Homogenization of some variational inequalities for elasto‐plastic torsion problems

Article type: Research Article

Authors: Piat, V. Chiadò | Sandrakov, G.V.

Affiliations: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10139, Italy E‐mail: [email protected] | State Center of Scientific and Technological Consultation, KPI, pros. Peremogi 37, k.17‐319, Kiev 03056, Ukraine E‐mail: [email protected]

Abstract: Methods of homogenization for variational inequalities with gradient constraints are presented. The variational inequalities are defined by a monotone operator of second order with periodic rapidly oscillating coefficients. The macroscopic homogenized (limiting) variational inequality satisfied by the limit of the solutions of the variational inequalities is deduced. Methods of variational inequalities theory and the notion of two‐scale convergence are used for passage to the limit. The relevant feature of the homogenized variational inequality is its twice‐nonlinear form, which is different from that of the initial variational inequality. A comparison with the homogenization for constrained minimization problems is given.

Journal: Asymptotic Analysis, vol. 40, no. 1, pp. 1-23, 2004