Bloch wave homogenization of linear elasticity system

Bloch Wave Homogenization of Linear Elasticity System

In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a re...

Bloch Wave Homogenization and Spectral Asymptotic Analysis

We consider a second-order elliptic equation in a bounded periodic heterogeneous medium and study the asymptotic behavior of its spectrum, as the structure period goes to zero. We use a new method of Eloch wave homogenization which, unlike the classical homogenization method, characterizes a renormalized limit of the spectrum, namely sequences of eigenvalues of the order of the square of. the m...

Homogenization in Fractional Elasticity

In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homog-enization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of non-local operators (in time and space).

Plane wave approximation in linear elasticity

Homogenization of Periodic Structures via Bloch Decomposition

In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and offers an alternate way to view the classical results. In a natural way, this method leads us to work in the Fourier space and thus in a framewor...