Pith. sign in

Paper Citation Record · LEDGER

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates

As of 13 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 1 inbound Pith citation observation for arXiv:2601.09160.

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

pith.paper-citation-record.v1
2601.09160 v1

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T06:37:38.650623Z

measured 58 of 58 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T06:07:28.458940Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

57 of 57 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved57
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1846d937-9d4c-4d07-8c68-9686ed2f4c45 · outbound

This paper cites Thin film materials: stress, defect formation and surface evolution.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Thin film materials: stress, defect formation and surface evolution

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.461024Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.461024Z digest=sha256:845706d5f0b7a3c702209497eccdc3202041ed63c2c8811fb529ef00953c46c9

Observation 111625d0-061a-4c08-8c63-93e4681bfcdb · outbound

This paper cites The tension of metallic films deposited by electrolysis.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates The tension of metallic films deposited by electrolysis

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.464757Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.464757Z digest=sha256:16715342f0116e159a985222ceb14cf2d9a16e080e9def429235f0933981c8d1

Observation fd2b062a-f31b-489b-b793-12732738952b · outbound

This paper cites Extensions of the stoney formula for substrate curvature to configu- rations with thin substrates or large deformations.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Extensions of the stoney formula for substrate curvature to configu- rations with thin substrates or large deformations

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.467855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.467855Z digest=sha256:d76d3d06ec0f94e18c0c5a0d0f0fccd1c35373a39ea50e499621b0e7d0825777

Observation d93c7c13-d513-4dc5-a3e6-517bdb85b245 · outbound

This paper cites Celebrating the 100th anniversary of the stoney equation for film stress: Developments from polycrystalline steel strips to single crystal silicon wafers.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Celebrating the 100th anniversary of the stoney equation for film stress: Developments from polycrystalline steel strips to single crystal silicon wafers

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.470511Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.470511Z digest=sha256:8326812cfd20bf261efabe9c487516d344af42c02e26e73fee0f98e9aeb589f5

Observation 0e5c0f39-ea73-4c01-a771-050fb9cc2229 · outbound

This paper cites On the stoney formula for a thin film/substrate system with nonuniform substrate thickness.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates On the stoney formula for a thin film/substrate system with nonuniform substrate thickness

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.474209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.474209Z digest=sha256:0b1d58336e115c250542a36238452a78ad7d9dd9487dd08a8f9b9a651fefe029

Observation 0c827aac-0918-41cd-ba53-19611af0110a · outbound

This paper cites Enhancing accuracy to stoney equation.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Enhancing accuracy to stoney equation

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.477309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.477309Z digest=sha256:6720cbec7ed68ec3192adcce68d4a79f3da7f99660d3dfed1aa88e741804eb4c

Observation 600fd0a2-c0c4-46e1-bfc5-e54276783184 · outbound

This paper cites Modified stoney’s equation for evaluation of residual stresses on thin film.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Modified stoney’s equation for evaluation of residual stresses on thin film

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.480762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.480762Z digest=sha256:a1b9c44e6ccc56dc11b575ef4f6894dfb2dadbe4100770e7b3e26e312c3ec79b

Observation 7345f9e0-8ddb-4bd6-86e3-db7990394172 · outbound

This paper cites Extending stoney’s equation to thin, elastically anisotropic substrates and bilayer films.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Extending stoney’s equation to thin, elastically anisotropic substrates and bilayer films

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.483843Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.483843Z digest=sha256:3ff4029bdfe6583597f892e0206af3b5ef89dbca0b4d8f5d6eb5ad9c5eeb8c54

Observation 4be6bcfb-8f11-4c86-9978-1788f3aec88f · outbound

This paper cites Extension of the stoney formula for the incremental stress of thin films.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Extension of the stoney formula for the incremental stress of thin films

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.486872Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.486872Z digest=sha256:6d87d3e507d3511379affe25c591495ee63dedf79c97a55a204e5ba61a15a790

Observation 383561f2-f9ff-47a4-b30e-60ff87316643 · outbound

This paper cites Large deformation and geometric instability of substrates with thin-film deposits.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Large deformation and geometric instability of substrates with thin-film deposits

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.489832Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.489832Z digest=sha256:292920ed584dbe0163d6ca6746c318b17d7cb0399048526f0a63ec6e494cfe6c

Observation 9fbcd9fe-acd5-47f3-a044-581275b10bdb · outbound

This paper cites Modified stoney formula for determining stress within thin films on large-deformation isotropic circular plates.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Modified stoney formula for determining stress within thin films on large-deformation isotropic circular plates

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.492625Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.492625Z digest=sha256:d1d16af5edafbab187eb1368b42dcbaef1ed1180cc3cdee1372f46892306b12e

