Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials

Lekszycki

Pawlikowski

et al. 2015

Z. Angew. Math. Phys.

158

117

mentioning

confidence: 66%

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

Lekszycki

Pawlikowski

et al. 2015

Z. Angew. Math. Phys.

158

117

“…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].…”

mentioning

confidence: 99%

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

Forest

2014

Z Angew Math Mech

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...

“…Forthcoming works should consider the application of thep r e s e n t e dt h e o r yt ot h ec a s eo fw a v e propagation in partially saturated media (using the methods proposed in [21,37,29,30,35]) and the more general case of unsaturated assemblies of elastic spherical grains (following micro-mechanical arguments of the type presented in [40,41]). …”

Section: Discussionmentioning

confidence: 99%

“…It can be remarked that the coupled system of PDEs which we obtain in this paper has a very involved structure. As already remarked, a first study should involve the characterization of the properties of waves propagating in our complex continuum: this is feasible when considering the results presented in [21,37,36,29,30,35] 8. An example of fluid capillarity leading to fluid second gradient macroscopic interactions…”

Section: Governing Equations For Isotropic Microscopically Homogeneomentioning

confidence: 99%

A continuum model for deformable, second gradient porous media partially saturated with compressible fluids

Madeo

Journal of the Mechanics and Physics of Solids

Darve

2013

In this paper a general set of equations of motion and duality conditions to be imposed at macroscopic surfaces of discontinuity in partially saturated, solid-second gradient porous media are derived by means of the Least Action Principle. The need of using a second gradient (of solid displacement) theory is shown to be necessary to include in the model effects related to gradients of porosity. The proposed governing equations include, in addition to balance of linear momentum for a second gradient porous continuum and to balance of water and air chemical potentials, the equations describing the evolution of solid and fluid volume fractions as supplementary independent kinematical fields. The presented equations are general in the sense that they are all written in terms of a macroscopic potential Psi which depends on the introduced kinematical fields and on their space and time derivatives. These equations are suitable to describe the motion of a partially saturated, second gradient porous medium in the elastic and hyper-elastic regime. In the second part of the paper an additive decomposition for the potential Psi is proposed which allows for describing some particular constitutive behaviors of the considered medium. While the potential associated to the solid matrix deformation is chosen in the form proposed by Cowin and Nunziato (1981) and Nunziato and Cowin (1979) and the potentials associated to water and air compressibility are chosen to assume a simple quadratic form, the macroscopic potentials associated to capillarity phenomena between water and air have to be derived with some additional considerations. In particular, two simple examples of microscopic distributions of water and air are considered: that of spherical bubbles and that of coalesced tubes of bubbles. Both these cases are suitable to describe capillarity phenomena in porous media which are close to the saturation state. Finally, an example of a simple microscopic distribution of water and air giving rise to a macroscopic capillary potential depending on the second gradient of fluid displacement is presented, showing the need of a further generalization of the proposed theoretical framework accounting for fluid second gradient effects. (C) 2013 Elsevier Ltd. All rights reserved