Optimization of non periodic homogenized microstructures

Non-local homogenized limits for composite media with highly anisotropic periodic fibres

We consider a homogenization problem for highly anisotropic conducting fibres embedded into an isotropic matrix. For a ‘double porosity’-type scaling in the expression of high contrast between the conductivity along the fibres and the conductivities in the transverse directions, we prove the homogenization theorem and derive two-scale homogenized equations using a version of the method of two-s...

Simultaneous shape, topology and homogenized properties optimization

In this brief note, we present an approach that combines the three classical techniques in structural optimization, i.e. the boundary variation, the topological and the homogenization methods. As a first test of this method, we apply it to the compliance optimization in R .

Magnetoactive elastomers with periodic and random microstructures

We investigate the behavior of magnetoactive elastomers (MAEs) with periodic and random distributions of circular and elliptical fibers. For the MAEs with periodic microstructures, we develop finite element models and determine the local fields as well as the effective properties of MAEs with rectangular and quasi-hexagonal unit cells. For the MAEs with random microstructures, we derive a close...

Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings

In quasi-periodic or nonlinear periodic homogenization, the corrector problem must be in general set on the whole space. Numerically computing the homogenization coefficient therefore implies a truncation error, due to the fact that the problem is approximated on a bounded, large domain. We present here an approach that improves the rate of convergence of this approximation.

Holographic Fabrication of Periodic Microstructures by Interfered Femtosecond Laser Pulses