{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T14:37:54Z","timestamp":1792075074865,"version":"4.4.0"},"reference-count":51,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T00:00:00Z","timestamp":1543449600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National High Technology Research and Development Program of China","award":["2015AA042501"],"award-info":[{"award-number":["2015AA042501"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The triply periodic minimal surface (TPMS) method is a novel approach for lattice design in a range of fields, such as impact protection and structural lightweighting. In this paper, we used the TPMS formula to rapidly and accurately generate the most common lattice structure, named the body centered cubic (BCC) structure, with certain volume fractions. TPMS-based and computer aided design (CAD) based BCC lattice structures with volume fractions in the range of 10\u201330% were fabricated by selective laser melting (SLM) technology with Ti\u20136Al\u20134V and subjected to compressive tests. The results demonstrated that local geometric features changed the volume and stress distributions, revealing that the TPMS-based samples were superior to the CAD-based ones, with elastic modulus, yield strength and compression strength increasing in the ranges of 18.9\u201342.2%, 19.2\u201329.5%, and 2\u201336.6%, respectively. The failure mechanism of the TPMS-based samples with a high volume fraction changed to brittle failure observed by scanning electron microscope (SEM), as their struts were more affected by the axial force and fractured on struts. It was also found that the TPMS-based samples have a favorable capacity to absorb energy, particularly with a 30% volume fraction, the energy absorbed up to 50% strain was approximately three times higher than that of the CAD-based sample with an equal volume fraction. Furthermore, the theoretic Gibson\u2013Ashby mode was established in order to predict and design the mechanical properties of the lattice structures. In summary, these results can be used to rapidly create BCC lattice structures with superior compressive properties for engineering applications.<\/jats:p>","DOI":"10.3390\/ma11122411","type":"journal-article","created":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T11:47:53Z","timestamp":1543492073000},"page":"2411","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":252,"title":["Improved Mechanical Properties and Energy Absorption of BCC Lattice Structures with Triply Periodic Minimal Surfaces Fabricated by SLM"],"prefix":"10.3390","volume":"11","author":[{"given":"Miao","family":"Zhao","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8094-9758","authenticated-orcid":false,"given":"Fei","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guang","family":"Fu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David Z.","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"},{"name":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hailun","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0079-6425(00)00016-5","article-title":"The topological design of multifunctional cellular metals","volume":"46","author":"Evans","year":"2001","journal-title":"Prog. Mater. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.matdes.2011.11.006","article-title":"Hybrid composite laminates reinforced with glass\/carbon woven fabrics for lightweight load bearing structures","volume":"36","author":"Zhang","year":"2012","journal-title":"Mater. Des. (1980\u20132015)"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ijimpeng.2013.04.007","article-title":"Drop weight impact behaviour of sandwich panels with metallic micro lattice cores","volume":"60","author":"Mines","year":"2013","journal-title":"Int. J. Impact Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, X.Y., Fang, G., and Zhou, J. (2017). Additively manufactured scaffolds for bone tissue engineering and the prediction of their mechanical behavior: A review. Materials, 10.","DOI":"10.3390\/ma10010050"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/S0079-6425(00)00002-5","article-title":"Manufacture, characterisation and application of cellular metals and metal foams","volume":"46","author":"Banhart","year":"2001","journal-title":"Prog. Mater. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6981","DOI":"10.1016\/S0020-7683(03)00349-4","article-title":"On the performance of truss panels with Kagom\u00e9 cores","volume":"40","author":"Wang","year":"2003","journal-title":"Int. J. Solids Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1557\/JMR.2001.0143","article-title":"Synthesis of open-cell metal foams by templated directed vapor deposition","volume":"16","author":"Queheillalt","year":"2011","journal-title":"J. Mater. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6249","DOI":"10.1016\/j.ijsolstr.2004.05.045","article-title":"A protocol for characterizing the structural performance of metallic sandwich panels: Application to pyramidal truss cores","volume":"41","author":"Zok","year":"2004","journal-title":"Int. J. Solids Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.compstruc.2014.03.004","article-title":"An error diffusion based method to generate functionally graded cellular structures","volume":"138","author":"Brackett","year":"2014","journal-title":"Comput. