Variational Homogenization of Micro-Electro-Elasticity

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).

Homogenization in micro-plasticity

Homogenized descriptions of plasticity on microand macro-scale are essentially different. A key distinction is that the energy of micron-size specimens, in contrast to that of macrospecimens, is not a functional of integral characteristics of the dislocation networks. Thus, energy must be considered as an independent characteristic of the body which is additional to all other characteristics. I...

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...

Homogenization of Variational Problems under Manifold Constraints

Abstract. Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna, Fonseca, Malý & Trivisa [18]. For energies with superlinear or linear growth, a Γ-convergence result is established i...

Micro - Electro - Mechanical - Systems ( Mems )