Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-10T16:45:31.546822Z
Paper Citation Record · LEDGER
As of 4 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 0 inbound Pith citation observations for arXiv:2604.09215.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-10T16:45:31.546822Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
58 of 58 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e65a39a6-d6bf-4516-b28c-d05bc57d6082 · outbound
Phase-Field Peridynamics Approximation of functional depending on jumps by elliptic functional via t-convergence
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation b658eee0-a7f3-440f-944c-6cd559bdfd40 · outbound
Phase-Field Peridynamics The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation bf7f4a1f-a343-4cd9-8ce2-e17d55b4fdd0 · outbound
Phase-Field Peridynamics SimulatingconcretefailureusingtheMicroplane(M7) constitutive model in correspondence-based peridynamics: Validation for classical fracture tests and extension to discrete fracture
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 0f3d5904-43dd-4017-8b96-83fc792a47e7 · outbound
Phase-Field Peridynamics A Unified, Stable and Accurate Meshfree Framework for Peridynamic Correspondence Modeling—Part II: Wave Propagation and Enforcement of Stress Boundary Conditions
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 3b46bd57-794c-4c05-ad9b-4b010be22e02 · outbound
Phase-Field Peridynamics A Unified, Stable and Accurate Meshfree Framework for Peridynamic Correspondence Modeling—Part I: Core Methods
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation d74ff28e-89e0-4839-bba5-c150936af56e · outbound
Phase-Field Peridynamics Elastic crack growth in finite elements with minimal remeshing
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 95bb9b35-fffa-440a-aab8-4260b84da05a · outbound
Phase-Field Peridynamics Computational Methods for Transient Analysis
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 6f8a69db-ad6e-4f73-8208-6a5a278f93aa · outbound
Phase-Field Peridynamics A meshfree unification: reproducing kernel peridynamics
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 3364b421-0f2e-4003-be49-faf94c08096b · outbound
Phase-Field Peridynamics On the crack-driving force of phase-field models in linearized and finite elasticity
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation de053875-8ad2-4e8a-be2e-e8ffb7b38469 · outbound
Phase-Field Peridynamics A detailed investigation of the model influencing parameters of the phase-field fracture approach
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 3c67a1b2-ce69-43a1-9347-3635cbf66d21 · outbound
Phase-Field Peridynamics Peridynamic Petrov–Galerkin method: A generalization of the peridynamic theory of correspondence materials
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 165ed6e2-c203-4879-89df-217123184692 · outbound
Phase-Field Peridynamics Cambridge University Press, Cambridge, UK (2008)
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 54765101-32eb-495f-ac98-5df116f0427a · outbound
Phase-Field Peridynamics A phase-field description of dynamic brittle fracture
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation ce9b849b-29cc-40d9-89be-c73fb68cfaac · outbound
Phase-Field Peridynamics Lewiner, O
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation b05377fc-81ab-4df1-b230-d72e44995712 · outbound
Phase-Field Peridynamics Journal of Elasticity , author =
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 0ccff21a-bd0f-4fd8-9079-2bf8bcf6ed64 · outbound
Phase-Field Peridynamics Non-ordinary state-based peridynamic analysis of stationary crack problems
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 14216435-855e-42b2-9f16-1b0afc705ce0 · outbound
Phase-Field Peridynamics Computational modelling of impact damage in brittle materials
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation d8f1b771-2470-4fa4-a04f-f40db8fb44ed · outbound
Phase-Field Peridynamics Bond-associated deformation gradients for peridynamic correspondence model
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation fe22500b-1a61-43a4-8f39-881c1487a47e · outbound
Phase-Field Peridynamics Peridynamic bond-associated correspondence model: Stability and convergence properties
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 4280c639-537b-400b-bf75-4e1b0582bc17 · outbound
Phase-Field Peridynamics Addendum to “Γ-convergence involving nonlocal gradients with varying horizon: Recovery of local and fractional models” [Nonlinear Analysis: Real World Applications, Volume 85 (2025), 104371]
Reference 20
Source-reported events for the cited work
correction dated 2025-04-25. Source: crossref record 10.1016/j.nonrwa.2025.104386->10.1016/j.nonrwa.2025.104371:correction, observed 2026-07-11T03:11:42.753538+00:00. This notice travels one citation hop only.
