book experiences contemporary theoretical, computational and experimental advancements in mechanics of random and multiscale reliable fabrics. the purpose is to supply instruments for greater figuring out and prediction of the results of stochastic (non-periodic) microstructures on fabrics’ mesoscopic and macroscopic houses. specific issues contain a evaluation of experimental suggestions for the microstructure description, a survey of key tools of chance conception utilized to the outline and illustration of microstructures by way 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 information versions, and computational micromechanics.
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This booklet reports contemporary theoretical, computational and experimental advancements in mechanics of random and multiscale sturdy fabrics. the purpose is to supply instruments for larger realizing and prediction of the results of stochastic (non-periodic) microstructures on fabrics’ mesoscopic and macroscopic homes.
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Additional resources for Mechanics of Random and Multiscale Microstructures
Serra : • a morphological transformation is applied to the structure (using image analysis); • some measurement is performed on the transformed object .. The choice of measures and of transformations is made according to morphological criteria, as illustrated below. <;urements: inV'ariance by translation, continuity (with respect to the mesh and to the sampling grid), local knowledge (to study of the structure from bounded measure fields), additivity (for the estimation of averages), and stereological properties (to estimate 3D properties from lD or 2D measurements).
12) Here U1 = 0 since the average (Jt(z')f(zo)} is zero This is seen from Eq. 7) because f(zo) is not determined by JL(z') when z' < zo. (We remember that Eq. 7) is solved by pro<:eeding in the negative z diroction). We also note that even if (Jt(z')r(zo)) were not equal to zero U1 would still be effectively zero as a result of the rapidly oscillating term exp[2ikz']. c. 13) From statistical homogeneity we have (Jt(z')Jt(z")} = a(s) where s = z'- z". z » Lc Eq. 15) The expression U:J is effectively equal to zero as a result of the rapidly varying exponential term exp[-2-ikz'].
Propagation phenomena (light in optics, sound in acoustics, fluid in a porom; medium, ... ) with different propagation velocities in heterogeneous media, involve the existence of paths (and of percolation) across a specimen; for a valued graph, one can estimate (in 2D or in 3D) the distance to a source, usually called the geodesic distance (namely the length of shortest paths), and its probability distribution function, characterizing the tortuosity of a network. This was applied to fracture of polycrystalline graphite, diffusion in polymers and in porous media , fracture of simulated random media at different scales (porous media, polycrystals) , fluid flow between rough surfaces .
Mechanics of Random and Multiscale Microstructures by Dominique Jeulin, Martin Ostoja-Starzewski