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

Locally Periodic Unfolding Method and Two-Scale Convergence on Surfaces of Locally Periodic Microstructures

In this paper we generalize the periodic unfolding method and the notion of twoscale convergence on surfaces of periodic microstructures to locally periodic situations. The methods that we introduce allow us to consider a wide range of nonperiodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforations distributed nonperiodically. Using the me...

A non-periodic and two-dimensional example of elliptic homogenization

Background. When studying the microscale behavior (beyond the reach of numerical solution methods) of physical systems, one is naturally lead to the concept of homogenization, i.e., the theory of the convergence of sequences of partial differential equations. The homogenization of periodic structures using the two-scale convergence technique is well-established due to the pioneering work by Gab...

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...

Two-Scale Convergence and Homogenization of Periodic Structures

Homogenization of the Nonlinear Bending Theory for Plates

We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Γ-convergence. In contrast to what one naturally would expect, our result shows that the limiting functional is not simply a quadratic functional of the second fundamental form of the deformed plate as it is the case in nonlinear plate theory. It turns out that t...