{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T08:31:57Z","timestamp":1762504317118,"version":"build-2065373602"},"reference-count":87,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T00:00:00Z","timestamp":1576454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.<\/jats:p>","DOI":"10.3390\/sym11121523","type":"journal-article","created":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T02:59:01Z","timestamp":1576551541000},"page":"1523","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations"],"prefix":"10.3390","volume":"11","author":[{"given":"Daria","family":"Scerrato","sequence":"first","affiliation":[{"name":"International Research Center on Mathematics and Mechanics of Complex Systems\u2014MeMoCS, Universit\u00e0 degli studi dell\u2019Aquila, 67100 L\u2019Aquila, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0044-9188","authenticated-orcid":false,"given":"Ivan","family":"Giorgio","sequence":"additional","affiliation":[{"name":"International Research Center on Mathematics and Mechanics of Complex Systems\u2014MeMoCS, Universit\u00e0 degli studi dell\u2019Aquila, 67100 L\u2019Aquila, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1007\/s00419-018-1399-1","article-title":"Discrete and continuous aspects of some metamaterial elastic structures with band gaps","volume":"88","author":"Placidi","year":"2018","journal-title":"Arch. 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