%0 Journal Article
%T Non-local effects by homogenization or 3D–1D dimension reduction in elastic materials reinforced by stiff fibers
%+ DADU, Università degli Studi di Sassari, Sassari
%+ Université de Toulon (UTLN)
%+ Institut de Mathématiques de Marseille (I2M)
%A Paroni, Roberto
%A Sili, Ali
%Z The first author gratefully acknowledges the hospitality and the support provided by the Insti- tut de Mathématiques de Marseille during the completion of this work.
%< avec comité de lecture
%@ 0022-0396
%J Journal of Differential Equations
%I Elsevier
%V 260
%N 3
%P 2026 - 2059
%8 2016
%D 2016
%Z 1503.07453
%R 10.1016/j.jde.2015.09.055
%K Dimension reduction
%K Homogenization
%K Non-local
%K Rods
%K Anisotropic
%Z 35B27; 35B40; 80M40; 74K10; 74B05
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem.
%G English
%L hal-01256313
%U https://hal.science/hal-01256313
%~ UNIV-TLN
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS