The periodic unfolding method

D Cioranescu, A Damlamian, G Griso - Theory and Applications to Partial …, 2018‏ - Springer
In the late 1960's and early 1970's, the theory of homogenization became in its own right a
new part of the branch of mathematics concerning partial differential equations and their …

The periodic unfolding method in homogenization

D Cioranescu, A Damlamian, G Griso - SIAM Journal on Mathematical …, 2008‏ - SIAM
The periodic unfolding method was introduced in 2002 in Cioranescu, Damlamian, and
Griso, CR Acad. Sci. Paris, Ser. 1, 335 (2002), pp. 99–104 (with the basic proofs in …

Asymptotic behavior for textiles with loose contact

J Orlik, R Falconi, G Griso… - Mathematical Methods in …, 2023‏ - Wiley Online Library
The paper is dedicated to the modeling of the elasticity problem for a textile structure. The
textile is made of long and thin fibers, crossing each other in a periodic pattern, forming a …

Homogenization of perforated elastic structures

G Griso, L Khilkova, J Orlik, O Sivak - Journal of Elasticity, 2020‏ - Springer
The paper is dedicated to the asymptotic behavior of ε ε-periodically perforated elastic (3-
dimensional, plate-like or beam-like) structures as ε→ 0 ε→0. In case of plate-like or beam …

[HTML][HTML] Thin domains with non-smooth periodic oscillatory boundaries

JM Arrieta, M Villanueva-Pesqueira - Journal of Mathematical Analysis and …, 2017‏ - Elsevier
In this work we study in detail how to adapt the unfolding operator method to thin domains
with periodic oscillatory boundaries. We present the unfolding method as a general …

Generalization of unfolding operator for highly oscillating smooth boundary domains and homogenization

S Aiyappan, AK Nandakumaran, R Prakash - Calculus of Variations and …, 2018‏ - Springer
Unfolding operators have been introduced and used to study homogenization problems.
Initially, they were introduced for problems with rapidly oscillating coefficients and porous …

Asymptotic Behavior of Unstable Structures Made of Beams

G Griso, L Khilkova, J Orlik - Journal of Elasticity, 2022‏ - Springer
In our previous papers (Griso et al. in J. Elast. 141: 181–225,; J. Elast.,, https://doi.
org/10.1007/s10659-021-09816-w), we considered thick periodic structures (first paper) and …

Junction of a periodic family of elastic rods with a thin plate. Part II

D Blanchard, A Gaudiello, G Griso - Journal de mathématiques pures et …, 2007‏ - Elsevier
In this second paper, we consider again a set of elastic rods periodically distributed over an
elastic plate whose thickness tends here to 0. This work is then devoted to describe the …

[PDF][PDF] Homogenization of oscillating boundaries

A Damlamian, K Pettersson - Homogenization of Some Elliptic …, 2009‏ - diva-portal.org
(Dedicated to Li Daqian, on the occasion of his 70th birthday) abstract. A variational problem
on a sequence of 2-dimensional domains with oscillating boundaries is studied. Using the …

[HTML][HTML] Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary

A Gaudiello, T Mel'Nyk - Journal of Differential Equations, 2018‏ - Elsevier
In this paper, we consider a domain Ω ε⊂ RN, N≥ 2, with a very rough boundary depending
on ε. For instance, if N= 3 Ω ε has the form of a brush with an ε-periodic distribution of thin …