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Both semi-analytical and asymptotic approaches are developed to analyze the elastic, axisymmetric and bifurcation stages. We show the existence of a fundamental branch where the damage field is asymmetric and localized within a finite thickness from the boundary. By minimizing a generalized Rayleigh quotient, the bifurcation time and modes are obtained as a function of the length scale <jats:inline-formula><jats:alternatives><jats:tex-math>$\\epsilon =\\ell \/R$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03f5<\/mml:mi>\n                  <mml:mo>=<\/mml:mo>\n                  <mml:mi>\u2113<\/mml:mi>\n                  <mml:mo>\/<\/mml:mo>\n                  <mml:mi>R<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> involving a material internal length and the cylinder radius. We will then focus on these size effects by assuming that <jats:inline-formula><jats:alternatives><jats:tex-math>$\\epsilon $<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03f5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is a small parameter in an asymptotic setting. After justification, specific spatial and temporal rescaled variables are introduced for the boundary layer problem. It is shown that the axisymmetric damage evolution and the bifurcation are governed by two universal functions independent of the length scale. The simulation results obtained by the semi-analytical approach are formally justified by the asymptotic methods.<\/jats:p>","DOI":"10.1007\/s10659-021-09815-x","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T11:58:29Z","timestamp":1612526309000},"page":"209-237","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Gradient Damage Analysis of a Cylinder Under Torsion: Bifurcation and Size Effects"],"prefix":"10.1007","volume":"143","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1972-2332","authenticated-orcid":false,"given":"Tianyi","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Radhi","family":"Abdelmoula","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,5]]},"reference":[{"issue":"1","key":"9815_CR1","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1016\/j.euromechsol.2007.11.010","volume":"27","author":"R. 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