{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T14:06:55Z","timestamp":1774620415533,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T00:00:00Z","timestamp":1684108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2022YFB4300101"],"award-info":[{"award-number":["2022YFB4300101"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2022M713515"],"award-info":[{"award-number":["2022M713515"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022YFB4300101"],"award-info":[{"award-number":["2022YFB4300101"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022M713515"],"award-info":[{"award-number":["2022M713515"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This study examines a hierarchical vertex-based structure that improves the crashworthiness of the conventional multi-cell square, a biological hierarchy of natural origin with exceptional mechanical properties. The vertex-based hierarchical square structure (VHS) is explored for its geometric properties, including infinite repetition and self-similarity. The cut-and-patch method is used to derive an equation for the material thicknesses of different orders of the VHS based on the principle of the same weight. A thorough parametric study of VHS was conducted using LS-DYNA, which examined the effects of material thickness, orders, and various structural ratios. The results were evaluated based on common crashworthiness criteria and demonstrated that the total energy absorption (TEA), specific energy absorption (SEA), and mean crushing force (Pm) of VHS exhibited similar monotonicity concerning the orders. SEA of the first-order VHS with \u03bb1=0.3 and the second-order VHS with \u03bb1=0.3 and \u03bb2=0.1 are improved by at most 59.9% and 102.4% respectively; the second-order VHS with 0.2\u2264\u03bb1\u22640.4 and 0.1\u2264\u03bb2\u22640.15 have the better overall performance of crashworthiness. Then, the half-wavelength equation of VHS and Pm of each fold was established based on the Super-Folding Element method. Meanwhile, a comparative analysis with the simulation results reveals three different out-of-plane deformation mechanisms of VHS. The study indicated that material thickness had a greater impact on crashworthiness. Finally, the comparison with conventional honeycombs demonstrated that VHS holds great promise as a structure for crashworthiness. These results provide a solid foundation for further research and development of new bionic energy-absorbing devices.<\/jats:p>","DOI":"10.3390\/ma16103749","type":"journal-article","created":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T02:27:04Z","timestamp":1684204024000},"page":"3749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Comparative Analysis of Out-of-Plane Deformation Mechanisms of Vertex-Based Hierarchical Structures for Crashworthiness"],"prefix":"10.3390","volume":"16","author":[{"given":"Chong","family":"Shi","sequence":"first","affiliation":[{"name":"The State Key Laboratory of Heavy-Duty and Express High-Power Electric Locomotive, Zhuzhou 412001, China"},{"name":"National & Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha 410075, China"},{"name":"Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Changsha 410017, China"},{"name":"Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Changsha 410017, China"},{"name":"Key Laboratory of Railway Industry of Aerodynamics, Changsha 410017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xifeng","family":"Liang","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Heavy-Duty and Express High-Power Electric Locomotive, Zhuzhou 412001, China"},{"name":"National & Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha 410075, China"},{"name":"Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Changsha 410017, China"},{"name":"Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Changsha 410017, China"},{"name":"Key Laboratory of Railway Industry of Aerodynamics, Changsha 410017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Xiong","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Heavy-Duty and Express High-Power Electric Locomotive, Zhuzhou 412001, China"},{"name":"National & Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha 410075, China"},{"name":"Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Changsha 410017, China"},{"name":"Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Changsha 410017, China"},{"name":"Key Laboratory of Railway Industry of Aerodynamics, Changsha 410017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiefu","family":"Liu","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Heavy-Duty and Express High-Power Electric Locomotive, Zhuzhou 412001, China"},{"name":"National & Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha 410075, China"},{"name":"Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Changsha 410017, China"},{"name":"Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Changsha 410017, China"},{"name":"Key Laboratory of Railway Industry of