Abstract:This paper addresses the problem of reflection and transmission of compression waves at the phase transition layer between the vapour and liquid phases of the same fluid. Within the framework of second gradient fluid modeling, we use a non-convex free energy in order to describe the phase transition phenomenon. A stationary solution for the fluid density is found for an infinite domain, and an analytical expression for the phase transition is presented. Then the propagation of linear waves superposed to this s… Show more
“…Besides, the use of the methods of metamaterials [72][73][74] like those for pantographic structures [75][76][77] could be considered even to take into account the effects of damage [78][79][80][81][82]. Another possible extension of this model is to include surface effects [83][84][85][86][87][88][89] and the anisotropy induced by the orientation of the NLC directors, as in [90] , or as it is done in granular materials [91].…”
“…Besides, the use of the methods of metamaterials [72][73][74] like those for pantographic structures [75][76][77] could be considered even to take into account the effects of damage [78][79][80][81][82]. Another possible extension of this model is to include surface effects [83][84][85][86][87][88][89] and the anisotropy induced by the orientation of the NLC directors, as in [90] , or as it is done in granular materials [91].…”
“…Then a quick list of possible extensions and applications are considered. For an exhaustive treatment of presented results the interested reader is referred to [33][34][35][40][41][42].…”
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...
“…These shells may be designed to carry a mass and be endowed with suitable properties in order to stop noise: some investigations generalizing those presented in [175,174,163,132,133,61] seem ready to give interesting results. The idea is again that of 'trapping' vibration energy in the internal degrees of freedom of the system, which this time are those of considered micro-structured shells.…”
Section: Conception Of Sound or Noise Screensmentioning
confidence: 99%
“…In particular, it has been shown (see e.g. [61], [163], [175], [174]) that for wave frequencies sufficiently high in order to interact with the underlying microstructure, very interesting screening or transmitting phenomena can be conceived and described. As a consequence, metamaterials designed by coupling second gradient materials with mirror electric waveguides could lead to the subsequent design of technologically relevant devices, e.g.…”
Section: Acoustic Metamaterials and Wave Propagation In Micromorphic mentioning
confidence: 99%
“…For instance in the studies by Neff ([149] and Ghiba et al [111]) a very specific class of acoustic metamaterials is investigated in which some frequency bands result to be forbidden to wave propagation (see also [163,174]). It is important to emphasize that the mathematical problems studied in ( [150,151]) are the basis of further scientific investigations in this topic.…”
Section: Acoustic Metamaterials and Wave Propagation In Micromorphic mentioning
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