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
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Identification of equivalent couple-stress continuum models for planar random fibrous media
TL;DR: In this paper, a couple-stress substitution continuum model is developed for 2D random fiber networks in the small deformation regime, where each fiber in the network is considered as a Timoshenko beam and the cross-links between fibers are modeled as welded joints in which the relative angles between the crossing beams remain constant during deformation.
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Against the Fragmentation of Knowledge: The Power of Multidisciplinary Research for the Design of Metamaterials
TL;DR: In this paper, a multidisciplinary approach to address the emerging issues in metamaterials design is presented, and an improvement in the degree and the depth of the cooperation between scientists from different areas is required.
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On nonlinear dilatational strain gradient elasticity
Victor A. Eremeyev,Victor A. Eremeyev,Victor A. Eremeyev,Antonio Cazzani,Francesco dell’Isola,Francesco dell’Isola +5 more
TL;DR: In this paper, the authors considered nonlinear dilatational strain gradient elasticity and derived the Euler-Lagrange equilibrium conditions in both Lagrangian and Eulerian descriptions.
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
Victor A. Eremeyev,Victor A. Eremeyev,Sergey A. Lurie,Yury Solyaev,Francesco dell’Isola,Francesco dell’Isola +5 more
TL;DR: In this paper, the authors prove an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity, where only one extra second gradient elastic coefficient is introduced.
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The effect of a pre-existing nanovoid on martensite formation and interface propagation: a phase field study:
TL;DR: In this article, the effect of a pre-existing nanovoid on martensitic phase transformation (PT) is investigated using the phase field approach, which is created as a solution of the coup...
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.