Analytical continuum mechanics à la Hamilton-Piola least action principle for second gradient continua and capillary fluids
TLDR
In this article, a Lagrangian action is proved to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments.Abstract:
In this paper a stationary action principle is proved to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments. We remark that these fluids are sometimes also called Korteweg–de Vries or Cahn–Allen fluids. In general, continua whose deformation energy depends on the second gradient of placement are called second gradient (or Piola–Toupin, Mindlin, Green–Rivlin, Germain or second grade) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both the material and spatial descriptions and the corresponding Euler–Lagrange equations and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and ∇C or on C−1 and ∇C−1, where C is the Cauchy–Green deformation tensor. When particularized to energies which characterize fluid materia...read more
Citations
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Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: New perspectives towards metastructural design
Angela Madeo,Angela Madeo,Gabriele Barbagallo,Manuel Collet,Marco Valerio d'Agostino,Marco Miniaci,Patrizio Neff +6 more
TL;DR: In this paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission proper tie...
Dissertation
Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus
TL;DR: In this article, Gordan et al. studied the geometries of a space of tenseurs in the second-gradient of R 3 and showed that these spaces can be classified into different classes of symetries.
Journal ArticleDOI
Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study.
Abstract: The study and imitation of the biological and mechanical systems present in nature and living beings always have been sources of inspiration for improving existent technologies and establishing new ones. Pursuing this line of thought, we consider an artificial graft typical in the bone reconstruction surgery with the same microstructure of the bone living tissue and examine the interaction between these two phases, namely bone and the graft material. Specifically, a visco-poroelastic second gradient model is adopted for the bone-graft composite system to describe it at a macroscopic level of observation. The second gradient formulation is employed to consider possibly size effects and as a macroscopic source of interstitial fluid flow, which is usually regarded as a key factor in bone remodeling. With the help of the proposed formulation and via a simple example, we show that the model can be used as a graft design tool. As a matter of fact, an optimization of the characteristics of the implant can be carried out by numerical investigations. In this paper, we observe that the size of the graft considerably influences the interaction between bone tissue and artificial bio-resorbable material and the possibility that the bone tissue might substitute more or less partially the foreign graft for better bone healing.
Posted Content
A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions
TL;DR: In this paper, the authors consider the indeterminate couple stress model in the general framework of second gradient elasticity and propose a new alternative formulation which obeys Cauchy-Boltzmann's axiom of the symmetry of the force stress tensor.
Journal ArticleDOI
An explicit solution for the dynamics of a taut string of finite length carrying a traveling mass: the subsonic case
TL;DR: In this paper, the linear vibrations induced in an elastic string by a loading point-like mass constrained to moving on it with constant horizontal velocity were investigated in terms of a power series determined by iteration, which was shown to converge to the solution of the problem.
References
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Book
A Treatise on Electricity and Magnetism
TL;DR: The most influential nineteenth-century scientist for twentieth-century physics, James Clerk Maxwell (1831-1879) demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field as discussed by the authors.
Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Book
Théorie des distributions
TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.
Book
A comprehensive introduction to differential geometry
TL;DR: Spivak's comprehensive introduction to differential geometry as discussed by the authors takes as its theme the classical roots of contemporary differential geometry, and explains why it is absurdly inefficient to eschew the modern language of manifolds, bundles, forms, etc., which was developed precisely to rigorize the concepts of classical differential geometry.
Journal ArticleDOI
XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
D. J. de Korteweg,G. de Vries +1 more
TL;DR: In this article, the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves were discussed, and a new model of long wave propagation was proposed.