{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T22:38:34Z","timestamp":1790030314259,"version":"4.0.1"},"reference-count":64,"publisher":"The Royal Society","issue":"2263","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"crossref","award":["W911NF-18-1-0003"],"award-info":[{"award-number":["W911NF-18-1-0003"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Science Foundation","award":["CMMI 1939901"],"award-info":[{"award-number":["CMMI 1939901"]}]}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Phil. Trans. R. Soc. A."],"published-print":{"date-parts":[[2023,12,25]]},"abstract":"<jats:p>\n                    In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting\u2013ablating bodies. This is a generalization of the theory of accretion mechanics of\u00a0Sozio &amp; Yavari (Sozio &amp; Yavari 2019\n                    <jats:italic>J. Nonlinear Sci.<\/jats:italic>\n                    <jats:bold>29<\/jats:bold>\n                    , 1813\u20131863 (doi:10.1007\/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads. In this formulation, the natural configuration of an accreting\u2013ablating body is a time-dependent Riemannian\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                        <mml:mn>3<\/mml:mn>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -manifold with a metric that is an unknown\n                    <jats:italic>a priori<\/jats:italic>\n                    and is determined after solving the accretion\u2013ablation initial-boundary-value problem. In addition to the time of attachment map, we introduce a time of detachment map that along with the time of attachment map, and the accretion and ablation velocities, describes the time-dependent reference configuration of the body. The kinematics, material manifold, material metric, constitutive equations and the balance laws are discussed in detail. As a concrete example and application of the geometric theory, we analyse a thick hollow circular cylinder made of an arbitrary incompressible isotropic material that is under a finite time-dependent extension while undergoing continuous ablation on its inner cylinder boundary and accretion on its outer cylinder boundary. The state of deformation and stress during the accretion\u2013ablation process, and the residual stretch and stress after the completion of the accretion\u2013ablation process, are computed.\n                  <\/jats:p>\n                  <jats:p>This article is part of the theme issue \u2018Foundational issues, analysis and geometry in continuum mechanics\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2022.0373","type":"journal-article","created":{"date-parts":[[2023,11,5]],"date-time":"2023-11-05T19:05:10Z","timestamp":1699211110000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["Accretion\u2013ablation mechanics"],"prefix":"10.1098","volume":"381","author":[{"given":"Satya Prakash","family":"Pradhan","sequence":"first","affiliation":[{"name":"School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7088-7984","authenticated-orcid":true,"given":"Arash","family":"Yavari","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"},{"name":"The George W.\u00a0Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"key":"e_1_3_8_2_2","volume-title":"Introduction to the theory of elasticity for engineers and physicists","author":"Southwell R","year":"1941","unstructured":"Southwell R. 1941 Introduction to the theory of elasticity for engineers and physicists. Oxford, UK: Oxford University Press."},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1963.0227"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-5193(82)90301-0"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002850050081"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(85)90056-5"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechrescom.2019.103457"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2018.0465"},{"key":"e_1_3_8_9_2","first-page":"86","article-title":"A mathematical model of a dynamically accreted deformable body. Part 1: kinematics and measure of deformation of the growing body","volume":"25","author":"Arutyunyan NK","year":"1990","unstructured":"Arutyunyan NK, Naumov V, Radaev YN. 1990 A mathematical model of a dynamically accreted deformable body. Part 1: kinematics and measure of deformation of the growing body. Mech. Solids 25, 86-99.","journal-title":"Mech. Solids"},{"key":"e_1_3_8_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-021-02044-y"},{"key":"e_1_3_8_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01463163"},{"key":"e_1_3_8_12_2","volume-title":"Viscoelastic structures: mechanics of growth and aging","author":"Drozdov AD","year":"1998","unstructured":"Drozdov AD. 1998 Viscoelastic structures: mechanics of growth and aging. New York, NY: Academic Press."},{"key":"e_1_3_8_13_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2010.0061"},{"key":"e_1_3_8_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2004.11.009"},{"key":"e_1_3_8_15_2","doi-asserted-by":"publisher","DOI":"10.3103\/S0025654411060069"},{"key":"e_1_3_8_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jappmathmech.2013.11.011"},{"key":"e_1_3_8_17_2","doi-asserted-by":"publisher","DOI":"10.3103\/S0025654413050117"},{"key":"e_1_3_8_18_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym13122331"},{"key":"e_1_3_8_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(95)00095-X"},{"key":"e_1_3_8_20_2","unstructured":"Manzhirov AV. 2014 Mechanics of growing solids: New track in mechanical engineering. In ASME 2014 Int. Mechanical Engineering Congress and Exposition Montreal Quebec Canada 14\u201320 November pp. V009T12A039. American Society of Mechanical Engineers."