{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T12:57:08Z","timestamp":1791205028876,"version":"4.1.0"},"reference-count":40,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009096","name":"Scientific Research Projects Coordination Unit of Firat University","doi-asserted-by":"publisher","award":["MF.25.120"],"award-info":[{"award-number":["MF.25.120"]}],"id":[{"id":"10.13039\/100009096","id-type":"DOI","asserted-by":"publisher"}]},{"award":["MF.25.120"],"award-info":[{"award-number":["MF.25.120"]}],"id":[{"id":"https:\/\/ror.org\/05teb7b63","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>Chiral auxetic lattices convert axial loading into node rotation, producing negative Poisson\u2019s ratios and high energy absorption. This purely numerical study establishes a quasi-static baseline for additively manufacturable polyamide-12 (PA12) tetra-chiral lattices in which the chiral arm angle (0\u201390\u00b0) is treated as a design variable; no experiments were performed, and the model is verified rather than validated. Geometrically non-linear elastoplastic finite element analyses with a data-sheet-derived bilinear PA12 card and frictional self-contact were carried to 20% nominal strain and supported by mesh convergence, seeded-imperfection and friction sensitivity studies, a full-field lateral-strain measure and a refined sweep at 5\u00b0 resolution. The arm angle switches the response between a stretch-dominated non-auxetic regime (0\u00b0, 50\u201390\u00b0) and a rotation-dominated auxetic regime (15\u201345\u00b0) whose lateral kinematics are not sensitive to mesh density, friction and seeded imperfections. The 15\u00b0 lattice maximizes stiffness and peak force but is an isolated spike in the refined sweep, exhibits a collapse-mode bifurcation whose branch is selected by the discretization, and reaches the PA12 ductility limit after 3.5 mm of stroke. The 30\u00b0 architecture sustains 9.4 mm before fracture onset and delivers the highest damage-bounded specific energy absorption of the auxetic window (820 J\/kg on the baseline mesh), emerging as the design optimum.<\/jats:p>","DOI":"10.3390\/polym18192427","type":"journal-article","created":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T12:31:31Z","timestamp":1791203491000},"page":"2427","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Effect of Chiral Arm Angle on the Stiffness, Auxeticity and Energy Absorption of Polyamide-12 Tetra-Chiral Lattices Under Quasi-Static Compression: A Numerical Baseline Study"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6102-6584","authenticated-orcid":false,"given":"Volkan","family":"Ar\u0131kan","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Osmaniye Korkut Ata University, 80000 Osmaniye, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5092-8734","authenticated-orcid":false,"given":"Cenk","family":"Yanen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, Firat University, 23119 Elaz\u0131\u011f, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1126\/science.235.4792.1038","article-title":"Foam structures with a negative Poisson\u2019s ratio","volume":"235","author":"Lakes","year":"1987","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/(SICI)1521-4095(200005)12:9<617::AID-ADMA617>3.0.CO;2-3","article-title":"Auxetic materials: Functional materials and structures from lateral thinking!","volume":"12","author":"Evans","year":"2000","journal-title":"Adv. Mater."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5111","DOI":"10.1039\/C6RA27333E","article-title":"Auxetic mechanical metamaterials","volume":"7","author":"Kolken","year":"2017","journal-title":"RSC Adv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"023001","DOI":"10.1088\/1361-665X\/aaa61c","article-title":"Auxetic metamaterials and structures: A review","volume":"27","author":"Ren","year":"2018","journal-title":"Smart Mater. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108340","DOI":"10.1016\/j.compositesb.2020.108340","article-title":"Large deformation and energy absorption of additively manufactured auxetic materials and structures: A review","volume":"201","author":"Zhang","year":"2020","journal-title":"Compos. Part B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"485","DOI":"10.5545\/sv-jme.2016.3656","article-title":"Auxetic cellular materials\u2014A review","volume":"62","author":"Novak","year":"2016","journal-title":"Stroj. Vestn. J. Mech. