Homogenization via unfolding in periodic layer with contact

Article type: Research Article

Authors: Griso, Georges^{a; *} | Migunova, Anastasia^b | Orlik, Julia^b

Affiliations: [a] Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France. E-mail: griso@ljll.math.upmc.fr | [b] Fraunhofer-ITWM, Kaiserslautern, Germany. E-mails: migunova@itwm.frauhofer.de, julia.orlik@itwm.frauhofer.de

Correspondence: [*] Corresponding author. E-mail: griso@ljll.math.upmc.fr.

Abstract: The elasticity problem for two domains separated by a heterogeneous layer of the thickness ε is considered. The layer has an ε-periodic structure, ε≪1, including a multiple cracks and the contact between the structural components. The inclusions are surrounded by cracks and can have rigid displacements. The contacts are described by the Signorini and Tresca-friction conditions. In order to obtain preliminary estimates, a modification of the Korn inequality for the ε-dependent periodic layer is performed. An asymptotic analysis with respect to ε→0 is provided and the limit elasticity problem is obtained, together with the transmission condition across the interface. The periodic unfolding method is used to study the limit behavior.

Keywords: Korn inequality for contact with inclusions, unfolding on the oscillating interface, homogenization of contact, linear elasticity

DOI: 10.3233/ASY-161374

Journal: Asymptotic Analysis, vol. 99, no. 1-2, pp. 23-52, 2016