2010/05/21 by Arnaud Anantharaman, Anantharaman, Arnaud, Claude Le Bris +1 · 1 citation
Computer Science · Engineering · Mathematics · #35B27 #35J15 #35R60 #82D30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #math.AP #msc:35B27 #msc:35J15 #msc:35R60 #msc:82D30
paper · pdf · doi:10.48550/arxiv.1005.3910
arxiv created 2010/05/21 · openalex publication_date 2010/05/21 · arxiv updated 2010/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a rare event at the microscopic level. It however affects the macroscopic properties of the material, and we indeed provide a method to compute the first and second-order corrections. To this end, we formally establish an asymptotic expansion of the macroscopic properties. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated.