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Displaying similar documents to “Modification of unfolding approach to two-scale convergence”

On periodic homogenization in perfect elasto-plasticity

Gilles A. Francfort, Alessandro Giacomini (2014)

Journal of the European Mathematical Society

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The limit behavior of a periodic assembly of a finite number of elasto-plastic phases is investigated as the period becomes vanishingly small. A limit quasi-static evolution is derived through two-scale convergence techniques. It can be thermodynamically viewed as an elasto-plastic model, albeit with an infinite number of internal variables.

Alternative approaches to the two-scale convergence

Luděk Nechvátal (2004)

Applications of Mathematics

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Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions ψ ( x , y ) . Properties and examples are added.

Some properties of two-scale convergence

Augusto Visintin (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We reformulate and extend G. Nguetseng’s notion of two-scale convergence by means of a variable transformation, and outline some of its properties. We approximate two-scale derivatives, and extend this convergence to spaces of differentiable functions. The two-scale limit of derivatives of bounded sequences in the Sobolev spaces W 1 , p ⁢ R N , L r ⁢ o ⁢ t 2 ⁢ R 3 3 , L d ⁢ i ⁢ v 2 ⁢ R 3 3 and W 2 , p ⁢ R N is then characterized. The two-scale limit behaviour of the potentials of a two-scale convergent sequence of irrotational fields is finally studied. ...