Rayleigh scattering in elastic composite materials

Boutin, Claude; Auriault, Jean‐Louis

doi:10.1016/0020-7225(93)90082-6

Cited by 103 publications

(106 citation statements)

References 8 publications

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“…The first corrective term generally presents a particular energetic property. In composite media, the work of the first corrector under the zero order solution is null at the period scale; see for example [Boutin and Auriault 1993;1995]. For discrete media, a similar result was obtained for braced framed structures in [Tollenaere 1994].…”

Section: B Numerical Validationmentioning

confidence: 57%

“…Investigate high order terms for improving the description in the presence of poor scale separation have already been proposed for continuous media [Bensoussan et al 1978;Bakhvalov and Panasenko 1989;Gambin and Kröner 1989;Boutin and Auriault 1993], for discrete media [Verna 1991;Tollenaere 1994;Pradel and Sab 1998] and for beams [Buannic and Cartraud 2001a;2001b]. A detailed analysis of higher order correctors is beyond the scope of this paper; the single case of the slender-Timoshenko beam is studied hereafter to identify its effective order.…”

Section: B Numerical Validationmentioning

confidence: 99%

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Dynamics of discrete framed structures: a unified homogenized description

Hans

Boutin

2008

JOMMS

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The dynamic behavior of discrete periodic one-dimensional structures is approached by considering transverse vibrations of structures made of repeated unbraced frames. Assuming the frame size is small compared to the modal wavelength, equivalent macroscopic beam descriptions are obtained by the homogenization method of periodic discrete media. The macroscopic parameters are expressed as functions of the mechanical and geometrical properties of the frame elements.Depending on the order of magnitude (relative to the scale ratio) of the shear force, the global bending and the inner bending, four families of beams are shown to be possible. A generic beam governed by a differential equation of the sixth degree is shown to encompass all the other types.Simple criteria are established to identify the relevant model for real structures. A comparison of these theoretical results with numerical modeling is satisfactory even in the case of weak scale separation. In fact, an investigation of the higher orders terms shows that zero order descriptions are valid up to the second order. Lastly, analogies with micromorphic media are discussed.

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Section: B Numerical Validationmentioning

confidence: 57%

Section: B Numerical Validationmentioning

confidence: 99%

Dynamics of discrete framed structures: a unified homogenized description

Hans

Boutin

2008

JOMMS

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“…However, this latter effects appears as correctors of the classical Cauchy behaviour at the leading order. Therefore, to enhance the non-local effects up to the leading order, the physics at the local scale must be modified, either by introducing a contrast in the "geometry" of the constituents (instead of O(1) aspect ratio as in [11]), or by increasing the contrast of elastic properties (taken O(1) in [11]). These options are analysed by considering reticulated materials or highly contrasted composites.…”

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confidence: 99%

Second Gradient and Generalized Continua. A workshop held on 12–16 March 2012 in Cisterna di Latina

Dell’Isola

Forest

2014

Z Angew Math Mech

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This editorial intends to complement the scientific content of the papers which follow in this special issue. The workshop "Second Gradient and Generalized Continua" held on 12-16 March 2012 at Palazzo Caetani in Cisterna di Latina, Italy was organized by Francesco dell'Isola and Samuel Forest. Very interesting, exciting and creative discussions started nearly immediately during the seminars and the round tables: the spirit of all participants was very productive and open minded and nobody felt necessary to hide his views, also when they were in contrast with those of other participants, so that a truly frank and direct scientific discussion was possible. The video-recorded seminars are available at the website http://memocs.univaq.it/?page id=2858, http://memocs.univaq.it/?page id=3071.In the following paragraphs we will reproduce, following the seminar order, only the abstracts of those presentations which did not produce a paper published in the present issue of ZAMM.Francesco dell'Isola: "Contact interactions in N-th gradient continua". Cauchy format for continuum mechanics is not general enough to include the description of some important phenomena occurring in a large class of "microscopically" inhomogeneous bodies. This circumstance has been recognized already by E. and F. Cosserat and later by Mindlin, Rivlin, Toupin, and Green. Particularly detailed is the development of second gradient model due to Paul Germain, which is the simplest continuum model which cannot be included in the Cauchy format. Actually Cauchy Continuum model has a wide but limited scope of predictivity: therefore the logical possibility of generalizing it truly corresponds to the need of describing some new and interesting phenomena, which include, but are not limited to, the formation of many different kinds of boundary layers. The class of generalized (N -th gradient) continua which is presented here is constituted by those models in which deformation energy may depend on N + 1 gradients of displacement field. The precise definition of N -th gradient continua and the nature of contact interactions which may arise in them can be mathematically formulated and characterized only by using suitable concepts from the theory of distribution and differential geometry, but it is definitively not so difficult to generalize -in the considered context -the Cauchy concept of stress state. The mathematical abstraction required does not seem inappropriate as it actually supplies a useful description of some phenomena of relevance in the mechanics of growing tissues and opens interesting perspectives in the design of artificial materials showing "exotic" mechanical behavior. More details about the presented ideas can be found in [17,18].Pierre Seppecher: "Linear elastic trusses leading to continua with exotic mechanical interactions". When studying the statics of a truss made of a discrete network of nodes joined by linear elastic springs, the kernel of the quadratic potential energy (space of floppy modes) plays an essential role. In particular w...

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“…We consider elastic anti-plane shear waves propagating in the transverse 1 2 x x plane through a periodic composite material consisting of an infinite matrix (1) Ω and a square lattice of cylindrical fibres (2) Ω of the volume fraction (2) c . The governing wave equation is:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In the low frequency range the effect of wave dispersion can be analysed by the higher-order AHM [2]. According to this approach, we search the unknown displacement field as a two-scale asymptotic expansion in powers of a small parameter l L ε =…”

Section: Introductionmentioning

confidence: 99%

Study of wave dispersion in periodic composites by higher‐order asymptotic homogenization method

Andrianov

Bolshakov

Danishevskyy

et al. 2007

Proc Appl Math and Mech

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We present [1] an application of the higher-order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable to the size of heterogeneities, successive reflections and refractions of the waves at the components interfaces lead to the formation of a complicated sequence of pass and stop frequency bands. The AHM provides a long-wave approximation valid in the low frequency range. Solution for the high frequencies is obtained on the basis of the Floquet-Bloch theorem by the plane-wave (PW) expansions method. Anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical fibres are considered. The dispersion curves are obtained, the pass and stop bands are identified.

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Rayleigh scattering in elastic composite materials

Cited by 103 publications

References 8 publications

Dynamics of discrete framed structures: a unified homogenized description

Dynamics of discrete framed structures: a unified homogenized description

Second Gradient and Generalized Continua. A workshop held on 12–16 March 2012 in Cisterna di Latina

Study of wave dispersion in periodic composites by higher‐order asymptotic homogenization method

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