On the simultaneous homogenization and dimension reduction in elasticity and locality of Gamma-closure. Bukal, M. & Velcic, I. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, June, 2017. Place: TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY Publisher: SPRINGER HEIDELBERG Type: Article
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We provide a framework for simultaneous homogenization and dimension reduction in the setting of linearized elasticity as well as non-linear elasticity for the derivation of homogenized von Karman plate and bending rod models. The framework encompasses even perforated domains and domains with oscillatory boundary, provided that the corresponding extension operator can be constructed. Locality property of Gamma-closure is established, i.e. every energy density obtained by the homogenization process can be in almost every point obtained as the limit of periodic energy densities.
@article{bukal_simultaneous_2017,
	title = {On the simultaneous homogenization and dimension reduction in elasticity and locality of {Gamma}-closure},
	volume = {56},
	issn = {0944-2669},
	doi = {10.1007/s00526-017-1167-z},
	abstract = {We provide a framework for simultaneous homogenization and dimension reduction in the setting of linearized elasticity as well as non-linear elasticity for the derivation of homogenized von Karman plate and bending rod models. The framework encompasses even perforated domains and domains with oscillatory boundary, provided that the corresponding extension operator can be constructed. Locality property of Gamma-closure is established, i.e. every energy density obtained by the homogenization process can be in almost every point obtained as the limit of periodic energy densities.},
	language = {English},
	number = {3},
	journal = {CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS},
	author = {Bukal, Mario and Velcic, Igor},
	month = jun,
	year = {2017},
	note = {Place: TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY
Publisher: SPRINGER HEIDELBERG
Type: Article},
}

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