Observation 546b2523-60cd-49af-8e6c-c3e4346b4676 · outbound

This paper cites Geometrically nonlinear stress-deflection relations for thin film/substrate systems.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Geometrically nonlinear stress-deflection relations for thin film/substrate systems

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.496014Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.496014Z digest=sha256:17b4a4df235a4bd42d1e587d5f027085b6278505c06255b34a31433b31801e52

Observation 7419529f-38db-4c3e-9a2a-8bcc95bdd0f9 · outbound

This paper cites Stress-warping relation in thin film coated wafers.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Stress-warping relation in thin film coated wafers

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.499101Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.499101Z digest=sha256:cd931c6a114b1b1dc0b910ea1b6c7c87ed5f6314fa3e62370bd93fc34dc8a963

Observation 52096b66-2d1e-4ab3-9979-ccd535b0e8cd · outbound

This paper cites Modified stoney’s equation with anisotropic substrates undergoing large deformations.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Modified stoney’s equation with anisotropic substrates undergoing large deformations

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.502128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.502128Z digest=sha256:d3b35db0e503b7c63f687c65c432f2557e271300ea645b9781117a66a1929e22

Observation 215bd06f-f4b3-4e55-b4f5-a405053c04d7 · outbound

This paper cites Methods for determining piezoelectric properties of thin epitaxial films: Theoretical foundations.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Methods for determining piezoelectric properties of thin epitaxial films: Theoretical foundations

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.505279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.505279Z digest=sha256:6a2bf60a69a29b4582afdb3ae8e600bf5a3afe75dd5ade7c39f93b1fd1bd435a

Observation af06a112-54b1-4e25-9f6e-385e1c53dd68 · outbound

This paper cites Stoney formula for piezo- electric film/elastic substrate system.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Stoney formula for piezo- electric film/elastic substrate system

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.508643Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.508643Z digest=sha256:d6f600802fa960149dd1b6a903b959135e8a156668f5691fdd281927b386d5ea

Observation bc13f4e8-7fce-40a9-a88e-1dc073fbc60e · outbound

This paper cites Fundamentals of flexoelectricity in solids.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Fundamentals of flexoelectricity in solids

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.511708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.511708Z digest=sha256:7864d1e0f99bf9cc052c6e7f301f59dd904481812e1affef46bd749a3893f940

Observation 672a71ae-2b0e-4d2b-b183-7d61540f6aa1 · outbound

This paper cites Comprehensive review on flexoelectric energy harvesting technology: Mechanisms, device configurations, and potential applications.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Comprehensive review on flexoelectric energy harvesting technology: Mechanisms, device configurations, and potential applications

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.515046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.515046Z digest=sha256:f6f8bf09d4c58d9fcf9b7f9b52e6e7e28c7d337b3772a8de0bda1140f0de974e

Observation b9f35d2d-2e47-4a39-98fb-de1dd3af80c5 · outbound

This paper cites Nanoscale flexoelectricity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Nanoscale flexoelectricity

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.521242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.521242Z digest=sha256:3d1c1cdd01fa11763e20a09acd506057a1366b62007debec6bf2d2bdb2d73df6

Observation e3323dd8-9844-4249-9666-8cfbc720827c · outbound

This paper cites Electroactive polymers for sensing.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Electroactive polymers for sensing

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.524461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.524461Z digest=sha256:4c184c79b7d2e31cf279bf6b5a781ee38d22bb25234a44e58c1bbda9118ee1b3

Observation 68bc97e2-afdf-4c17-8754-97c919e1a7b9 · outbound

This paper cites On the possibility of piezoelectric nanocompos- ites without using piezoelectric materials.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates On the possibility of piezoelectric nanocompos- ites without using piezoelectric materials

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.527529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.527529Z digest=sha256:cd59658debb94d70385d0f6935f08231bd7707c594955a4874bc21ec9751e035

Observation 65fd93cc-d32a-4710-a86e-e95ba030e8ef · outbound

This paper cites Computational evaluation of the flexoelectric effect in dielectric solids.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Computational evaluation of the flexoelectric effect in dielectric solids

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.530759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.530759Z digest=sha256:412b574c36707238010823c8be957456e16a6621ff1b76ecc2e8025ccb71caf7

Observation 297b128c-f784-4a91-a7bb-71bacf67f4b6 · outbound

This paper cites Flexoelectricity in atomic monolayers from first principles.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Flexoelectricity in atomic monolayers from first principles

Reference 24

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.533724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.533724Z digest=sha256:b9c3a08de0e6fd00b11f1f1ab77eaa45d6c5ce98436ac3c55a919d9627ec5c41

