0576553 - ÚTIA 2025 RIV DE eng J - Článek v odborném periodiku
Davoli, E. - Kružík, Martin - Pagliari, V.
Homogenization of high-contrast composites under differential constraints.
Advances in Calculus of Variations. Roč. 17, č. 2 (2024), s. 277-318. ISSN 1864-8258. E-ISSN 1864-8266
Grant CEP: GA MŠMT(CZ) 8J19AT013; GA ČR(CZ) GF19-29646L
Institucionální podpora: RVO:67985556
Klíčová slova: Homogenization * high-contrast * two-scale convergence
Obor OECD: Pure mathematics
Impakt faktor: 1.3, rok: 2023 ; AIS: 1.132, rok: 2023
Způsob publikování: Open access
Web výsledku:
http://library.utia.cas.cz/separaty/2023/MTR/kruzik-0576553.pdf

DOI: https://doi.org/10.1515/acv-2022-0009

We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a heterogeneous material which, at a microscopic level, consists of a periodically perforated matrix whose cavities are occupied by a filling with very different physical properties. Our main result provides a Γ-convergence analysis as the periodicity tends to zero, and shows that the variational limit of the functionals at stake is the sum of two contributions, one resulting from the energy stored in the matrix and the other from the energy stored in the inclusions. As a consequence of the underlying high-contrast structure, the study is faced with a lack of coercivity with respect to the standard topologies in Lp , which we tackle by means of two-scale convergence techniques. In order to handle the differential constraints, instead, we establish new results about the existence of potentials and of constraint-preserving extension operators for linear, k-th order, homogeneous differential operators with constant coefficients and constant rank.
Trvalý link: https://hdl.handle.net/11104/0346459