@article{26787d914f154075b25ff5e7b097882a,

title = "A Degenerating Robin-Type Traction Problem in a Periodic Domain",

abstract = "We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then, we inves-tigate the asymptotic behavior of the displacement solution as the Robin condition turns into a pure traction one. To wit, there will be a matrix function b[k](·) that depends analytically on a real parameter k and vanishes for k = 0 and we multiply the Dirichlet-like part of the Robin condition by b[k](·). We show that the displacement solution can be written in terms of power series of k that converge for k in a whole neighborhood of 0. For our analysis we use the Functional Analytic Approach.",

keywords = "integral equations methods, integral operators, integral representations, linearized elastostatics, periodic domain, Robin boundary value problem",

author = "{Dalla Riva}, Matteo and Gennady Mishuris and Paolo Musolino",

note = "Funding Information: P.M. and G.M. acknowledge the support from EU through the H2020-MSCA-RISE-2020 project EffectFact, Grant agreement ID: 101008140. M.D.R. and P.M. are members of the Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Prob-abilit{\`a} e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). G.M. acknowledges also Ser Cymru Future Generation Industrial Fellowship number AU224 – 80761 and thanks the Royal Society for the Wolfson Research Merit Award. P.M. acknowledges also the support of the SPIN Grant “DOMain perturbation problems and INteractions Of scales” (DOMINO) of Ca{\textquoteright} Foscari University of Venice. Publisher Copyright: {\textcopyright} 2023 The Author(s). Published by Vilnius Gediminas Technical University.",

year = "2023",

month = sep,

day = "4",

doi = "10.3846/mma.2023.17681",

language = "English",

volume = "28",

pages = "509--521",

journal = "Mathematical Modelling and Analysis",

issn = "1392-6292",

publisher = "Vilnius Gediminas Technical University",

number = "3",

}