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s11465-013-0248-8","article-title":"Additive manufacturing: Technology, applications and research needs","volume":"8","author":"Guo","year":"2013","journal-title":"Front. Mech. Eng."},{"key":"ref_11","first-page":"1","article-title":"A voxel-based method of constructing and skinning conformal and functionally graded lattice structures suitable for additive manufacturing","volume":"13","author":"Aremu","year":"2017","journal-title":"Addit. Manuf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.matdes.2016.05.020","article-title":"Strength analysis and modeling of cellular lattice structures manufactured using selective laser melting for tooling applications","volume":"104","author":"Mahshid","year":"2016","journal-title":"Mater. Des."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bai, L., Zhang, J., Chen, X., Yi, C., Chen, R., and Zhang, Z. (2018). Configuration optimization design of Ti6Al4V lattice structure formed by SLM. Materials, 11.","DOI":"10.3390\/ma11101856"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1080\/14786446408643668","article-title":"On the calculation of the equilibrium and stiffness of frames","volume":"27","author":"Maxwell","year":"1864","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1016\/S1359-6454(00)00379-7","article-title":"Foam topology: Bending versus stretching dominated architectures","volume":"49","author":"Deshpande","year":"2001","journal-title":"Acta Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.matdes.2018.05.059","article-title":"Fabrication of polymeric lattice structures for optimum energy absorption using Multi Jet Fusion technology","volume":"155","author":"Habib","year":"2018","journal-title":"Mater. Des."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1177\/1099636210380997","article-title":"An investigation into the compressive properties of stainless steel micro-lattice sturctures","volume":"13","author":"Ushijima","year":"2010","journal-title":"J. Sandw. Struct. Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.ijmecsci.2012.12.017","article-title":"Prediction of the mechanical properties of micro-lattice structures subjected to multi-axial loading","volume":"68","author":"Ushijima","year":"2013","journal-title":"Int. J. Mech. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.msea.2013.07.070","article-title":"Static mechanical behaviours of stainless steel micro-lattice structures under different loading conditions","volume":"586","author":"Mines","year":"2013","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ijmecsci.2018.03.027","article-title":"Stiffness and specific energy absorption of additively-manufactured metallic BCC metamaterials composed of tapered beams","volume":"141","author":"Mohr","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1007\/s00170-015-8237-1","article-title":"Direct porous structure generation of tissue engineering scaffolds for layer-based additive manufacturing","volume":"86","author":"Papazetis","year":"2016","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Liu, F., Zhang, D., Zhang, P., Zhao, M., and Jafar, S. (2018). Mechanical properties of optimized diamond lattice structure for bone scaffolds fabricated via selective laser melting. Materials, 11.","DOI":"10.3390\/ma11030374"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.cma.2018.03.044","article-title":"Topology optimization of viscoelastic materials on damping and frequency of macrostructures","volume":"337","author":"Liu","year":"2018","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6909","DOI":"10.1016\/j.biomaterials.2010.05.068","article-title":"Mathematically defined tissue engineering scaffold architectures prepared by stereolithography","volume":"31","author":"Melchels","year":"2010","journal-title":"Biomaterials"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.jmbbm.2016.05.027","article-title":"Additive manufacturing and mechanical characterization of graded porosity scaffolds designed based on triply periodic minimal surface architectures","volume":"62","author":"Afshar","year":"2016","journal-title":"J. Mech. Behav. Biomed. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.polymer.2017.11.049","article-title":"Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing","volume":"152","author":"Maskery","year":"2017","journal-title":"Polymer"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/j.actbio.2017.02.024","article-title":"Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties","volume":"53","author":"Bobbert","year":"2017","journal-title":"Acta Biomater."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.cad.2014.06.006","article-title":"Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering","volume":"56","author":"Yang","year":"2014","journal-title":"Comput.-Aided Des."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.jmbbm.2015.06.024","article-title":"Ti-6Al-4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting","volume":"51","author":"Yan","year":"2015","journal-title":"J. Mech. Behav. Biomed. Mater."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/j.matdes.2013.10.027","article-title":"Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting","volume":"55","author":"Yan","year":"2014","journal-title":"Mater. Des."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1016\/j.medengphy.2014.05.006","article-title":"Design of tissue engineering scaffolds based on hyperbolic surfaces: Structural numerical evaluation","volume":"36","author":"Almeida","year":"2014","journal-title":"Med. Eng. