Periodic unfolding and homogenization

By Doina Cioranescu, Alain Damlamian, Georges Griso. 2002

512 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6f0e08d837486c8c47df326a577a101fa42752ba

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence (2010, background): “It si worth mentioning that there is an intimate link between the two-scale convergence and weak convergence of the unfolded sequences; see [35,15].”
Periodic unfolding and Robin problems in perforated domains (2006, methodology): “Following [4], we decompose any function ϕ in the form , where R ε is designed in order to capture the oscillations.”
Two-scale convergence of some integral functionals (2007, methodology): “Here, we reformulate the notion of two-scale convergence and review some of its basic properties, using a scale-decomposition (or periodic unfolding) along the lines of [26,57,58].”
Convergence Rates in Periodic Homogenization of Systems of Elasticity (2015, methodology): “8) was proved by Griso in [4, 5] for scalar elliptic equations with either Dirichlet or Neumann bounda ry conditions, using the method of periodic unfolding [2, 3].”
The periodic unfolding method in perforated domains. (2006, methodology): “The main properties given in [4] for fixed domains can easily be adapted for the perforated ones without any major difficulty in the proofs.”
Towards a two-scale calculus (2006, methodology): “), along the lines of [5, 8, 13, 15, 20, 21] we set uε⇀ 2 u in L2(Ω×Y ) ⇔ uε ◦ Sε ⇀ u in L2(RN×Y ); (2)”
Coupled reaction–diffusion processes inducing an evolution of the microstructure: Analysis and homogenization (2009, unknown): “In order to obtain an equation in Ω, we use the periodic unfolding operator Tε [9]: writing [x]Y for the unique integer combination ∑n i=1 kiei of the periods such that {x}Y = x− [y]Y belongs to [0, 1) (where ei is the ith unit vector), Tε L(2)(Ω) → L(2)(Ω × Y ) is defined by Tε(u)(x, y) = u(ε[x/ε]Y”
The periodic unfolding method for perforated domains and Neumann sieve models (2008, methodology): “The periodic unfolding method (see [8]), as a simpler alternative to the two-scale convergence, was developed to study the limit behavior of periodic problems depending on a small parameter ε.”
The Periodic Unfolding Method in Homogenization (2008, methodology): “The ﬁnal section gives a list of papers where the method has been successfully applied since the publication of [24].”