Paper Citation Record · LEDGER

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application

As of 14 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2507.22072.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.22072 v1

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

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measured 60 of 60 standing notices

One-hop event checks from named stored sources.

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

59 of 59 outbound references displayed

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verified fuzzy11
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External citation measurements

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Outbound references

Observation 4ddb97e9-570e-42df-a72e-ebde6513684f · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 1

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Observation d39b2fba-b15b-4826-88d8-014506c711d6 · outbound

This paper cites Marigo, Initiation of Cracks in Griffith’s Theory: An Argument of Continuity in Favor of Global Minimization, Journal of Nonlinear Science 20 (2010) 831–868.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Marigo, Initiation of Cracks in Griffith’s Theory: An Argument of Continuity in Favor of Global Minimization, Journal of Nonlinear Science 20 (2010) 831–868

Reference 2

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Observation bab11d77-9952-49b3-9953-34685bb59916 · outbound

This paper cites Tanné, T.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Tanné, T

Reference 3

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Observation bfbe4f3e-7d7d-46d0-a223-30fc0ba2087e · outbound

This paper cites Kumar, B.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Kumar, B

Reference 4

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Observation 19cf8b6c-13e0-4406-b0e8-ab151aaf1860 · outbound

This paper cites Marigo, Modelling of fracture by cohesive force models: A path to pursue, European Journal of Mechanics, A/Solids 102 (2023).

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Marigo, Modelling of fracture by cohesive force models: A path to pursue, European Journal of Mechanics, A/Solids 102 (2023)

Reference 5

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Observation 0fa96deb-e1ee-4533-bb1a-516089b18317 · outbound

This paper cites Dugdale, Yielding of steel sheets containing slits, Journal of Mechanics Physics of Solids 8 (1960) 100–104.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Dugdale, Yielding of steel sheets containing slits, Journal of Mechanics Physics of Solids 8 (1960) 100–104

Reference 6

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Observation c8d69317-2426-4fd1-b78e-9afcaa559f53 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:38:59.653053Z

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Observation 71551e70-7554-4bf5-9628-234df36bc136 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 8

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Observation 4a12ece3-3aa4-4d1d-9295-ab5c0ec78f1e · outbound

This paper cites Focardi, On the variational approximation of free-discontinuity problems in the vec- torial case, Mathematical Models and Methods in Applied Sciences 11 (2001) 663–.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Focardi, On the variational approximation of free-discontinuity problems in the vec- torial case, Mathematical Models and Methods in Applied Sciences 11 (2001) 663–

Reference 9

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Observation 8d4b54b5-3c61-40c2-a951-39fcc5f661da · outbound

This paper cites Bourdin, G.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Bourdin, G

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-06T16:38:54.892944Z

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Observation d28dd733-7e4c-480d-b2d3-75b258a8f90c · outbound

This paper cites Bourdin, G.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Bourdin, G

Reference 11

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Observation c04f4151-92c1-4ab3-94a6-0f6dd2f4f562 · outbound

This paper cites Ambrosio, V.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Ambrosio, V

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:38:58.873176Z

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Observation db3c1300-7f6d-412e-b2f5-b0bb26edf34b · outbound

This paper cites Braides, Approximation of Free-Discontinuity Problems, volume 1694 ofLecture Notes in Math- ematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 1998.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Braides, Approximation of Free-Discontinuity Problems, volume 1694 ofLecture Notes in Math- ematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 1998

Reference 13

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Observation 37817e5f-ded4-448f-8280-b8cccb516ee0 · outbound

This paper cites Bourdin, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Bourdin, J.-J

Reference 14

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Observation ee4cdbcf-342d-4fc0-a7d1-79edc5ffd6ce · outbound

This paper cites Mesgarnejad, B.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Mesgarnejad, B

Reference 15

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Observation 9657e63f-fb62-4607-ad91-113a299bb0fb · outbound

This paper cites Lemaitre, J.-L.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Lemaitre, J.-L

Reference 16

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Observation 6160fcfb-248c-4b8b-b189-e296d941a22a · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 17

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Observation 4c862635-5a7b-4116-a7c3-96fba13c3019 · outbound

This paper cites Pham, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Pham, J.-J

