{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T17:46:16Z","timestamp":1762364776641,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"National Funds through the Portuguese funding agency, FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["LA\/P\/0063\/2020"],"award-info":[{"award-number":["LA\/P\/0063\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"project iRAIL Innovation in Railway Systems and Technologies Doctoral Programme funds and by national funds through FCT\u2014Portuguese Foundation for Science and Technology","award":["PD\/BD\/114096\/2015"],"award-info":[{"award-number":["PD\/BD\/114096\/2015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Compos. Sci."],"abstract":"<jats:p>The deformation mechanisms of classic lattice topologies (e.g., Cubic, Diamond, Octet, and Double Pyramid lattices) and their specific density-dependent mechanical properties have already been thoroughly explored by the scientific community. This study details a novel approach to designing lattices by generating the topologies that correspond to the voids of these classic lattice designs. This is achieved by using a Boolean operation performed to create a solid topology from the original voided fraction. The resultant topologies are proposed to be named Inverse lattices. Static structural numerical analysis shows that this process may generate significant changes in the lattice deformation mechanism and stiffness. For this effect, elastic properties such as the Specific modulus and Apparent Poisson\u2019s ratio were determined as a function of Specific density. Specifically, for Octet and Double Pyramid inverse lattice topologies, results show a reduction in stiffness by promoting a change to a bending deformation mechanism. However, the inverse Diamond inverse lattice topologies present a higher stiffness (i.e., specific modulus) relative to the original classic design. This new lattice model may be a promising design for future lattice applications.<\/jats:p>","DOI":"10.3390\/jcs9110605","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T17:06:06Z","timestamp":1762362366000},"page":"605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inverse Cellular Lattices"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8504-3525","authenticated-orcid":false,"given":"Vitor H.","family":"Carneiro","sequence":"first","affiliation":[{"name":"Centre for Robotics in Industry and Intelligent Systems, INESC TEC\u2014Institute for Systems and Computer Engineering, Technology and Science, 4200-465 Porto, Portugal"},{"name":"Department of Engineering, School of Science and Technology, University of Tr\u00e1s-os-Montes e Alto Douro, 5000-801 Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1121-6793","authenticated-orcid":false,"given":"H\u00e9lder","family":"Puga","sequence":"additional","affiliation":[{"name":"CMEMS-UMinho, Department of Mechanical Engineering, University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bari, K. (2023). Design, Simulation, and Mechanical Testing of 3D-Printed Titanium Lattice Structures. J. Compos. Sci., 7.","DOI":"10.3390\/jcs7010032"},{"key":"ref_2","first-page":"101301","article-title":"Mechanical Properties of Additively Manufactured Metal Lattice Structures: Data Review and Design Interface","volume":"35","author":"Hanks","year":"2020","journal-title":"Addit. Manuf."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Papageorgiou, V., Tsongas, K., Mansour, M.T., Tzetzis, D., and Mansour, G. (2025). Mechanical Properties and Vibrational Behavior of 3D-Printed Carbon Fiber-Reinforced Polyphenylene Sulfide and Polyamide-6 Composites with Different Infill Types. J. Compos. Sci., 9.","DOI":"10.3390\/jcs9020059"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/j.pnsc.2021.10.015","article-title":"Structural Metamaterials with Negative Mechanical\/Thermomechanical Indices: A Review","volume":"31","author":"Cardoso","year":"2021","journal-title":"Prog. Nat. Sci. Mater. Int."},{"key":"ref_5","unstructured":"Gibson, L.J., Ashby, M.F., and Harley, B.A. (2010). Cellular Materials in Nature and Medicine, Cambridge University Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"100219","DOI":"10.1016\/j.mtla.2019.100219","article-title":"Multi-Scale Foam: 3D Structure\/Compressive Behaviour Relationship of Agglomerated Cork","volume":"5","author":"Girardot","year":"2019","journal-title":"Materialia"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"115102","DOI":"10.1016\/j.compstruct.2021.115102","article-title":"Bio-Inspired Repeatable Lattice Structures for Energy Absorption: Experimental and Finite Element Study","volume":"283","author":"Sharma","year":"2022","journal-title":"Compos. Struct."