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- Francesco dell’Isola, Henri Gouin, Pierre Seppecher
- 2008

The classical theory of Laplace is not suitable for describing the behavior of microscopic bubbles. The theory of second gradient fluids (which are able to exert shear stresses in equilibrium conditions) allows us to obtain a new expression for surface tension and radius of these bubbles in terms of functionals of the chemical potential. This relationship… (More)

- Pierre SEPPECHER
- 2010

The relationship between edge contact forces, double forces and interstitial working allowed by the principle of virtual power Abstract-We consider continuous media in which contact edge forces are present. Introducing the notion of quasi-balanced contact force distribution, we are able to prove the conjectures made in [Noll, 1990] concerning the… (More)

We consider functionals of the form F (u) = f (x, Du) dµ u ∈ D(R n) where µ is a finite Borel measure on R n , and their relaxation F with respect to the weak convergence of a suitable Sobolev space W 1,p µ. Applications to low dimensional structures and junctions are given.

- Francesco dell’Isola, Pierre Seppecher, Angela Madeo
- 2012

Navier-Cauchy format for Continuum Mechanics is based on the concept of contact interaction between subbodies of a given continuous body. In this paper it is shown how-by means of the Principle of Virtual Powers-it is possible to generalize Cauchy representation formulas for contact interactions to the case of N-th gradient continua, i.e. continua in which… (More)

- Pierre Seppecher, Jean-Jacques Alibert, Francesco Dell Isola
- 2011

We study the statics of some trusses, i.e. networks of nodes linked by linear springs. The trusses are designed in such a way that a few number of floppy modes are present and remain when considering the homogenized limit of the truss. We then obtain linear elastic materials with exotic mechanical interactions which cannot be described in the classical… (More)

The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of them. They consist of thin triangular magnetic components joined at the edges by cylindrical dielectric components. (There… (More)

Electromagnetic circuits are the electromagnetic analog at fixed frequency of mass-spring networks in elas-todynamics. By interchanging the roles of ε and µ in electromagnetic circuits one obtains magnetoelectric circuits. Here we show that by introducing tetrahedral connectors having ε = µ = 0 one can join electromagnetic and magnetoelectric circuits to… (More)

We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in the three-dimensional case and in the two-dimensional case. Specifically we construct… (More)

We carry out the asymptotic analysis of the following shape optimization problem: a given volume fraction of elastic material must be distributed in a cylindrical design region of infinites-imal cross section in order to maximize the resistance to a twisting load. We derive a limit rod model written in different equivalent formulations and for which we are… (More)