Homogenization and Two-Scale Convergence

Homogenization and Two - Scale Convergence *

Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale" limit, up to a st...

Two-Scale Convergence and Homogenization of Periodic Structures

Two-Scale Convergence for Locally Periodic Microstructures and Homogenization of Plywood Structures

Abstract. The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The compactness theorem for locally periodic two-scale convergence and the characterization of the limit for a sequence bounded in H1(Ω) are proven. The underlying analysis comprises the approximation of functions, with the periodicity w...

Multiple Integrals under Di erential Constraints: Two-Scale Convergence and Homogenization

Two-scale techniques are developed for sequences of maps {uk} ⊂ L(Ω; R ) satisfying a linear di erential constraint Auk = 0. These, together with Γconvergence arguments and using the unfolding operator, provide a homogenization result for energies of the type

Two-scale homogenization of piezoelectric perforated structures

We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of two-scale convergence. A two-scale homogenized system is obtained as th...