},{"key":"ref_8","first-page":"104036","article-title":"3D-Printed Bioinspired Cage Lattices with Defect-Tolerant Mechanical Properties","volume":"82","author":"Yang","year":"2024","journal-title":"Addit. Manuf."},{"key":"ref_9","first-page":"103507","article-title":"Topology Optimization of Self-Supporting Lattice Structure","volume":"67","author":"Wang","year":"2023","journal-title":"Addit. Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Song, W., Zhao, L., Liu, J., Liu, S., Yu, G., Qin, B., and Xiao, L. (2025). Mechanical Behavior of Topology-Optimized Lattice Structures Fabricated by Additive Manufacturing. Materials, 18.","DOI":"10.3390\/ma18153614"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gongora, A.E., Friedman, C., Newton, D.K., Yee, T.D., Doorenbos, Z., Giera, B., Duoss, E.B., Han, T.Y.-J., Sullivan, K., and Rodriguez, J.N. (2024). Accelerating the Design of Lattice Structures Using Machine Learning. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-63204-7"},{"key":"ref_12","first-page":"103238","article-title":"Machine Learning Based Lattice Generation Method Derived from Topology Optimisation","volume":"60","author":"Wang","year":"2022","journal-title":"Addit. Manuf."},{"key":"ref_13","first-page":"103833","article-title":"Topology Optimisation for Design and Additive Manufacturing of Functionally Graded Lattice Structures Using Derivative-Aware Machine Learning Algorithms","volume":"78","author":"Wu","year":"2023","journal-title":"Addit. Manuf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.mattod.2021.04.019","article-title":"A Review of Additive Manufacturing of Metamaterials and Developing Trends","volume":"50","author":"Fan","year":"2021","journal-title":"Mater. Today"},{"key":"ref_15","first-page":"98","article-title":"Effect of Yttria Mould Coating on the Investment Casting of AZ91D-1 Wt% CaO Magnesium Alloy","volume":"14","author":"Lopes","year":"2020","journal-title":"Int. J. Met."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1007\/s00170-023-11124-7","article-title":"Replication Casting and Additive Manufacturing for Fabrication of Cellular Aluminum with Periodic Topology: Optimization by CFD Simulation","volume":"126","year":"2023","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1098\/rsta.2005.1678","article-title":"The Properties of Foams and Lattices","volume":"364","author":"Ashby","year":"2006","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"100829","DOI":"10.1016\/j.mtla.2020.100829","article-title":"Laser-Based Powder-Bed Fusion Strategies for the Fabrication of Cellular Structures with a Fine Resolution","volume":"13","author":"Hejripour","year":"2020","journal-title":"Materialia"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108137","DOI":"10.1016\/j.matdes.2019.108137","article-title":"SLM Lattice Structures: Properties, Performance, Applications and Challenges","volume":"183","author":"Maconachie","year":"2019","journal-title":"Mater. Des."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"100606","DOI":"10.1016\/j.mser.2021.100606","article-title":"Architected Cellular Materials: A Review on Their Mechanical Properties towards Fatigue-Tolerant Design and Fabrication","volume":"144","author":"Benedetti","year":"2021","journal-title":"Mater. Sci. Eng. R Rep."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Arretche, I., and Matlack, K.H. (2018). On the Interrelationship Between Static and Vibration Mitigation Properties of Architected Metastructures. Front. Mater., 5.","DOI":"10.3389\/fmats.2018.00068"}],"container-title":["Journal of Composites Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-477X\/9\/11\/605\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T17:41:45Z","timestamp":1762364505000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-477X\/9\/11\/605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":21,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["jcs9110605"],"URL":"https:\/\/doi.org\/10.3390\/jcs9110605","relation":{},"ISSN":["2504-477X"],"issn-type":[{"value":"2504-477X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,5]]}}}