Multiscale analysis of composite structures based on higher-order asymptotic homogenization with boundary layer correction

Asymptotic Analysis of Boundary Layer Correctors in Periodic Homogenization

This paper is devoted to the asymptotic analysis of boundary layers in periodic homogenization. We investigate the behaviour of the boundary layer corrector, de ned in the half-space Ωn,a := {y · n− a > 0}, far away from the boundary and prove the convergence towards a constant vector eld, the boundary layer tail. This problem happens to depend strongly on the way the boundary ∂Ωn,a intersects ...

Asymptotic analysis of second-order boundary layer correctors

Homogenization and boundary layer

This paper deals with the homogenization of elliptic systems with Dirichlet boundary condition, when the coefficients of both the system and the boundary data are ε-periodic. We show that, as ε → 0, the solutions converge in L2 with a power rate in ε, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the bounda...

Regularization of first order computational homogenization for multiscale analysis of masonry structures

This paper investigates the possibility of using classical first order computational homogenization together with a simple regularization procedure based on the fracture energy of the micro-scale-constituents. A generalized geometrical characteristic length takes into account the size of the macro-scale element as well as the size of the RVE (and its constituents). The proposed regularization e...

Multiscale Analysis for Higher-order Tensors

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches focused on matrix and vector based methods to represent these higher-order data, more recently it has been shown that tensor decomposition methods are better equip...