{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T12:28:05Z","timestamp":1789648085403,"version":"4.0.0"},"reference-count":89,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:00:00Z","timestamp":1725494400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:00:00Z","timestamp":1725494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"EPFL Lausanne"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Fract"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In fracture mechanics, polyacrylamide hydrogel has been widely used as a model material in experiments due to its optical transparency, the brittle nature of its failure, and low Rayleigh wave velocity. Indeed, linear elastic fracture mechanics has been used successfully to model the fracture of polyacrylamide hydrogels. However, in soft materials such as hydrogels, the crack opening can be extremely large, leading to substantial geometric and material nonlinearity at the crack tip. Furthermore, poroelasticity may also modify the local mechanical state within the polymer network due to solvent migration. Direct characterization of the kinematic fields and the poroelastic response at the crack tip is lacking. Here we use a hybrid digital image correlation\u2014particle tracking technique to retrieve high-resolution 3D particle trajectories near the tip of a slowly propagating crack, and measure the near-tip 3D kinematic fields in-situ. With this method, we charactherize the displacement fields, rotation fields, stretch fields, strain fields, and swelling fields. These measurements confirm the complex multi-axial stretching near the crack tip and the substantial geometric nonlinearity, particularly in the wake of the crack, where material rotation exceeds\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$30^{\\circ }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msup>\n                            <mml:mn>30<\/mml:mn>\n                            <mml:mo>\u2218<\/mml:mo>\n                          <\/mml:msup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Comparison between the measured fields and the corresponding prediction from linear elastic fracture mechanics highlights an increasing disagreement in the direct vicinity of the crack tip, particularly for displacement component\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$u_x$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>u<\/mml:mi>\n                            <mml:mi>x<\/mml:mi>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and the through-thickness strain component\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varepsilon _{zz}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>\u03b5<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mi>zz<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Significant swelling occurs due to solvent migration, with a strong correlation to the local stretch.\n                  <\/jats:p>","DOI":"10.1007\/s10704-024-00810-6","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T08:04:29Z","timestamp":1725523469000},"page":"221-235","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["3D characterization of kinematic fields and poroelastic swelling near the tip of a propagating crack in a hydrogel"],"prefix":"10.1007","volume":"248","author":[{"given":"Chenzhuo","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Danila","family":"Zubko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Damien","family":"Delespaul","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John Martin","family":"Kolinski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,9,5]]},"reference":[{"key":"810_CR1","doi-asserted-by":"crossref","DOI":"10.1201\/9781420058215","volume-title":"Fracture mechanics: fundamentals and applications","author":"TL Anderson","year":"2005","unstructured":"Anderson TL, Anderson TL (2005) Fracture mechanics: fundamentals and applications. CRC Press, Boca Raton"},{"key":"810_CR2","volume-title":"Dynamic fracture mechanics","author":"LB Freund","year":"1998","unstructured":"Freund LB, Freud L (1998) Dynamic fracture mechanics. Cambridge University Press, Cambridge"},{"issue":"2","key":"810_CR3","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1115\/1.3601206","volume":"35","author":"JR Rice","year":"1968","unstructured":"Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35(2):379. https:\/\/doi.org\/10.1115\/1.3601206","journal-title":"J Appl Mech"},{"key":"810_CR4","doi-asserted-by":"crossref","unstructured":"Williams M (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension. 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