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1016\/j.actbio.2013.10.024","article-title":"Current trends in the design of scaffolds for computer-aided tissue engineering","volume":"10","author":"Giannitelli","year":"2014","journal-title":"Acta Biomater."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.msea.2016.06.013","article-title":"A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting","volume":"670","author":"Maskery","year":"2016","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.ijmecsci.2012.12.004","article-title":"Finite element modelling of the compressive response of lattice structures manufactured using the selective laser melting technique","volume":"67","author":"Smith","year":"2013","journal-title":"Int. J. Mech. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.matdes.2016.02.127","article-title":"Selective laser melting (SLM) of AlSi12Mg lattice structures","volume":"98","author":"Leary","year":"2016","journal-title":"Mater. Des."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.ijmecsci.2018.07.006","article-title":"Mechanical properties of an improved 3D-printed rhombic dodecahedron stainless steel lattice structure of variable cross section","volume":"145","author":"Cao","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/BF01313411","article-title":"Nodal surfaces of Fourier series: Fundamental invariants of structured matter","volume":"83","author":"Nesper","year":"1991","journal-title":"Z. Phys. B Condens. Matter"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1016\/j.medengphy.2015.08.006","article-title":"Novel real function based method to construct heterogeneous porous scaffolds and additive manufacturing for use in medical engineering","volume":"37","author":"Yang","year":"2015","journal-title":"Med. Eng. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.matdes.2017.06.006","article-title":"Compressive properties of functionally graded lattice structures manufactured by selective laser melting","volume":"131","author":"Choy","year":"2017","journal-title":"Mater. Des."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.msea.2015.01.031","article-title":"Influence of processing conditions on strut structure and compressive properties of cellular lattice structures fabricated by selective laser melting","volume":"628","author":"Qiu","year":"2015","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_41","unstructured":"British Standards Institution (2011). Mechanical Testing of Metals\u2014Ductility Testing\u2014Compression Test for Porous and Cellular Metals, British Standards Institution."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.matlet.2017.07.018","article-title":"Quasi-static compressive behavior of the ex-situ aluminum-alloy foam-filled tubes under elevated temperature conditions","volume":"206","author":"Movahedi","year":"2017","journal-title":"Mater. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1016\/j.compstruct.2018.11.006","article-title":"Cryogenic and high temperature compressive properties of Metal Foam Matrix Composites","volume":"209","author":"Linul","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_44","first-page":"213","article-title":"Compressive properties of Ti-6Al-4V lattice structures fabricated by selective laser melting: Design, orientation and density","volume":"16","author":"Choy","year":"2017","journal-title":"Addit. Manuf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.ijmecsci.2018.08.039","article-title":"Mechanical response of a triply periodic minimal surface cellular structures manufactured by selective laser melting","volume":"148","author":"Yang","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1016\/j.jallcom.2018.01.102","article-title":"The temperature and anisotropy effect on compressive behavior of cylindrical closed-cell aluminum-alloy foams","volume":"740","author":"Linul","year":"2018","journal-title":"J. Alloys Compd."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.matdes.2017.10.040","article-title":"Anisotropic Ti-6Al-4V gyroid scaffolds manufactured by electron beam melting (EBM) for bone implant applications","volume":"137","author":"Ataee","year":"2018","journal-title":"Mater. Des."},{"key":"ref_48","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_49","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.ijmecsci.2013.01.006","article-title":"Compressive behaviour of stainless steel micro-lattice structures","volume":"68","author":"Mines","year":"2013","journal-title":"Int. J. Mech. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Gibson, L.J., and Ashby, M.F. (1997). Cellular Solids: Structure and Properties, Cambridge University Press.","DOI":"10.1017\/CBO9781139878326"},{"key":"ref_51","unstructured":"ISO (2009). Metallic Materials\u2014Tensile Testing\u2014Part 1: Method of Test at Room Temperature, International Organization for Standardization."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/11\/12\/2411\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:33:17Z","timestamp":1760196797000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/11\/12\/2411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,29]]},"references-count":51,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["ma11122411"],"URL":"https:\/\/doi.org\/10.3390\/ma11122411","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,29]]}}}