Reference 18

Resolution: verified exact; doi, observed 2026-08-06T16:38:50.789473Z

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Observation 4279502a-2f99-4762-baac-aa4efe89d673 · outbound

This paper cites Pham, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Pham, J.-J

Reference 19

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Observation acb045da-204e-4104-9a95-fc133cb88cea · outbound

This paper cites Miehe, F.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Miehe, F

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T16:38:43.944640Z

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Observation 71f56733-6979-4d3d-8b1c-2517c9e25af3 · outbound

This paper cites Marigo, C.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Marigo, C

Reference 21

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Observation 0c970b34-8199-400b-8008-48fd85877231 · outbound

This paper cites Classical variational phase-field models cannot predict fracture nucleation.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Classical variational phase-field models cannot predict fracture nucleation

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:38:54.544406Z

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Observation 32d8d5e0-007b-4008-b341-6d036bae115d · outbound

This paper cites Lorentz, S.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Lorentz, S

Reference 23

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Observation 5d3ae9b2-da7a-40c9-8be2-fd143a6616b0 · outbound

This paper cites Lorentz, V.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Lorentz, V

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T16:38:50.532591Z

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Observation b07cb618-b594-461d-8272-9caa1bf9e41f · outbound

This paper cites Phase field approximation of cohesive fracture models.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Phase field approximation of cohesive fracture models

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:38:54.307673Z

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Observation e0e53e18-57e7-4bf3-9e7b-452792b5a9fe · outbound

This paper cites Freddi, F.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Freddi, F

Reference 26

Resolution: verified exact; doi, observed 2026-08-06T16:38:50.327906Z

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Observation c4c68646-467f-4e02-90b7-91280fae53e0 · outbound

This paper cites Wu, A unified phase-field theory for the mechanics of damage and quasi- brittle failure, Journal of the Mechanics and Physics of Solids 103 (2017) 72–.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Wu, A unified phase-field theory for the mechanics of damage and quasi- brittle failure, Journal of the Mechanics and Physics of Solids 103 (2017) 72–

Reference 27

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Observation 2061a64f-594d-4917-8d65-20d348bbd656 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-08-06T16:38:49.835597Z

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Observation 41544218-943f-457d-931e-00dfca153285 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 29

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Observation 74cae050-9197-4806-81ff-2c8fd3f231fb · outbound

This paper cites URL:https://linkinghub.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application URL:https://linkinghub

Reference 30

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Observation 8c2a93a9-3c53-4028-a38e-a85de80671df · outbound

This paper cites Lammen, S.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Lammen, S

Reference 31

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Observation 417f1931-a9e5-40c6-a20d-69abe8c20e90 · outbound

This paper cites Alessi, F.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, F

Reference 32

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Observation 9ed08911-a213-4631-b0c8-4cf607ccb7da · outbound

This paper cites Alessi, F.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, F

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:38:56.977953Z

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Observation 47592267-4ca9-48a7-a6be-a8dab47832f8 · outbound

This paper cites Alessi, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, J.-J

Reference 34

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Observation 4b2f2425-ef14-434c-bc66-4c68a0da748c · outbound

This paper cites Alessi, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, J.-J

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T16:38:45.826194Z

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This paper cites Alessi, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, J.-J

Reference 36

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Observation 39e5537d-4d2d-4be6-ba10-41927a668c9b · outbound

This paper cites Conti, M.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Conti, M

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T16:38:46.082941Z

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Observation 566f77c0-b4bb-42fe-85ff-6baa21049bf8 · outbound

This paper cites Colasanto, Phase field approximation of cohesive functionals in the vectorial case, In preparation (2025).