Observation 25fb8f5a-6b07-4fab-8fb6-064977ef3105 · outbound

This paper cites Ab initio study of flexoelectricity in mxene monolayers.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Ab initio study of flexoelectricity in mxene monolayers

Reference 25

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.536811Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.536811Z digest=sha256:7febc5bf92869e80eca6f1cf90a129c0143bdee7778c2b0a03663405875eb1a6

Observation eb2ac4c5-dd91-4499-831b-76dd9b36b2b2 · outbound

This paper cites Transversal flexoelectric coefficient for nanostruc- tures at finite deformations from first principles.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Transversal flexoelectric coefficient for nanostruc- tures at finite deformations from first principles

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.539840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.539840Z digest=sha256:9ed73092b5bf3a078903ad639fd0d0808837e095f6a2523effd8f414da450736

Observation 636981b2-7016-4d9b-b47e-d750cb328aa9 · outbound

This paper cites Critical curvature localization in graphene.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Critical curvature localization in graphene

Reference 27

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.543347Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.543347Z digest=sha256:70b77d58d61b964bfea73a94402b76ccfffa071d00fbeb5f2e77a5f6e27716e7

Observation 37be2edb-8796-478d-a2d3-7cfaf7de1e09 · outbound

This paper cites Critical curvature localiza- tion in graphene.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Critical curvature localiza- tion in graphene

Reference 28

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.546632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.546632Z digest=sha256:7a5fec594383e11ce05042f5883ecf19bb8a6cad085c1dd548a2693a3caf7ae3

Observation b69d641b-e306-41a9-b983-da5e7aa58df0 · outbound

This paper cites Flexoelectricity in soft materials and biological membranes.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Flexoelectricity in soft materials and biological membranes

Reference 29

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.550416Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.550416Z digest=sha256:60a4e950042290af0e8afdce07bb82d0dbc68e7b51938f0ef3396af2a582d721

Observation f228450e-72f7-4c74-8487-9df11ab69856 · outbound

This paper cites Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity

Reference 30

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.554359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.554359Z digest=sha256:32bc37b300f90a46702986dd72f3f36c8cccabf8faed0113c2035c56e3b982a1

Observation ec956543-c8af-4c45-a710-fbdf4fd71127 · outbound

This paper cites Modeling flexoelectricity in soft dielectrics at finite deformation.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Modeling flexoelectricity in soft dielectrics at finite deformation

Reference 31

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.557801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.557801Z digest=sha256:8c4cab6d9a96427f72e4a72739ce985c4e409056f767e0e2f7b3471eac24ea7d

Observation b562f9b4-261e-4761-af5f-41c1c1951dbe · outbound

This paper cites A static and dynamic theory for photo-flexoelectric liquid crystal elastomers and the coupling of light, deformation and electricity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates A static and dynamic theory for photo-flexoelectric liquid crystal elastomers and the coupling of light, deformation and electricity

Reference 32

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.561548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.561548Z digest=sha256:824b3d2cf3bfa4788319a45457d4bfae46248510f8eb31fe9eef1912ff59bf5d

Observation 8578346d-70a2-4831-9b57-ac673d44f667 · outbound

This paper cites The collusion of flexoelec- tricity and hopf bifurcation in the hearing mechanism.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates The collusion of flexoelec- tricity and hopf bifurcation in the hearing mechanism

Reference 33

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.565181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.565181Z digest=sha256:16909263001b4771c5ec79a83ffbe1d3c948e8a13d357bc67632e8c467abc545

Observation e40409d8-d9ca-4818-a275-d355b9b71e2d · outbound

This paper cites An electromechanical liquid crystal model of vesicles.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates An electromechanical liquid crystal model of vesicles

Reference 34

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.569465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.569465Z digest=sha256:bcb3699c3ff5ac887a46518cdb958d52d294e64acd293c1ef2fb9c1dd60badcf

Observation c9117383-34a0-4ace-9da2-11dd345507db · outbound

This paper cites Modelling and numerical simulation of remodelling processes in cortical bone: An iga approach to flexoelectricity-induced osteocyte apoptosis and subsequent bone cell diffusion.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Modelling and numerical simulation of remodelling processes in cortical bone: An iga approach to flexoelectricity-induced osteocyte apoptosis and subsequent bone cell diffusion

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.572777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.572777Z digest=sha256:00818a719bcba7487b7eef41085b887f0c0c5a5bd60d5b9f3648f7e650b4c323

Observation 609eb2fb-c072-44ed-a172-6d69698e0048 · outbound

This paper cites The number and types of all possible rotational symmetries for flexoelectric tensors.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates The number and types of all possible rotational symmetries for flexoelectric tensors