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Duncan, O., Shepherd, T., Moroney, C., Foster, L., Venkatraman, P.D., Winwood, K., Allen, T., and Alderson, A. (2018). Review of auxetic materials for sports applications: Expanding options in comfort and protection. Appl. Sci., 8.","DOI":"10.3390\/app8060941"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Farokhi Nejad, A., Alipour, R., Shokri Rad, M., Yazid Yahya, M., Rahimian Koloor, S.S., and Petru, M. (2020). Using finite element approach for crashworthiness assessment of a polymeric auxetic structure subjected to the axial loading. Polymers, 12.","DOI":"10.3390\/polym12061312"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Plewa, J., Plonska, M., and Junak, G. (2025). Dynamics of polymeric re-entrant auxetic structures: Cyclic compression studies. Polymers, 17.","DOI":"10.3390\/polym17060825"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Schneider, Y., Guski, V., Schmauder, S., Kadkhodapour, J., Hufert, J., Grebhardt, A., and Bonten, C. (2023). Deformation behavior investigation of auxetic structure made of poly(butylene adipate-co-terephthalate) biopolymers using finite element method. Polymers, 15.","DOI":"10.3390\/polym15071792"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hasanzadeh, R. (2024). A new polymeric hybrid auxetic structure additively manufactured by fused filament fabrication 3D printing: Machine learning-based energy absorption prediction and optimization. Polymers, 16.","DOI":"10.3390\/polym16243565"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1177\/10996362251390299","article-title":"Influence of infill design on mechanical behavior of PLA-TPU hybrid sandwich beams","volume":"28","author":"Arikan","year":"2026","journal-title":"J. Sandw. Struct. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Mocerino, D., Ricciardi, M.R., Antonucci, V., and Papa, I. (2023). Fused deposition modelling of polymeric auxetic structures: A review. Polymers, 15.","DOI":"10.3390\/polym15041008"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0020-7403(96)00025-2","article-title":"Properties of a chiral honeycomb with a Poisson\u2019s ratio of \u22121","volume":"39","author":"Prall","year":"1997","journal-title":"Int. J. Mech. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1002\/pssb.200777704","article-title":"On the properties of auxetic meta-tetrachiral structures","volume":"245","author":"Grima","year":"2008","journal-title":"Phys. Status Solidi B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1016\/j.compscitech.2009.07.009","article-title":"Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading","volume":"70","author":"Alderson","year":"2010","journal-title":"Compos. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.jmps.2011.09.012","article-title":"Elasto-static micropolar behavior of a chiral auxetic lattice","volume":"60","author":"Spadoni","year":"2012","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1016\/j.ijsolstr.2012.12.004","article-title":"Elasticity of anti-tetrachiral anisotropic lattices","volume":"50","author":"Chen","year":"2013","journal-title":"Int. J. Solids Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.compstruct.2014.05.033","article-title":"Homogenization of periodic hexa- and tetrachiral cellular solids","volume":"116","author":"Bacigalupo","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.taml.2016.02.004","article-title":"Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach","volume":"6","author":"Mousanezhad","year":"2016","journal-title":"Theor. Appl. Mech. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12575","DOI":"10.1038\/s41598-018-30737-7","article-title":"Deformation mechanism of innovative 3D chiral metamaterials","volume":"8","author":"Wu","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1600609","DOI":"10.1002\/adem.201600609","article-title":"3D printed chiral cellular solids with amplified auxetic effects due to elevated internal rotation","volume":"19","author":"Jiang","year":"2017","journal-title":"Adv. Eng. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"He, Q., Hou, Y., Li, X., Li, S., and Meng, L. (2023). Investigation on the compressive behavior of hybrid polyurethane (PU)-foam-filled hyperbolic chiral lattice metamaterial. Polymers, 15.","DOI":"10.3390\/polym15092030"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lee, K.P.M., and Kajtaz, M. (2022). Experimental characterization and finite element modelling of polyamide-12 fabricated via Multi Jet Fusion. Polymers, 14.","DOI":"10.3390\/polym14235258"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/17452759.2019.1644184","article-title":"Compressive properties of 3D printed auxetic structures: Experimental and numerical studies","volume":"15","author":"Alomarah","year":"2020","journal-title":"Virtual Phys. Prototyp."