106 research outputs found
The postulations á la D'Alembert and á la Cauchy for higher gradient continuum theories are equivalent. A review of existing results
In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces
A lattice model for the line tension of a sessile drop
Within a semi--infinite thre--dimensional lattice gas model describing the
coexistence of two phases on a substrate, we study, by cluster expansion
techniques, the free energy (line tension) associated with the contact line
between the two phases and the substrate. We show that this line tension, is
given at low temperature by a convergent series whose leading term is negative,
and equals 0 at zero temperature
On the existence of compression-only discrete force networks that support assigned sets of nodal forces
We formulate a linear programming approach to the limit analysis of discrete element models of masonry structures. Numerical results show the ability of the given procedure to predict the limit value of the multiplier of variable horizontal forces, which are applied to masonry walls in association with a fixed vertical loading
Phase coexistence in consolidating porous media
The appearence of the fluid-rich phase in saturated porous media under the
effect of an external pressure is investigated. For this purpose we introduce a
two field second gradient model allowing the complete description of the
phenomenon. We study the coexistence profile between poor and rich fluid phases
and we show that for a suitable choice of the parameters non-monotonic
interfaces show-up at coexistence
Hydrodynamic bubble coarsening in off-critical vapour-liquid phase separation
Late-stage coarsening in off-critical vapour-liquid phase separation is
re-examined. In the limit of bubbles of vapour distributed throughout a
continuous liquid phase, it is argued that coarsening proceeds via inertial
hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner
mechanism seen in binary liquid mixtures. The arguments are strongly supported
by simulations in two dimensions using a novel single-component soft sphere
fluid.Comment: 5 pages, 3 figures, revtex3.
Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics
The hydrodynamic phase field model is applied to the problem of film
spreading on a solid surface. The disjoining potential, responsible for
modification of the fluid properties near a three-phase contact line, is
computed from the solvability conditions of the density field equation with
appropriate boundary conditions imposed on the solid support. The equation
describing the motion of a spreading film are derived in the lubrication
approximation. In the case of quasi-equilibrium spreading, is shown that the
correct sharp-interface limit is obtained, and sample solutions are obtained by
numerical integration. It is further shown that evaporation or condensation may
strongly affect the dynamics near the contact line, and accounting for kinetic
retardation of the interphase transport is necessary to build up a consistent
theory.Comment: 14 pages, 5 figures, to appear in PR
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
A new approach for the limit to tree height using a liquid nanolayer model
Liquids in contact with solids are submitted to intermolecular forces
inferring density gradients at the walls. The van der Waals forces make liquid
heterogeneous, the stress tensor is not any more spherical as in homogeneous
bulks and it is possible to obtain stable thin liquid films wetting vertical
walls up to altitudes that incompressible fluid models are not forecasting.
Application to micro tubes of xylem enables to understand why the ascent of sap
is possible for very high trees like sequoias or giant eucalyptus.Comment: In the conclusion is a complementary comment to the Continuum
Mechanics and Thermodynamics paper. 21 pages, 4 figures. Continuum Mechanics
and Thermodynamics 20, 5 (2008) to appea
- …