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Paper Citation Record · LEDGER

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

As of 16 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 1 inbound Pith citation observation for arXiv:2601.09160.

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pith.paper-citation-record.v1
2601.09160 v1

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measured 57 of 57 reference resolution

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measured 58 of 58 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

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57 of 57 outbound references displayed

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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source=pdf_text observed=2026-08-04T06:37:38.587644Z digest=sha256:e70e886e3441f496673652f86730feadf01252c0f02c5d2e3284e647ffc96ed4

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

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source=pdf_text observed=2026-08-04T06:37:38.591193Z digest=sha256:1a3a3badb22baddf4a96c084bc8ff25f0f46f3e8e07b86b0fa4930926db17ffc

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

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source=pdf_text observed=2026-08-04T06:37:38.594587Z digest=sha256:a36ffed3d40f48c164118aee984e9cf53c9adddc496fc682e1201d6bd80b6d50

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

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source=pdf_text observed=2026-08-04T06:37:38.597974Z digest=sha256:0e665149274fe51b7a532ef6c69a713e629d4fc3a0ee1550ef8c73ddd6dff591

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

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source=pdf_text observed=2026-08-04T06:37:38.601304Z digest=sha256:1805112f31cd9b1f487c2026723011a25d03a2816969381008941b5d4fc02d7f

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

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source=pdf_text observed=2026-08-04T06:37:38.604580Z digest=sha256:ee2542675e417ded82f0411d55233382c6211289f2c6560d47c95b1ad1bd9c40

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

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source=pdf_text observed=2026-08-04T06:37:38.608177Z digest=sha256:f36be098cc72b29b0bdbf812232fb55720d68e1b29d9d7c575b4f1eca6ef6242

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

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source=pdf_text observed=2026-08-04T06:37:38.611537Z digest=sha256:db9efb00f066f006b08fc2c5aa0c2adf04db66d5310147f2847d67615964361f

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

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source=pdf_text observed=2026-08-04T06:37:38.614803Z digest=sha256:4f2a92906caed20cc1fd97d21e6a49927e91db8588df77c7f58b83cab54e6381

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

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source=pdf_text observed=2026-08-04T06:37:38.618094Z digest=sha256:8928b89a1b87e757402f2c21632810c351dd30d2f58ba6f81be8cb3cdb95bbe4

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

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source=pdf_text observed=2026-08-04T06:37:38.621261Z digest=sha256:4d557ce6d2aba618f07eac9304074a4542b8e403bc05a00a743d80e91b5d4052

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

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source=pdf_text observed=2026-08-04T06:37:38.624547Z digest=sha256:78f22d87440083d463427f3b4df62de1bf3bf98631da1e80276b3472cac1b035

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

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source=pdf_text observed=2026-08-04T06:37:38.627724Z digest=sha256:5edd83339818093e116bb811baee6cb19eefe879010cef7f049b12a0606f921b

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
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source=pdf_text observed=2026-08-04T06:37:38.630942Z digest=sha256:564508a12603b45bb54104a417793fa2998b58f6aa0009496349f87c45d30fa1

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
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source=pdf_text observed=2026-08-04T06:37:38.634331Z digest=sha256:20540df678006e3adf0d325c3db206567a1dac6632f4bd66dc1eb6f66db092c5

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
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source=pdf_text observed=2026-08-04T06:37:38.637750Z digest=sha256:7643df618d4ef26d9ae0cb3e404f089094d70e794936e554193ea5cdcd215611

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

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source=pdf_text observed=2026-08-04T06:37:38.641014Z digest=sha256:6e9bc1658492f77cfb5d2ac8ab0d18190009a3b6a77495f82f52a73fbdd43ca0

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
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source=pdf_text observed=2026-08-04T06:37:38.644200Z digest=sha256:508d3fd8ab906f506c7515face945d92c3d47026e0bcd1577c0c59cd8aef811e

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

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source=pdf_text observed=2026-08-04T06:37:38.647464Z digest=sha256:94cab9ad17fa1fbb69ada08611e702c5ab303a9f9e5de10eca536883f308e7d4

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

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source=pdf_text observed=2026-08-04T06:37:38.650623Z digest=sha256:ce20d7e4f20fa26de2efbde83347293aa1c661bd91afcae85a411c88b45361cf

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

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source=pdf_text observed=2026-08-04T06:07:28.458940Z digest=sha256:96c60547ee447b43ab17d9927c4f0340ba6e7b5fb12ae1548936a42561edd9b6