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A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials

Vincenzo Nesi, Enrico Rogora (2007)

ESAIM: Control, Optimisation and Calculus of Variations

The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank-r convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank-r convex forms arises. In the present paper, we define the concept of extremal 2-forms and characterize them in the rotationally invariant jointly...

A new method for numerical solution of checkerboard fields.

Berggren, Stein A., Lukkassen, Dag, Meidell, Annette, Simula, Leon (2001)

Journal of Applied Mathematics

A property of the $H$ -convergence for elasticity in perforated domains.

Haddadou, Hamid (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A variational approach to the local character of $G$ -closure : the convex case

Jean-François Babadjian, Marco Barchiesi (2009)

Annales de l'I.H.P. Analyse non linéaire

A viscoelastic model with non-local damping application to the human lungs

Céline Grandmont, Bertrand Maury, Nicolas Meunier (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The...

Acoustics of a stratified poroelastic composite.

Gilbert, R.P., Panchenko, A. (1999)

Zeitschrift für Analysis und ihre Anwendungen

Alternative approaches to the two-scale convergence

Luděk Nechvátal (2004)

Applications of Mathematics

Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions $ψ (x, y)$ . Properties and examples are added.

Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain

M. Sango (2003)

Colloquium Mathematicae

We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains $Q_{T}^{(s)}$ , s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of $Q_{T}^{(s)}$ . We give an explicit construction of that limit problem.

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