Observation 4cdce70f-6b82-48d2-9f4b-7e93189cedac · outbound
Phase-Field Peridynamics A variational theory for integral functionals involv- ing finite-horizon fractional gradients
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 69438231-7064-433c-bb45-ef0cf7d0cd75 · outbound
Phase-Field Peridynamics A comparative review of peridynamics and phase-field models for engineering fracture mechanics
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 127103f1-a08e-46fb-bce6-77eb37dd82a2 · outbound
Phase-Field Peridynamics Yielding of steel sheets containing slits
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 14391214-32d0-4fea-b049-b7ea5b75073b · outbound
Phase-Field Peridynamics Revisitingbrittlefractureasanenergyminimizationproblem
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 87e5f367-f42f-47ca-a6b8-f0b3ece7c394 · outbound
Phase-Field Peridynamics Pneumatic Fracture Computations with Peridynamics
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 5d68bb09-fd95-4e2c-b983-3432dded6ad6 · outbound
Phase-Field Peridynamics Dynamic fracture with continuum- kinematics-based peridynamics
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation ba248a7f-5ab7-4808-b669-dec4c6cee247 · outbound
Phase-Field Peridynamics Dynamic fracture with a continuum-kinematics-based peridy- namic and a phase-field approach
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation db6abbba-43c3-46c5-b72d-c48ac5be2a7f · outbound
Phase-Field Peridynamics Dynamic Phase-Field Fracture in Viscoelastic Materials using a First-Order Formulation
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 27454e59-d129-4a6f-a3b8-c635ee34a1b4 · outbound
Phase-Field Peridynamics The phenomena of rupture and flow in solids , volume=
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 1cb71041-5428-482a-974f-aa536e0813cf · outbound
Phase-Field Peridynamics Studies of dynamic crack propagation and crack branching with peridy- namics
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 5db06b25-a8d5-4533-9a49-08b20c15bdcd · outbound
Phase-Field Peridynamics Hillman, M
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation d83d6c03-8eeb-4075-9069-b63487c02388 · outbound
Phase-Field Peridynamics Fracture
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation ea874748-f68b-4ebd-b5a0-5af1b570647a · outbound
Phase-Field Peridynamics Modes of dynamic shear failure in solids
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 518950b3-fe91-4120-8ce3-30ced91d96e8 · outbound
Phase-Field Peridynamics On the use of peridynamics in fracture of ultra-high performance concrete
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation cfb01c4d-c77c-4cea-a982-cbbff98ccb7b · outbound
Phase-Field Peridynamics Surface corrections for peridynamic models in elasticity and fracture
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 8cc6bb42-0c27-4a4f-9873-26119b690fc9 · outbound
Phase-Field Peridynamics A review on phase field models for fracture and fatigue
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation a2ea61bb-e953-4ab7-9a2f-cd6ae8bb2761 · outbound
Phase-Field Peridynamics Cohesive Dynamics and Brittle Fracture
Reference 37
Source-reported events for the cited work
correction dated 2016-08-16. Source: crossref record 10.1007/s10659-016-9588-z->10.1007/s10659-015-9564-z:correction, observed 2026-07-11T02:56:18.152346+00:00. This notice travels one citation hop only.
Observation a755621e-0fcd-4d9f-a4b9-fc5937741609 · outbound
Phase-Field Peridynamics Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 18fa3fdb-b20f-4059-88ef-bc1a21ede758 · outbound
Phase-Field Peridynamics Energy Balance and Damage for Dynamic Fast Crack Growth from a Nonlocal Formulation
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 6e4625af-1d9a-4ea9-9b7d-edc5d0dbe777 · outbound
Phase-Field Peridynamics Simulation of Dynamic Fracture Using Peridynamics, Finite Element Modeling, and Contact
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 20afca7d-97c6-41db-aec0-8132dd0de5e4 · outbound
Phase-Field Peridynamics Madenci and E
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 06a12ce5-c7ec-4d02-930a-43fe289db562 · outbound
Phase-Field Peridynamics Miehe, M
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation c8b1e33d-13ff-4f4a-b682-1016a16f893f · outbound
Phase-Field Peridynamics International Journal for Numerical Methods in Engineering , author =
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 229f8356-c8e9-4679-8b27-3ac92f7d047e · outbound
Phase-Field Peridynamics Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 035d0dcb-9f49-4f22-9060-63114d626aa2 · outbound
Phase-Field Peridynamics A comparative accuracy and convergence study of eigen- erosion and phase-field models of fracture
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation af402273-c6fb-4e79-8207-c33970b035cf · outbound
Phase-Field Peridynamics Partmann, M
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 2f247577-b930-4ed4-af96-630cb2f7ab02 · outbound
Phase-Field Peridynamics Simulation of fracture and damage with Peridynamics.jl
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 5ed3e9a8-ff22-4c53-8791-eeb2e3742d3f · outbound
Phase-Field Peridynamics Continuum-kinematics-based peridynamics and phase- field approximation of non-local dynamic fracture
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 05439927-7bd3-4b6a-af90-604f1c7cbe50 · outbound
Phase-Field Peridynamics Local continuum consistent peridynamics with bond-associated modeling and dynamic fracture
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 333def92-10c0-477c-a252-14e2bdb525a1 · outbound
Phase-Field Peridynamics Peridynamics with a Cube-Shaped Neighborhood
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation e5730b03-a316-4a15-b229-ff81b1da3f3d · outbound
Phase-Field Peridynamics Gradient Damage Models and Their Use to Approximate Brittle Fracture
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation d1c4ed4d-f350-4d2e-b1db-9a23b996b41e · outbound
Phase-Field Peridynamics Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the- Art Review and Future Perspectives
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 7ad93083-fea1-44f0-a9ad-fcc59b832584 · outbound
Phase-Field Peridynamics Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids 48 (2000) 175–209
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 5c5c30bb-9243-4dd6-9c9b-b07abdff7736 · outbound
Phase-Field Peridynamics Peridynamic States and Constitutive Modeling
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 0ce89ba6-a19a-49c3-b60b-9fb2a11f1e66 · outbound
Phase-Field Peridynamics doi:10.1016/j.cma
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation 54ac6a4e-53f6-4b07-9ee3-1d456aca83f7 · outbound
Phase-Field Peridynamics A meshfree method based on the peridynamic model of solid mechanics
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation ff7ed113-2265-434d-baea-e204fb691a3f · outbound
Phase-Field Peridynamics Peridynamic Modeling of the Kalthoff-Winkler Experiment
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
Observation ffb4cf14-581e-4fae-88ec-e0dcecdbde68 · outbound
Phase-Field Peridynamics Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.
No inbound Pith citation observations are available.