A phase field approach for damage propagation in periodic microstructured materials | Paper Citation Record

Observation f1236a80-d476-4ffc-b3d9-7dd0b85d19b1 · outbound

This paper cites Micromechanical analysis of heterogeneous materials subjected to overall cosserat strains.

A phase field approach for damage propagation in periodic microstructured materials Micromechanical analysis of heterogeneous materials subjected to overall cosserat strains

Reference 1

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This paper cites Homogenization and two-scale convergence.

A phase field approach for damage propagation in periodic microstructured materials Homogenization and two-scale convergence

Reference 2

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This paper cites Phase-field modeling of ductile fracture.

A phase field approach for damage propagation in periodic microstructured materials Phase-field modeling of ductile fracture

Reference 3

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This paper cites Higher order asymptotic homogenization and wave propagation in periodic composite materials.

A phase field approach for damage propagation in periodic microstructured materials Higher order asymptotic homogenization and wave propagation in periodic composite materials

Reference 4

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This paper cites Phase-field analysis of finite-strain plates and shells including element subdivision.

A phase field approach for damage propagation in periodic microstructured materials Phase-field analysis of finite-strain plates and shells including element subdivision

Reference 5

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This paper cites R., Linde, P., Camanho, P.

A phase field approach for damage propagation in periodic microstructured materials R., Linde, P., Camanho, P

Reference 6

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Observation 27a35b02-fd8f-4270-a345-83a2ad01b7c0 · outbound

This paper cites Mindlin second-gradient elastic properties from dilute two-phase cauchy-elastic composites.

A phase field approach for damage propagation in periodic microstructured materials Mindlin second-gradient elastic properties from dilute two-phase cauchy-elastic composites

Reference 7

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This paper cites Mindlin second-gradient elastic properties from dilute two-phase cauchy-elastic composites part ii: Higher-order constitutive properties and application cases.

A phase field approach for damage propagation in periodic microstructured materials Mindlin second-gradient elastic properties from dilute two-phase cauchy-elastic composites part ii: Higher-order constitutive properties and application cases

Reference 8

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This paper cites Anisotropic effective higher-order response of heterogeneous cauchy elastic materials.

A phase field approach for damage propagation in periodic microstructured materials Anisotropic effective higher-order response of heterogeneous cauchy elastic materials

Reference 9

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This paper cites Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits.

A phase field approach for damage propagation in periodic microstructured materials Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits

Reference 10

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This paper cites Micro-polar and second order homogenization of periodic masonry.

A phase field approach for damage propagation in periodic microstructured materials Micro-polar and second order homogenization of periodic masonry

Reference 11

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This paper cites A multi-scale strain-localization analysis of a layered strip with debonding interfaces.

A phase field approach for damage propagation in periodic microstructured materials A multi-scale strain-localization analysis of a layered strip with debonding interfaces

Reference 12

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Observation 3547e6ef-26d7-41b9-a659-446c087c53dd · outbound

This paper cites Computational dynamic homogenization for the analysis of dispersive waves in layered rock masses with periodic fractures.

A phase field approach for damage propagation in periodic microstructured materials Computational dynamic homogenization for the analysis of dispersive waves in layered rock masses with periodic fractures

Reference 13

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Observation 2ec4ee4f-06e7-4629-abe0-1bf2c86b80b2 · outbound

This paper cites Second-gradient homogenized model for wave propagation in heterogeneous periodic media.

A phase field approach for damage propagation in periodic microstructured materials Second-gradient homogenized model for wave propagation in heterogeneous periodic media

Reference 14

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Observation ac53b6f2-913a-4f3d-bacd-e63a0ddc7b7b · outbound

This paper cites Effective elastic properties of planar sofcs: A non-local dynamic homogenization approach.

A phase field approach for damage propagation in periodic microstructured materials Effective elastic properties of planar sofcs: A non-local dynamic homogenization approach

Reference 15

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This paper cites Homogenization: Averaging Processes in Periodic Media.

A phase field approach for damage propagation in periodic microstructured materials Homogenization: Averaging Processes in Periodic Media

Reference 16

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Observation 4a1d4114-a7b7-43f0-9cd0-cabd24fdd255 · outbound

This paper cites Non local integral formulations of plasticity and damage: survey of progress.

A phase field approach for damage propagation in periodic microstructured materials Non local integral formulations of plasticity and damage: survey of progress

Reference 17

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This paper cites Asymptotic analysis for periodic structures.

A phase field approach for damage propagation in periodic microstructured materials Asymptotic analysis for periodic structures

Reference 18

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This paper cites Analytical derivation of cosserat moduli via homogenization of heterogeneous elastic materials.

A phase field approach for damage propagation in periodic microstructured materials Analytical derivation of cosserat moduli via homogenization of heterogeneous elastic materials

Reference 19

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Observation 5ba0fb32-ba9e-4b5b-b0ea-624ad268659d · outbound

This paper cites Phase-field modeling of anisotropic brittle fracture including several damage mechanisms.

A phase field approach for damage propagation in periodic microstructured materials Phase-field modeling of anisotropic brittle fracture including several damage mechanisms

Reference 20

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Observation dade7eb2-b3ee-4501-8418-e3cab6e39b23 · outbound

This paper cites The variational approach to fracture.

A phase field approach for damage propagation in periodic microstructured materials The variational approach to fracture

Reference 21

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Observation 2f2d8c4c-b91a-4c25-8818-86a387d6c752 · outbound

This paper cites A., Marigo, J.-J., 2000.

