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
More filters
Journal ArticleDOI
Numerical simulation of equilibrium air plasma flow in the induction chamber of a high-power plasmatron
Journal ArticleDOI
Geometric variational approach to the dynamics of porous media filled with incompressible fluid.
TL;DR: In this article, the authors derived the equations of motion for the dynamics of a porous media filled with an incompressible fluid using a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of a fluid coupled through the constraint of incompressibility.
Book ChapterDOI
The Effect of Mechanical Load-induced Intraosseous Pressure Gradients on Bone Remodeling
TL;DR: The exploitation of a 2D continuum model based on classical poroelasticity is presented within a variational framework and the introduction of a physically motivated strain energy contribution is aimed to take into account the presence of saturating fluid in the interconnected pores of bone tissue.
Journal ArticleDOI
Analyzing size effects in a cracked orthotropic layer under antiplane shear loading
Richardson P Joseph,Richardson P Joseph,Chunwei Zhang,Baolin Wang,Bijan Samali,Kheng Lim Goh,Judha Purbolaksono +6 more
TL;DR: In this article, scale-dependent stress intensity factors in an anti-plane cracked orthotropic material layer are evaluated using strain gradient theory, and both volumetric and surface strain gradient material characteristic lengths represented as l and $$l^{'}$$676, respectively, are employed to obtain semi-analytical solutions.
Book ChapterDOI
Hamilton Principle in Piola’s work published in 1825
Fabio Di Cosmo,Marco Laudato +1 more
TL;DR: In this article, the authors assess how a version of Hamilton Principle is formulated by Piola in his Memoir composed between 1822 and 1824 and published in 1825, and they observe that the Stigler's Law of Eponymy is not formulated at first by Hamilton.
References
More filters
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.