Paper Citation Record · LEDGER

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations

As of 8 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2506.14788.

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

pith.paper-citation-record.v1
2506.14788 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:40:20.064362Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

41 of 41 outbound references displayed

verified exact0
verified fuzzy31
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8e4b9068-188d-4580-870a-e5a945fd855c · outbound

This paper cites Akagi, M.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Akagi, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:27.445581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a0a784e5-aac4-45a8-ae97-71d0ea61b9a2 · outbound

This paper cites Alessi, S.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Alessi, S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:27.096888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7cc9d43c-2d61-4ac2-a76b-4ecae956e058 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:26.953307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9d61b3b0-2908-4b1e-894a-780c57845758 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:26.754172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 49921b69-3f18-467b-ad8e-713cfd8297c7 · outbound

This paper cites Ambrosio, M.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Ambrosio, M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:26.457255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 557f4f70-8d4f-4697-966f-7f903f497d8e · outbound

This paper cites Amor, J.-J.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Amor, J.-J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:26.176074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0d284413-64f9-41ae-a210-8da3270fea8e · outbound

This paper cites Arriaga, H.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Arriaga, H

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:25.897453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dbd03368-cb34-4928-bbe9-ebd8ae063574 · outbound

This paper cites Borden, C.V.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Borden, C.V

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:25.725985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f5300b29-fd93-4790-a827-673c0fddc849 · outbound

This paper cites Bourdin, G.A.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Bourdin, G.A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:25.525678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 330170cf-d34f-4cdb-9b7c-0b2defed25cf · outbound

This paper cites Caginalp: Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Caginalp: Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:25.367031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 943051db-ce0c-403e-9402-a8893fbc112c · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:25.183245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f0dce7a5-f265-4744-a858-b016eecc1f93 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:25.003587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 89fb7fec-b926-439b-bdc9-1d0e4abbfa28 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:24.847722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 27834111-09d2-43d7-bb30-c23e37b38ef8 · outbound

This paper cites Francfort, J.-J.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Francfort, J.-J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:24.737660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a1ea0569-e425-4d35-84fd-b2fbe5aa1de6 · outbound

This paper cites Freddi, G.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Freddi, G

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:24.570961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f9743333-2874-4a00-8144-7b2a2f1c626c · outbound

This paper cites Guo and S-Q.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Guo and S-Q

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:24.409779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bbf37a56-b414-474d-957a-b84d5bf9fcfb · outbound

This paper cites Hecht: New development in FreeFem++.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Hecht: New development in FreeFem++

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:24.252090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 482ecd5d-52ef-466c-bb1e-4e5f14d6a08e · outbound

This paper cites Henry, H.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Henry, H

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:24.098964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b6f4921b-37b9-4666-bdb5-c4ba75514fd2 · outbound

This paper cites Karma, D.A.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Karma, D.A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:23.863199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31706405-66ce-461f-8aee-0680467ccfae · outbound

This paper cites Kimura and M.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Kimura and M

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:23.636609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c60ca2a5-b965-4636-92a0-513912a9dc97 · outbound

This paper cites Kimura, T.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Kimura, T

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:23.550155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation de490f95-3f15-4a0d-80ca-0057eb81584b · outbound

This paper cites Kimura, T.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Kimura, T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:23.404527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 857afddc-382c-4b74-b06d-b755ee12d681 · outbound

This paper cites Kobayashi: Modeling and numerical simulations of dendritic crystal growth, Physica D 63(1993), 410–423.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Kobayashi: Modeling and numerical simulations of dendritic crystal growth, Physica D 63(1993), 410–423

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:23.254584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 93c722b1-6d98-4cfd-8fc8-18403580b0fd · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:23.130967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8a6e8046-fe54-49a6-9639-484f982d9bc8 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:23.017513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 352dbf64-d39e-4050-ab22-891d442a4526 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:22.892045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b4a6bd3b-0a76-4b9d-950c-10bb941e3514 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:22.760450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d080ee6a-06b3-48f0-b8cc-8769d98d39cf · outbound

This paper cites Mandal, V.P.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Mandal, V.P

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.620600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7ede1cd3-f5d5-4730-8c30-7c4cd53ef873 · outbound

This paper cites Miehe, M.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Miehe, M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.469405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a89ebd9a-fc9d-4e94-b232-179e84f55767 · outbound

This paper cites Miehe, S.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Miehe, S

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.319932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6b804d7b-96ec-49be-b9b9-cf7b05a5d5e5 · outbound

This paper cites Nguyen, J.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Nguyen, J

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.167197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c9ed6e29-6255-4cd8-8991-1e2f79d619b0 · outbound

This paper cites Nguyen, J.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Nguyen, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.015829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a4f901cc-4221-44d0-8622-250dd5333852 · outbound

This paper cites Nguyen, J.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Nguyen, J

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.880422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c1c0dfe6-fe8d-4951-b286-4d785d86199c · outbound

This paper cites Ounissi, M.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Ounissi, M

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.706344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e3423cf7-6e3b-4a2b-9d2d-fd9a28d3fa74 · outbound

This paper cites Rudshaug, T.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Rudshaug, T

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.536781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 75399b6c-4c86-446b-b623-7aedecf78ba6 · outbound

This paper cites Schl¨ uter, A.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Schl¨ uter, A

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.359507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 56b6a403-a1da-4fef-b9e9-3ae611c28085 · outbound

This paper cites an unresolved cited work.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:21.191209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dd4cff91-631a-4d48-a390-361ed15d59de · outbound

This paper cites Takaishi, M.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Takaishi, M

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.941118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 45d06afe-ba18-4eb9-8f7f-b71c26dcf958 · outbound

This paper cites Teichtmeister, D.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Teichtmeister, D

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.700613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a3770773-da48-4a56-9515-eb8bae75c277 · outbound

This paper cites Xing, T.T.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Xing, T.T

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.454581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 29e69291-d831-476e-9a2b-743c6a8953f8 · outbound

This paper cites Zhang, T.Q.

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations Zhang, T.Q

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.289501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.