{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T17:50:01Z","timestamp":1762624201191,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T00:00:00Z","timestamp":1560124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11002162 and 11072262"],"award-info":[{"award-number":["11002162 and 11072262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the increase of battlefield target diversity and protection mobility, the disadvantages of traditional armor piercing warheads have gradually become prominent. The conception of the PELE (penetration with enhanced lateral efficiency) projectile was thus proposed. The axial residual velocity of the projectile is a very important indicator of a PELE projectile, which mainly reflects the penetration ability of the PELE projectile. The PELE projectile is a symmetrical structure, so the collision problem can be simplified to plane collision. Furthermore, the two-dimensional plane is axisymmetric, and so it can be further simplified to one-dimensional collision. Based on simplification and assumptions, the mechanism of a PELE projectile penetrating a thin metal target plate was studied using the shock wave theory, and a theoretical model of axial residual velocity has been established in this article. The energy loss during the penetration process was divided into the following parts: the kinetic energy increment of the target plug in the impact region, the internal energy increment of the outer casing and inner core, and the shear energy dissipation of the projectile against the target plate. In addition, the specific methods of determining the energy loss of each part are given in detail. According to the conservation of energy, the approximate calculation formulae of the axial residual velocity of a PELE projectile have been deduced. Finally, the theoretical results were compared with the experimental results under different working conditions, and the results were in good agreement. Therefore, the theoretical model has application value and guiding significance in the field of engineering.<\/jats:p>","DOI":"10.3390\/sym11060776","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T11:39:47Z","timestamp":1560166787000},"page":"776","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Theoretical Model of the Axial Residual Velocity of PELE Projectiles Penetrating Thin Metal Targets"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7642-3016","authenticated-orcid":false,"given":"Liangliang","family":"Ding","sequence":"first","affiliation":[{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9528-6536","authenticated-orcid":false,"given":"Wenhui","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1907-087X","authenticated-orcid":false,"given":"Xianwen","family":"Ran","sequence":"additional","affiliation":[{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zijian","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Aeronautics and Astronautics, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weike","family":"Chen","sequence":"additional","affiliation":[{"name":"Minghua Machinery Limited Company of Guangdong, Foshan 528231, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,10]]},"reference":[{"key":"ref_1","unstructured":"Kesberg, G., Schirm, V., and Kerk, S. 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