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.577185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.577185Z digest=sha256:969a4b78fd4e072e16465a0c38a369c91233b456ea07e59e7fe53220c5cb0fcd

Observation e4ceb16d-3aad-4535-b86c-3c105733ddfe · outbound

This paper cites Second gradient of strain and surface-tension in linear elasticity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Second gradient of strain and surface-tension in linear elasticity

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.580898Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.580898Z digest=sha256:7a4960697a24e857c16667819152fcc4add4f54c702f940382bb58ebde003b9b

Observation 69f27e4a-dad3-439a-9781-e7cea6d64690 · outbound

This paper cites Insights into flexoelectric solids from strain-gradient elasticity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Insights into flexoelectric solids from strain-gradient elasticity

Reference 38

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.584412Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.584412Z digest=sha256:46e6af420579022b5919473de7e965741854bb0c75f8e105d99f083ecc1ab8db

Observation 851f2e97-d0be-4654-a35b-cf499036b2a8 · outbound

This paper cites A theory of flexoelectricity with surface effect for elastic dielectrics.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates A theory of flexoelectricity with surface effect for elastic dielectrics

Reference 39

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.587644Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.587644Z digest=sha256:e957e1172e86dc6ff137048e14fa690cf61cd931053a282373fa777c76e4e9b2

Observation 46bd347f-0b07-473e-8865-54cfa0cf48e7 · outbound

This paper cites Flexoelectric effect on the electroelastic responses of bending piezoelectric nanobeams.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Flexoelectric effect on the electroelastic responses of bending piezoelectric nanobeams

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.591193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.591193Z digest=sha256:3d98332adbca3b8e7351d20c8f09c3c275870a2450cde4acce8b17b516e55fe7

Observation fcbae1f6-3bed-40a3-bb11-fa5f7764958c · outbound

This paper cites Defects in flexoelectric solids.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Defects in flexoelectric solids

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.594587Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.594587Z digest=sha256:84b75a04ce59e37a728a0afdd1f7eb2c6ff27960e64e31a0696420e86e4a9ce1

Observation f2f0f580-df09-4283-bc46-b3db61de5b38 · outbound

This paper cites Asymmetric mechanical properties in ferroelectrics driven by flexo-deformation effect.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Asymmetric mechanical properties in ferroelectrics driven by flexo-deformation effect

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.597974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.597974Z digest=sha256:d7db18173dad01a7f952704ffe756740e42207efa91d481a357684c4164ff622

Observation c5e5511b-adef-45ff-9931-922eb9508b37 · outbound

This paper cites Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.601304Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.601304Z digest=sha256:69bb324f3851a7a7101745b44f18417841979f8c7b9ec5682f173659c2a7d8ea

Observation 6fbb2ba1-277e-4156-b0d1-a3978604b76f · outbound

This paper cites Inhomogeneous electron gas.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Inhomogeneous electron gas

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.604580Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.604580Z digest=sha256:3e782ac3fd1a4dd46cdee56b540357f3480883471d89c5af67857e28b81cdd9f

Observation 2368081b-973b-41f8-8670-6bf3fd7cea1a · outbound

This paper cites Self-consistent equations including exchange and correlation effects.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Self-consistent equations including exchange and correlation effects

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.608177Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.608177Z digest=sha256:54942d1490dce02291b5268ea4ed24042b8198b9fb4ce0ca178dc2b015622a30

Observation 1b6bbbe9-4d30-4709-9f5c-60dc0e87ff5e · outbound

This paper cites Cyclic density functional theory: A route to the first principles simulation of bending in nanostructures.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Cyclic density functional theory: A route to the first principles simulation of bending in nanostructures

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.611537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.611537Z digest=sha256:9180183a92363b9db77b724a53eadc758c815b7f63e53c04f2fe714f60c0c654

Observation a0c25de9-46f9-4641-a060-37169a823ff2 · outbound

This paper cites Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-iv nanotubes.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-iv nanotubes

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.614803Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.614803Z digest=sha256:279791bc7a71796d83389db53f2d0744633cea420959668619355f99b7ff7875

Observation 7c2e7ef3-e611-49d3-8e8b-df2cfe0264b9 · outbound

This paper cites Sparc: Accurate and efficient finite-difference formulation and parallel implementation of density functional theory: Isolated clusters.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Sparc: Accurate and efficient finite-difference formulation and parallel implementation of density functional theory: Isolated clusters

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.618094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.618094Z digest=sha256:cb03be63d5e48c8e225a69ca87d200f61bf6a818c8b4ad039b271de014aecc30

