{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T18:10:52Z","timestamp":1790014252991,"version":"4.0.1"},"reference-count":40,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T00:00:00Z","timestamp":1789862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["24CX03015A"],"award-info":[{"award-number":["24CX03015A"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science and Technology Major Project for New Oil and Gas Exploration and Development","award":["2025ZD1402205"],"award-info":[{"award-number":["2025ZD1402205"]}]},{"name":"National Science and Technology Major Project for New Oil and Gas Exploration and Development","award":["2025ZD140220204"],"award-info":[{"award-number":["2025ZD140220204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Compression packers are widely used in oil and gas well operations for zonal isolation, yet the large-deformation mechanical behavior of their rubber sealing elements lacks a closed-form analytical solution. This paper presents a complete theoretical analysis of the axisymmetric compression of an annular rubber cylinder based on the incompressible Mooney\u2013Rivlin hyper-elastic model. The deformation process is divided into three successive stages: free expansion, casing-constrained deformation, and fully constrained deformation. Analytical expressions for the principal stretches, stress fields, and axial force are derived for each stage by integrating the radial equilibrium equation with proper treatment of the Lagrange multiplier. The frictionless analytical results are validated against axisymmetric finite element simulations, showing excellent agreement for all stress components. The applicability of the frictionless theory to frictional conditions is then examined. Results show that although friction introduces non-uniform axial deformation and end bulging, the average contact pressure on the rubber\u2013mandrel interface agrees closely with the theoretical prediction, especially at higher axial forces (150\u2013250 kN). A linear relationship between the average contact pressure and the axial force is confirmed, providing a simple design tool. The theoretical solution offers a computationally efficient alternative to finite element analysis for preliminary packer design and parametric studies.<\/jats:p>","DOI":"10.3390\/ma19184010","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T17:23:17Z","timestamp":1790011397000},"page":"4010","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Closed-Form Analytical Solution for the Axisymmetric Compression of Packer Rubber Cylinders Based on the Mooney\u2013Rivlin Model"],"prefix":"10.3390","volume":"19","author":[{"given":"Jianyu","family":"Li","sequence":"first","affiliation":[{"name":"SINOPEC Research Institute of Petroleum Engineering Co., Ltd., Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"given":"Peng","family":"Jia","sequence":"additional","affiliation":[{"name":"College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266580, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"given":"Hang","family":"Li","sequence":"additional","affiliation":[{"name":"SINOPEC Research Institute of Petroleum Engineering Co., Ltd., Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Chenliang","family":"Ruan","sequence":"additional","affiliation":[{"name":"SINOPEC Research Institute of Petroleum Engineering Co., Ltd., Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Heming","family":"Zhu","sequence":"additional","affiliation":[{"name":"SINOPEC Research Institute of Petroleum Engineering Co., Ltd., Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Hongqian","family":"Liao","sequence":"additional","affiliation":[{"name":"SINOPEC Research Institute of Petroleum Engineering Co., Ltd., Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"given":"Xinliang","family":"Li","sequence":"additional","affiliation":[{"name":"SINOPEC Research Institute of Petroleum Engineering Co., Ltd., Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"investigation","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"025511","DOI":"10.1088\/2631-8695\/adc16c","article-title":"Sealing performance analysis and structure optimization of metal expandable packer","volume":"7","author":"Shi","year":"2025","journal-title":"Eng. 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