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Colasanto, Phase field approximation of cohesive functionals in the vectorial case, In preparation (2025)

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:38:56.796608Z

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Observation 840db86f-83c6-4a77-8a9b-426b1ac90870 · outbound

This paper cites Superlinear free-discontinuity models: relaxation and phase-field approximation.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Superlinear free-discontinuity models: relaxation and phase-field approximation

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T16:38:46.328476Z

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Observation 5859dbbe-540b-4216-95bd-c46412f180c4 · outbound

This paper cites Pham, J.-J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Pham, J.-J

Reference 40

Resolution: verified exact; doi, observed 2026-08-06T16:38:49.564315Z

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Observation 4ca745f3-2f52-4dfc-b8a8-db445154c8e3 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 41

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Observation 53019e80-3a13-48ac-811c-83d4b7506bfa · outbound

This paper cites Mielke, A Mathematical Framework for Generalized Standard Materials in the Rate-Independent Case, in: R.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Mielke, A Mathematical Framework for Generalized Standard Materials in the Rate-Independent Case, in: R

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T16:38:46.713535Z

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Observation a3f0236b-6d50-4d3a-96c3-b93263f33855 · outbound

This paper cites Mielke, T.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Mielke, T

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:38:56.608882Z

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Observation cd0ac331-b23d-4bbd-8d29-bc6b50d4a360 · outbound

This paper cites Wu, A generalized phase-field cohesive zone model (µPF-CZM) for fracture, Journal of the Me- chanics and Physics of Solids 192 (2024).

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Wu, A generalized phase-field cohesive zone model (µPF-CZM) for fracture, Journal of the Me- chanics and Physics of Solids 192 (2024)

Reference 44

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:38:53.014646Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7d2fc53e-a9a5-453b-bc3c-5aa905f40b82 · outbound

This paper cites Crismale, G.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Crismale, G

Reference 45

Resolution: verified exact; doi, observed 2026-08-06T16:38:49.332381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6bf358ff-025d-40a3-9b9b-59cee26c04ca · outbound

This paper cites Bonacini, S.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Bonacini, S

Reference 46

Resolution: verified exact; doi, observed 2026-08-06T16:38:49.070128Z

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Observation 5e80fb9b-8deb-4622-b113-9e648faf569c · outbound

This paper cites 1007/BF02472827.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application 1007/BF02472827

Reference 47

Resolution: verified exact; doi, observed 2026-08-06T16:38:48.847661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9430bcc0-a5d6-461e-be82-1c904a140fae · outbound

This paper cites Roesler, G.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Roesler, G

Reference 48

Resolution: verified exact; doi, observed 2026-08-06T16:38:48.619408Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 291f8409-697e-4a31-9bbd-9150f29ad55e · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 49

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Observation 6f44e968-32ac-4749-a8b6-d7aa75d75534 · outbound

This paper cites Dourado, M.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Dourado, M

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:38:56.384089Z

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Observation b7a7a82f-fa4d-467b-a787-9a8035b58cc2 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 51

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Observation a6fa905b-bb85-4da2-803f-1630ac692d49 · outbound

This paper cites Kumar, R.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Kumar, R

Reference 52

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:38:52.646326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 66490079-5b77-4e14-a4ca-079b3fd3d285 · outbound

This paper cites Alessi, V.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, V

Reference 53

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T16:38:55.845304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 654c37fc-d942-41f7-972f-cd7254e627a0 · outbound

This paper cites doi:10.1016/ j.mechmat.2012.02.004.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application doi:10.1016/ j.mechmat.2012.02.004

Reference 54

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T16:38:56.144599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2d279275-c1b0-4ff3-8e27-67b89508391e · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 55

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:38:52.042153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2bc531a0-d30b-486d-ae35-02b2fcd3110a · outbound

This paper cites Alessi, J.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, J

Reference 58

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:38:52.346935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a581c277-d820-406c-9260-ef39f4293b8b · outbound

This paper cites doi:10.1016/j.jmps.2017.03.015.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application doi:10.1016/j.jmps.2017.03.015

Reference 99

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T16:38:50.072801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 132a7263-b508-4db8-ba74-eb371ab0bf19 · outbound

This paper cites an unresolved cited work.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Unresolved cited work

Reference 437

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T16:38:58.330184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 866a22a9-eef8-4b41-b4f2-b2c8949f117b · outbound

This paper cites com/doi/10.1142/S0218202501001045.

Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application com/doi/10.1142/S0218202501001045

Reference 684

Resolution: verified exact; doi, observed 2026-08-06T16:38:51.375913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 1572cd5e-dabf-4f59-81f2-03b4c1f872a5 · inbound

Strength-degradation phase-field regularization of cohesive fracture: the antiplane case cites this paper.

Strength-degradation phase-field regularization of cohesive fracture: the antiplane case Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T12:38:24.613851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.