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"107779","DOI":"10.1016\/j.matdes.2019.107779","article-title":"A new auxetic structure with significantly reduced stress concentration effects","volume":"173","author":"Meena","year":"2019","journal-title":"Mater. Des."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"109393","DOI":"10.1016\/j.compositesb.2021.109393","article-title":"Advanced honeycomb designs for improving mechanical properties: A review","volume":"227","author":"Qi","year":"2021","journal-title":"Compos. Part B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107950","DOI":"10.1016\/j.matdes.2019.107950","article-title":"Mechanical design and multifunctional applications of chiral mechanical metamaterials: A review","volume":"180","author":"Wu","year":"2019","journal-title":"Mater. Des."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"115028","DOI":"10.1088\/1361-665X\/ab47c9","article-title":"In-plane compression behavior of anti-tetrachiral and re-entrant lattices","volume":"28","author":"Gunaydin","year":"2019","journal-title":"Smart Mater. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Szeles, L., Horvath, R., and Cveticanin, L. (2024). Analysis of mechanical properties and parameter dependency of novel, doubly re-entrant auxetic honeycomb structures. Polymers, 16.","DOI":"10.3390\/polym16172524"},{"key":"ref_31","unstructured":"(2019). Plastics\u2014Determination of Tensile Properties\u2014Part 1: General Principles (Standard No. ISO 527-1:2019)."},{"key":"ref_32","unstructured":"(2025). Plastics\u2014Determination of Tensile Properties\u2014Part 2: Test Conditions for Moulding and Extrusion Plastics (Standard No. ISO 527-2:2025)."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"103566","DOI":"10.1016\/j.ijimpeng.2020.103566","article-title":"Compressive behavior of chiral auxetic cellular structures at different strain rates","volume":"141","author":"Novak","year":"2020","journal-title":"Int. J. Impact Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0013-7944(85)90052-9","article-title":"Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures","volume":"21","author":"Johnson","year":"1985","journal-title":"Eng. Fract. Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"135301","DOI":"10.1088\/2053-1591\/ae85db","article-title":"A non-linear energy-based framework for fatigue life prediction in semi-crystalline thermoplastics: Application to PEEK","volume":"13","author":"Arikan","year":"2026","journal-title":"Mater. Res. Express"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Gibson, L.J., and Ashby, M.F. (1997). Cellular Solids: Structure and Properties, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9781139878326"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"121293","DOI":"10.1016\/j.engstruct.2025.121293","article-title":"Study and application of higher-order effects in the crashworthiness of corrugated spacer tubes","volume":"343","author":"He","year":"2025","journal-title":"Eng. Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"107682","DOI":"10.1016\/j.tws.2021.107682","article-title":"Design, manufacturing and applications of auxetic tubular structures: A review","volume":"163","author":"Luo","year":"2021","journal-title":"Thin-Walled Struct."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"112628","DOI":"10.1016\/j.istruc.2026.112628","article-title":"Multifunctional lattice structures: Synergistic design for energy absorption, sound insulation, and thermal protection","volume":"91","author":"He","year":"2026","journal-title":"Structures"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/S0734-743X(99)00153-0","article-title":"High strain rate compressive behavior of aluminum alloy foams","volume":"24","author":"Deshpande","year":"2000","journal-title":"Int. J. Impact Eng."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/19\/2427\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T12:38:19Z","timestamp":1791203899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/19\/2427"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,5]]},"references-count":40,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2026,10]]}},"alternative-id":["polym18192427"],"URL":"https:\/\/doi.org\/10.3390\/polym18192427","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,5]]}}}