{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T22:06:26Z","timestamp":1778796386920,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T00:00:00Z","timestamp":1627171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"open foundations of national and local union engineering laboratory for building health monitor-ing and disaster prevention","award":["GG19KF001"],"award-info":[{"award-number":["GG19KF001"]}]},{"name":"open foundations of Anhui province key laboratory of building structure and underground engineering","award":["JD20KF003"],"award-info":[{"award-number":["JD20KF003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Explosively formed projectiles (EFPs) are widely used in civil applications and the military field for their excellent impact performance. How to give full play to the energy accumulation effect of explosives and improve the penetration performance has become the main problem of EFP design. The aim of the present study was to investigate the effect of liner structure on EFP formation and its penetration behavior. In order to achieve this, a finite element (FE) model was first established on the basis of the Lagrange and ALE method. Then, formation and penetration performance tests of EFP were performed to verify the validity and feasibility of the proposed FE model, where the configuration, velocity of EFP, and penetration diameter left on the target plate were compared. Finally, by using the proposed FE model, the entire process of the formation and penetration behavior of EFP with axial symmetrical variable thickness liners were analyzed, where spherical-segment liners with uniform and non-uniform thickness were developed. The results were drawn as follows: the numerical simulation error of EFP velocity was less than 5%, and the simulated penetration diameter was compared to the 8.6% error obtained from the experimental method. It demonstrated that the proposed FE model had higher prediction precision. After the explosive was detonated, a forward-folding EFP was formed by the liner with a thin edge thickness, while the EFP formed by the liner with uniform thickness had a backward-folded configuration. It was also found that the liner with a thin edge thickness gave the largest steady velocity of EFP, and it was the lowest by using the liner with uniform thickness. There were two types of loads generated after the formation of an EFP, those were shock wave loading and an EFP, both causing damage in the target plate during the process of an EFP\u2019s penetration into it. The shock wave induced by liners with non-uniform thickness caused higher damage in the target plate, the maximum value of stress was reached at about 4.0 GPa. The forward-folding EFP formed by the liner with the thinnest edge thickness had the largest penetration ability. The backward-folded EFP, owing to the hollow structure, had the worst penetration ability, which failed to penetrate the target plate.<\/jats:p>","DOI":"10.3390\/sym13081342","type":"journal-article","created":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T22:07:00Z","timestamp":1627250820000},"page":"1342","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Numerical Investigation on the Formation and Penetration Behavior of Explosively Formed Projectile (EFP) with Variable Thickness Liner"],"prefix":"10.3390","volume":"13","author":[{"given":"Dong","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Anhui University, Hefei 230601, China"},{"name":"Anhui Province Key Laboratory of Aviation Equipment Testing, Monitoring and Reverse Engineering, Wuhu State-Owned Machinery Factory, Wuhu 241007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiajian","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.ijimpeng.2016.02.014","article-title":"Modelling the formation of explosively formed projectiles (EFP)","volume":"93","author":"Cardoso","year":"2016","journal-title":"Int. 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