Aerodynamics, Changsha 410017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.tws.2017.03.029","article-title":"Experimental Investigation of an Active\u2013Passive Integration Energy Absorber for Railway Vehicles","volume":"117","author":"Gao","year":"2017","journal-title":"Thin-Walled Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.compositesb.2017.07.036","article-title":"On Folding Mechanics of Multi-Cell Thin-Walled Square Tubes","volume":"132","author":"Wang","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.tws.2014.03.007","article-title":"Collision Performance of Square Tubes with Diaphragms","volume":"80","author":"Gao","year":"2014","journal-title":"Thin-Walled Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.tws.2017.11.031","article-title":"Crushing Analysis and Multi-Objective Optimization of a Cutting Aluminium Tube Absorber for Railway Vehicles Under Quasi-Static Loading","volume":"123","author":"Guan","year":"2018","journal-title":"Thin-Walled Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.tws.2017.10.003","article-title":"A Numerical Study on the Energy Absorption of a Bending-Straightening Energy Absorber with Large Stroke","volume":"122","author":"Yu","year":"2018","journal-title":"Thin-Walled Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/j.matdes.2013.10.054","article-title":"Multiobjective Crashworthiness Optimization Design of Functionally Graded Foam-Filled Tapered Tube Based on Dynamic Ensemble Metamodel","volume":"55","author":"Yin","year":"2014","journal-title":"Mater. Des."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"106683","DOI":"10.1016\/j.ijmecsci.2021.106683","article-title":"Crashworthiness Index of Honeycomb Sandwich Structures Under Low-Speed Oblique Impact","volume":"208","author":"Wang","year":"2021","journal-title":"Int. J. Mech. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107001","DOI":"10.1016\/j.tws.2020.107001","article-title":"Bending Behavior of Sandwich Beam with Tailored Hierarchical Honeycomb Cores","volume":"157","author":"Li","year":"2020","journal-title":"Thin-Walled Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1016\/0020-7403(93)90054-X","article-title":"Plastic Deformation Mechanisms in Axially Compressed Metal Tubes Used as Impact Energy Absorbers","volume":"35","author":"Reid","year":"1993","journal-title":"Int. J. Mech. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.ijmecsci.2017.07.019","article-title":"Axial Crushing of Embedded Multi-Cell Tubes","volume":"131\u2013132","author":"Zhang","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.ijmecsci.2015.12.006","article-title":"Bending Collapse of Square Tubes with Variable Thickness","volume":"106","author":"Zhang","year":"2016","journal-title":"Int. J. Mech. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.ijmecsci.2011.09.006","article-title":"Deformation and Energy Absorption of Aluminum Foam-Filled Tubes Subjected to Oblique Loading","volume":"54","author":"Li","year":"2012","journal-title":"Int. J. Mech. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.ijmecsci.2016.12.005","article-title":"Crashworthiness Analysis of Multi-Cell Square Tubes Under Axial Loads","volume":"121","author":"Xie","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ijmecsci.2016.01.003","article-title":"Crush Resistance of Square Tubes with Various Thickness Configurations","volume":"107","author":"Zhang","year":"2016","journal-title":"Int. J. Mech. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.ijmecsci.2018.02.034","article-title":"Dynamic Axial Crush Analysis and Design Optimization of a Square Multi-Cell Thin-Walled Tube with Lateral Variable Thickness","volume":"140","author":"Ding","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cheng, X., Bai, Z., Zhu, F., Chou, C.C., Jiang, B., and Xu, S. (2022). An optimized bio-inspired thin-walled structure with controllable crashworthiness based on magnetorheological fluid. Mech. Adv. Mater. Struct., 1\u201316.","DOI":"10.1080\/15376494.2022.2146240"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1080\/15376494.2014.994150","article-title":"Theoretical assessment methodology on axial compressed hexagonal honeycomb\u2019s energy absorption capability","volume":"23","author":"Wang","year":"2016","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.compstruct.2016.05.108","article-title":"Analytical Method for the Axial Crushing Force of Fiber-Reinforced Tapered Square Metal Tubes","volume":"153","author":"Ying","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.compositesb.2018.03.005","article-title":"Blast Resistance and Parametric Study of Sandwich Structure Consisting of Honeycomb Core Filled with Circular Metallic Tubes","volume":"145","author":"Liu","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.compositesb.2018.01.015","article-title":"On the Influence of Structural Defects for Honeycomb Structure","volume":"142","author":"Wang","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"114164","DOI":"10.1016\/j.compstruct.2021.114164","article-title":"Crashworthiness