2015/09/03 by Kirill Cherednichenko, Kirill D. Cherednichenko, James A. Evans +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Physical sciences #Geotechnical and Geomechanical Engineering #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1509.01071
26 pages
openalex publication_date 2015/09/03 · arxiv created 2015/11/17 · arxiv updated 2015/11/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
For the system of Maxwell equations of electromagnetism in an l-periodic composite medium of overall size L (0<l<L<∞), in the low-frequency quasistatic approximation, we develop an electromagnetic version of strain-gradient theories, where the magnetic field is not a function of the magnetic induction alone but also of its spatial gradients, and the electric field depends not only on the displacement but also on displacement gradients. Following the work (Smyshlyaev, V.P., Cherednichenko, K.D., 2000. On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media, \mathit J. Mech. Phys. Solids 48, 1325-1357), we develop a combination of variational and asymptotic approaches to the multiscale analysis of the Maxwell system. We provide rigorous convergence estimates of higher order of smallness with respect to the inverse of the "scale separation parameter" L/l. Using a special "ensemble averaging" procedure for a family of periodic problems, we derive an infinite-order version of the classical homogenised system of Maxwell equations.