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The study demonstrates that, under small far-field strains, the crack tip field can be generally divided into three regions: Region I\u2014the asymptotic neo-Hookean crack tip field as\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$r\\rightarrow 0$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ; Region II\u2014a finite-radius nonlinear neo-Hookean zone; and Region III\u2014an outer linear elastic region. Within Region III, a subregion may still obey the asymptotic linear elastic solution when the radial distance is sufficiently small. As the far-field strain increases, both the asymptotic linear subregion and the broader linear region shrink and eventually vanish, leaving only the nonlinear zones. This multiscale structure reflects the principle of small-scale nonlinearity, wherein nonlinear effects are confined to an inner core. The inner core consists of Region I, where asymptotic neo-Hookean fields dominate, and Region II, where general nonlinear effects prevail. Initially, this inner core is nested inside Region III. At sufficiently small far-field strains, Region III itself contains an inner core that follows asymptotic linear elastic crack tip fields. As loading intensifies, Regions I and II expand, and Region III\u2014first its asymptotic core, then the broader linear zone \u2013 .- progressively diminishes, culminating in a large-scale nonlinearity regime. We also identify and quantify the characteristic length scales over which each region exists and dominates\u2014nonlinear fields in Regions I and II and linear elastic behavior in Region III. An important point is that at the crack tip, Region I always governs the local field, although its extent may be small under small far-field strains, making it difficult to capture in computational simulations. To address this, we introduce a rescaling method to better resolve this near-tip behavior.\n                  <\/jats:p>","DOI":"10.1007\/s10704-025-00880-0","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T11:17:06Z","timestamp":1755083826000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On small scale nonlinearity and nested crack tip fields in a neo-Hookean material"],"prefix":"10.1007","volume":"249","author":[{"given":"Yuan","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brian","family":"Moran","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,13]]},"reference":[{"key":"880_CR1","unstructured":"Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K., 2014. 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