},{"key":"e_1_3_8_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijengsci.2004.07.010"},{"key":"e_1_3_8_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2016.08.012"},{"key":"e_1_3_8_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-019-09531-w"},{"key":"e_1_3_8_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-020-01309-5"},{"key":"e_1_3_8_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2016.05.015"},{"key":"e_1_3_8_26_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.053001"},{"key":"e_1_3_8_27_2","first-page":"1","article-title":"Finite extension of accreting nonlinear elastic solid circular cylinders","author":"Yavari A","year":"2023","unstructured":"Yavari A, Safa Y, Soleiman Fallah A. 2023 Finite extension of accreting nonlinear elastic solid circular cylinders. Continuum Mech. Thermodyn. 1-17.","journal-title":"Continuum Mech. Thermodyn."},{"key":"e_1_3_8_28_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.048001"},{"key":"e_1_3_8_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechrescom.2018.01.007"},{"key":"e_1_3_8_30_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1994)120:2(207)"},{"key":"e_1_3_8_31_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.73.373"},{"key":"e_1_3_8_32_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3313537"},{"key":"e_1_3_8_33_2","doi-asserted-by":"publisher","DOI":"10.1177\/1081286515599458"},{"key":"e_1_3_8_34_2","first-page":"103","article-title":"On finite thermal deformations","volume":"16","author":"Stojanovic R","year":"1964","unstructured":"Stojanovic R, Djuric S, Vujosevic L. 1964 On finite thermal deformations. Archiwum Mechaniki Stosowanej 16, 103-108.","journal-title":"Archiwum Mechaniki Stosowanej"},{"key":"e_1_3_8_35_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-018-0973-2"},{"key":"e_1_3_8_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-016-9294-9"},{"key":"e_1_3_8_37_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-012-0500-0"},{"key":"e_1_3_8_38_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2012.0342"},{"key":"e_1_3_8_39_2","doi-asserted-by":"publisher","DOI":"10.1177\/1081286511436137"},{"key":"e_1_3_8_40_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2014.0403"},{"key":"e_1_3_8_41_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/91\/18001"},{"key":"e_1_3_8_42_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-010-9266-5"},{"key":"e_1_3_8_43_2","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/hxh049"},{"key":"e_1_3_8_44_2","doi-asserted-by":"publisher","DOI":"10.1177\/1081286504046481"},{"key":"e_1_3_8_45_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-007-9102-8"},{"key":"e_1_3_8_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2005.04.008"},{"key":"e_1_3_8_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0749-6419(99)00081-9"},{"key":"e_1_3_8_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87710-5"},{"key":"e_1_3_8_49_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-010-9073-y"},{"key":"e_1_3_8_50_2","doi-asserted-by":"publisher","DOI":"10.1177\/1081286515612280"},{"key":"e_1_3_8_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2022.105101"},{"key":"e_1_3_8_52_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2020.0462"},{"key":"e_1_3_8_53_2","first-page":"29","article-title":"A proposal of a new theory concerning the yielding of materials based on Riemannian geometry","volume":"2","author":"Kondo K","year":"1949","unstructured":"Kondo K. 1949 A proposal of a new theory concerning the yielding of materials based on Riemannian geometry. J. Jpn Soc. Aeronaut. Eng. 2, 29-31. (doi:10.2322\/jjsass1948.2.29)","journal-title":"J. Jpn Soc. Aeronaut. Eng."},{"key":"e_1_3_8_54_2","doi-asserted-by":"publisher","DOI":"10.2322\/jjsass1948.3.107"},{"key":"e_1_3_8_55_2","doi-asserted-by":"publisher","DOI":"10.1177\/1081286519884719"},{"key":"e_1_3_8_56_2","volume-title":"Science and hypothesis","author":"Poincar\u00e9 H","year":"1905","unstructured":"Poincar\u00e9 H. 1905 Science and hypothesis. New York, NY: The Walter Scott Publishing Company."},{"key":"e_1_3_8_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2008.12.004"},{"key":"e_1_3_8_58_2","doi-asserted-by":"publisher","DOI":"10.1177\/10812865211054573"},{"key":"e_1_3_8_59_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijengsci.2010.09.015"},{"key":"e_1_3_8_60_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-022-09957-6"},{"key":"e_1_3_8_61_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01601214"},{"key":"e_1_3_8_62_2","volume-title":"Mathematical foundations of elasticity","author":"Marsden J","year":"1983","unstructured":"Marsden J, Hughes T. 1983 Mathematical foundations of elasticity. New York, NY: Dover."},{"key":"e_1_3_8_63_2","volume-title":"Non-linear elastic deformations","author":"Ogden RW","year":"1984","unstructured":"Ogden RW. 1984 Non-linear elastic deformations. Mineola, NY: Dover."},{"key":"e_1_3_8_64_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2156(08)70371-5"},{"key":"e_1_3_8_65_2","doi-asserted-by":"crossref","unstructured":"Simo J Marsden J. 1984 Stress tensors Riemannian metrics and the alternative descriptions in elasticity. In Trends and applications of pure mathematics to mechanics \u00a0(eds GC Ciarlet M Roseau) pp. 369\u2013383. Berlin Germany: Springer.","DOI":"10.1007\/3-540-12916-2_67"}],"container-title":["Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsta.2022.0373","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsta.2022.0373","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsta.2022.0373","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T21:26:02Z","timestamp":1778621162000},"score":1,"resource":{"primary":{"URL":"http:\/\/royalsocietypublishing.org\/rsta\/article\/112529"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,6]]},"references-count":64,"journal-issue":{"issue":"2263","published-print":{"date-parts":[[2023,12,25]]}},"alternative-id":["10.1098\/rsta.2022.0373"],"URL":"https:\/\/doi.org\/10.1098\/rsta.2022.0373","relation":{},"ISSN":["1364-503X","1471-2962"],"issn-type":[{"value":"1364-503X","type":"print"},{"value":"1471-2962","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,6]]},"assertion":[{"value":"2023-06-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-08-09","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-11-06","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"20220373"}}