Design of Periodic Cellular Structures Using Topology Optimization","volume":"271","author":"Jia","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.compstruct.2019.01.076","article-title":"Designing Hierarchical Metamaterials by Topology Analysis with Tailored Poisson\u2019S Ratio and Young\u2019S Modulus","volume":"214","author":"Yang","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1622","DOI":"10.1080\/13588265.2021.1981125","article-title":"Crashworthiness Performance of Thin-Walled, Square Tubes with Circular Hole Discontinuities Under High-Speed Impact Loading","volume":"27","author":"Taghipoor","year":"2022","journal-title":"Int. J. Crashworthiness"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"107457","DOI":"10.1016\/j.ijmecsci.2022.107457","article-title":"Topology Optimization of Thin-Walled Tubes Filled with Lattice Structures","volume":"227","author":"Li","year":"2022","journal-title":"Int. J. Mech. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.msea.2011.09.093","article-title":"A Study on the Static and Dynamic Loading of the Foam Filled Metal Hexagonal Honeycomb\u2014Theoretical and Experimental","volume":"530","author":"Sadeghi","year":"2011","journal-title":"Mater. Sci. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.tws.2019.04.029","article-title":"Dynamic Response of Sandwich Panel with Hierarchical Honeycomb Cores Subject to Blast Loading","volume":"142","author":"Sun","year":"2019","journal-title":"Thin-Walled Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.istruc.2020.08.082","article-title":"Experimental Investigation of the Three-Point Bending Properties of Sandwich Beams with Polyurethane Foam-Filled Lattice Cores","volume":"28","author":"Taghipoor","year":"2020","journal-title":"Structures"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.tws.2015.11.007","article-title":"Crashworthiness Performance of Conical Tubes with Nonlinear Thickness Distribution","volume":"99","author":"Zhang","year":"2016","journal-title":"Thin-Walled Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ijimpeng.2006.11.005","article-title":"Energy Absorption of a Thin-Walled Cylinder with Ribs Subjected to Axial Impact","volume":"35","author":"Adachi","year":"2008","journal-title":"Int. J. Impact Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.matdes.2016.08.032","article-title":"Crashworthiness of Vertex Based Hierarchical Honeycombs in Out-of-Plane Impact","volume":"110","author":"Sun","year":"2016","journal-title":"Mater. Des."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.ijmecsci.2018.03.006","article-title":"A More Weight-Efficient Hierarchical Hexagonal Multi-Cell Tubular Absorber","volume":"140","author":"Li","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.tws.2018.09.017","article-title":"Mechanical Performance of Vertex-Based Hierarchical Vs Square Thin-Walled Multi-Cell Structure","volume":"134","author":"Wang","year":"2019","journal-title":"Thin-Walled Struct."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1038\/361511a0","article-title":"Materials with Structural Hierarchy","volume":"361","author":"Lakes","year":"1993","journal-title":"Nature"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1016\/j.pmatsci.2007.06.001","article-title":"Nature\u2019S Hierarchical Materials","volume":"52","author":"Fratzl","year":"2007","journal-title":"Prog. Mater. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1038\/nmat1912","article-title":"Hierarchical Architectures by Synergy Between Dynamical Template Self-Assembly and Biomineralization","volume":"6","author":"Pouget","year":"2007","journal-title":"Nat. Mater."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"10772","DOI":"10.1038\/ncomms10772","article-title":"Nanotwin-governed toughening mechanism in hierarchically structured biological materials","volume":"7","author":"Shin","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1126\/science.1112255","article-title":"Skeleton Ofeuplectella Sp.: Structural Hierarchy from the Nanoscale to the Macroscale","volume":"309","author":"Aizenberg","year":"2005","journal-title":"Science"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1126\/science.3823866","article-title":"Hierarchical Structure in Polymeric Materials","volume":"235","author":"Baer","year":"1987","journal-title":"Science"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1038\/nmat906","article-title":"Nanostructured Artificial Nacre","volume":"2","author":"Tang","year":"2003","journal-title":"Nat. Mater."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1146\/annurev-matsci-070909-104424","article-title":"Mechanical Principles of Biological Nanocomposites","volume":"40","author":"Ji","year":"2010","journal-title":"Ann. Rev. Mater. Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5597","DOI":"10.1073\/pnas.0631609100","article-title":"Materials Become Insensitive to Flaws at Nanoscale: Lessons from Nature","volume":"100","author":"Gao","year":"2003","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Gao, H. (2010, January 3\u201310). Learning from nature about principles of hierarchical materials. Proceedings of the 2010 3rd International Nanoelectronics Conference (INEC), Hong Kong, China.","DOI":"10.1109\/INEC.2010.5424525"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1557\/PROC-1188-LL01-01","article-title":"Mechanical Principles of a Self-Similar Hierarchical Structure","volume":"1188","author":"Gao","year":"2009","journal-title":"MRS Proc."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.msec.2006.05.055","article-title":"Multiscale Mechanics of Hierarchical Structure\/Property Relationships in Calcified Tissues and Tissue\/Material Interfaces","volume":"27","author":"Katz","year":"2007","journal-title":"Mater. Sci. Eng. C"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.ijengsci.2018.05.005","article-title":"Approaching Perfect Energy Absorption through Structural Hierarchy","volume":"130","author":"Fan","year":"2018","journal-title":"Int. J. Eng. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"111866","DOI":"10.1016\/j.ijsolstr.2022.111866","article-title":"Mechanical Performance of Bio-Inspired Hierarchical Honeycomb Metamaterials","volume":"254\u2013255","author":"Xu","year":"2022","journal-title":"Int. J. Solids Struct."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.ijmecsci.2018.03.015","article-title":"Crushing Analysis for Novel Bio-Inspired Hierarchical Circular Structures Subjected to Axial Load","volume":"140","author":"Zhang","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.ijmecsci.2014.02.011","article-title":"Mechanics of Anisotropic Hierarchical Honeycombs","volume":"81","author":"Oftadeh","year":"2014","journal-title":"Int. J. Mech. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.compstruct.2018.03.099","article-title":"Crashworthiness Design of Novel Hierarchical Hexagonal Columns","volume":"194","author":"Xu","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.compstruct.2018.04.057","article-title":"Impact Energy Absorption of Bio-Inspired Tubular Sections with Structural Hierarchy","volume":"195","author":"Tsang","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.compstruct.2018.02.082","article-title":"Numerical and Analytical Investigation on Crushing of Fractal-Like Honeycombs with Self-Similar Hierarchy","volume":"192","author":"Zhang","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.compstruct.2012.11.004","article-title":"Stretch-Bend-Hybrid Hierarchical Composite Pyramidal Lattice Cores","volume":"98","author":"Yin","year":"2013","journal-title":"Compos. Struct."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"116304","DOI":"10.1016\/j.compstruct.2022.116304","article-title":"Study on Mechanical Properties of Lattice Structures Strengthened by Synergistic Hierarchical Arrangement","volume":"304","author":"Liu","year":"2023","journal-title":"Compos. Struct."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"106436","DOI":"10.1016\/j.tws.2019.106436","article-title":"Crushing of Vertex-Based Hierarchical Honeycombs with Triangular Substructures","volume":"146","author":"Zhang","year":"2020","journal-title":"Thin-Walled Struct."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1016\/j.ijsolstr.2012.02.029","article-title":"Hierarchical Honeycombs with Tailorable Properties","volume":"49","author":"Ajdari","year":"2012","journal-title":"Int. J. Solids Struct."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1177\/1099636218761315","article-title":"Experimental and Numerical Investigation of Lattice Core Sandwich Beams Under Low-Velocity Bending Impact","volume":"21","author":"Taghipoor","year":"2017","journal-title":"J. Sandw. Struct. Mater."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1016\/j.istruc.2022.07.030","article-title":"Experimental Investigation of Single and Hybrid-Fiber Reinforced Concrete Under Drop Weight Test","volume":"43","author":"Taghipoor","year":"2022","journal-title":"Structures"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0263-8231(02)00082-4","article-title":"Thin-Walled Structures as Impact Energy Absorbers","volume":"41","author":"Abramowicz","year":"2003","journal-title":"Thin-Walled Struct."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0734-743X(83)90004-0","article-title":"Crushing Analysis of Metal Honeycombs","volume":"1","author":"Wierzbicki","year":"1983","journal-title":"Int. J. Impact Eng."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/16\/10\/3749\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:35:32Z","timestamp":1760124932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/16\/10\/3749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,15]]},"references-count":59,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["ma16103749"],"URL":"https:\/\/doi.org\/10.3390\/ma16103749","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,15]]}}}