Observation 3d62c6c4-273f-45f4-b6cc-991355001d25 · outbound

This paper cites Sparc: Accurate and efficient finite-difference formulation and parallel implementation of density functional theory: Extended systems.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Sparc: Accurate and efficient finite-difference formulation and parallel implementation of density functional theory: Extended systems

Reference 49

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.621261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.621261Z digest=sha256:355e4f894aabf87a0b9e6b3f13f9d288a3028039ead27ef6058ff6c2a4f715cd

Observation 4662ea4f-3068-4b06-8ce8-81e58e1ec790 · outbound

This paper cites Modeling direct and converse flexoelectricity in soft dielectric rods with application to the follower load.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Modeling direct and converse flexoelectricity in soft dielectric rods with application to the follower load

Reference 50

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.624547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.624547Z digest=sha256:fc95b17cd79789bb4c7422eed97e4ae4877389409b412270f53db3b5f4e0a3bf

Observation 9dfef958-3a1c-48df-9da6-e32df76c12e0 · outbound

This paper cites Giant flexoelectric effect through interfacial strain relaxation.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Giant flexoelectric effect through interfacial strain relaxation

Reference 51

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.627724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.627724Z digest=sha256:a658c3522538fb4b3b65166b5e3249711e1e7c7c121e2ae3bf0fbaa7d1ce30dd

Observation 867b5499-67c0-4ebb-b9f2-32b5df8a5e07 · outbound

This paper cites Piezoelectric thin-film superlattices without using piezo- electric materials.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Piezoelectric thin-film superlattices without using piezo- electric materials

Reference 52

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.630942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.630942Z digest=sha256:949a7e6e60bd648ff2796b503525be1e0c5a15d8609f79829f31b3665a260e39

Observation c06790b0-07d4-482d-a87c-1e425d4851b9 · outbound

This paper cites Mechanical switching of ferroelectric domains beyond flexoelectricity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Mechanical switching of ferroelectric domains beyond flexoelectricity

Reference 53

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.634331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.634331Z digest=sha256:77c1dac0b8791f4b0444b643c6f2df72c3f57b64d2a6b7f2fcc5246d7ecc91b0

Observation af6eba0a-2c8d-4f3a-a919-004c3992a95d · outbound

This paper cites Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.637750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.637750Z digest=sha256:3fe8f665e20660cdc5bbfbbbdd3bba2d73ccfcbdead3fe5b0aded9b62fa3db17

Observation 79873bf9-427e-4a46-8fc0-2db3b571cc9b · outbound

This paper cites Analyzing flexoelectric polarization of suspended membrane by nonlinear bending theory of plate.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Analyzing flexoelectric polarization of suspended membrane by nonlinear bending theory of plate

Reference 55

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.641014Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.641014Z digest=sha256:605361677412abe2668faf66449cedf5fa5d5d0d4fe00a1fac8bf2d8ac173507

Observation d1b50e48-1bf2-4c20-aba5-155aecece595 · outbound

This paper cites Mathematical and computational modeling of flexoelectricity.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Mathematical and computational modeling of flexoelectricity

Reference 56

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.644200Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.644200Z digest=sha256:90a7c4a464e8e0f601035573b34879841457ee01a52fe6f320b64a577b64c894

Observation d733567f-5d3f-4ec2-b04c-c5e06bf26f9a · outbound

This paper cites Continuum mechanics of solids.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Continuum mechanics of solids

Reference 57

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.647464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.647464Z digest=sha256:2b6edcad9d43ad195d5e4f9ebe2f5a01db9a3c51495e016bcf67cc8da596002b

Observation 6bfb4064-85bc-44e5-a17e-fc6cc79c319c · outbound

This paper cites Stability and post-bifurcation of film-substrate systems.

Generalization of Stoney's equation for flexoelectric thin films on elastic substrates Stability and post-bifurcation of film-substrate systems

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-04T06:37:38.650623Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:37:38.650623Z digest=sha256:9c31e02c237b04df31f7f483ba04cb619af85afebda4e4fdcdb7ca538513628f

Pith citing papers

Observation dedc0301-b025-454c-b936-2345fe3d471f · inbound

Propagation of elastic waves in a flexomagnetic solid cites this paper.

Propagation of elastic waves in a flexomagnetic solid Generalization of Stoney's equation for flexoelectric thin films on elastic substrates

Reference 2004

Resolution
unresolved
no resolver link, observed 2026-08-04T06:07:28.458940Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T06:07:28.458940Z digest=sha256:04521a4658c8ae09a9d1092ec4cf54dfdbcb437ca8bd481849c25f92ae15faa4