A phase field approach for damage propagation in periodic microstructured materials A., Marigo, J.-J., 2000

Reference 22

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Observation 1485c9ce-245d-4cc9-91cb-a3fee9b0a3b9 · outbound

This paper cites Microstructural effects in elastic composites.

A phase field approach for damage propagation in periodic microstructured materials Microstructural effects in elastic composites

Reference 23

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This paper cites Computational modelling of impact damage in brittle materials.

A phase field approach for damage propagation in periodic microstructured materials Computational modelling of impact damage in brittle materials

Reference 24

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Observation e69abb4f-b57f-4ce6-a466-83060811b2d7 · outbound

This paper cites Modeling complex crack paths in ceramic laminates: A novel variational framework combining the phase field method of fracture and the cohesive zone model.

A phase field approach for damage propagation in periodic microstructured materials Modeling complex crack paths in ceramic laminates: A novel variational framework combining the phase field method of fracture and the cohesive zone model

Reference 25

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Observation 1ec4b564-9fe9-46a9-b051-ea6219e3fb76 · outbound

This paper cites Computational modelling of gradient-enhanced damage in quasi-brittle materials.

A phase field approach for damage propagation in periodic microstructured materials Computational modelling of gradient-enhanced damage in quasi-brittle materials

Reference 26

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Observation bf438fbe-56e3-4b2e-b8d7-297b62165acf · outbound

This paper cites L., Addessi, D., 2011.

A phase field approach for damage propagation in periodic microstructured materials L., Addessi, D., 2011

Reference 27

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This paper cites Characterization of wave propagation in periodic viscoelastic materials via asymptotic-variational homogenization.

A phase field approach for damage propagation in periodic microstructured materials Characterization of wave propagation in periodic viscoelastic materials via asymptotic-variational homogenization

Reference 28

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Observation cc9f9d4b-3265-49f8-8f5a-129c7e1cfdea · outbound

This paper cites A regularization framework for damage--plasticity models via gradient enhancement of the free energy.

A phase field approach for damage propagation in periodic microstructured materials A regularization framework for damage--plasticity models via gradient enhancement of the free energy

Reference 29

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Observation b63c0392-51b7-40ec-9b6a-9baae27b2a8b · outbound

This paper cites Computational homogenization of architectured materials.

A phase field approach for damage propagation in periodic microstructured materials Computational homogenization of architectured materials

Reference 30

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Observation d63cddba-8349-4cb6-b652-7fda1f60fee1 · outbound

This paper cites Multi-field asymptotic homogenization of thermo-piezoelectric materials with periodic microstructure.

A phase field approach for damage propagation in periodic microstructured materials Multi-field asymptotic homogenization of thermo-piezoelectric materials with periodic microstructure

Reference 31

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Observation 0a34f9c1-f40a-4125-a63a-bcac47eb3780 · outbound

This paper cites Design of thermo-piezoelectric microstructured bending actuators via multi-field asymptotic homogenization.

A phase field approach for damage propagation in periodic microstructured materials Design of thermo-piezoelectric microstructured bending actuators via multi-field asymptotic homogenization

Reference 32

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This paper cites A multilevel finite element method (fe2) to describe the response of highly non-linear structures using generalized continua.

A phase field approach for damage propagation in periodic microstructured materials A multilevel finite element method (fe2) to describe the response of highly non-linear structures using generalized continua

Reference 33

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Observation 654b253f-d909-47c5-a6fe-a04cd713f66e · outbound

This paper cites Homogenization methods and the mechanics of generalized continua-part 2.

A phase field approach for damage propagation in periodic microstructured materials Homogenization methods and the mechanics of generalized continua-part 2

Reference 34

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Observation 82ce6c47-9b3d-4936-b8be-be3065f29578 · outbound

This paper cites Cosserat overall modeling of heterogeneous materials.

A phase field approach for damage propagation in periodic microstructured materials Cosserat overall modeling of heterogeneous materials

Reference 35

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Observation 76d93187-8315-4905-bdf6-9ca4c8bae8b8 · outbound

This paper cites Generalized continua and non‐homogeneous boundary conditions in homogenisation methods.

A phase field approach for damage propagation in periodic microstructured materials Generalized continua and non‐homogeneous boundary conditions in homogenisation methods

Reference 36

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Observation f24685b0-cb03-4cb9-aa7a-fd25df13d375 · outbound

This paper cites Revisiting brittle fracture as an energy minimization problem.

A phase field approach for damage propagation in periodic microstructured materials Revisiting brittle fracture as an energy minimization problem

Reference 37

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Observation 79a77ca8-63d0-44f3-aa94-6125cf97e968 · outbound

This paper cites Higher order terms in the homogenized stress‐strain relation of periodic elastic media.

A phase field approach for damage propagation in periodic microstructured materials Higher order terms in the homogenized stress‐strain relation of periodic elastic media

Reference 38

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Observation 1078356b-9e2f-433b-a997-3778b1097edd · outbound

This paper cites A., 1921.

A phase field approach for damage propagation in periodic microstructured materials A., 1921

Reference 39

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Observation 49c88cd0-05e5-4008-92c3-9964d5d51fa2 · outbound

This paper cites G., Reinoso, J., Paggi, M., 2019.

A phase field approach for damage propagation in periodic microstructured materials G., Reinoso, J., Paggi, M., 2019

Reference 40

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Observation 606e3f57-833f-4314-8bff-622648bfc18a · outbound

This paper cites A., 2018.

A phase field approach for damage propagation in periodic microstructured materials A., 2018

Reference 41

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Observation 83dcfdea-9367-4e0f-8f8b-8ffdcf9c735c · outbound

This paper cites o rr, A. C., de Borst, R., Hennig, P., K \.

A phase field approach for damage propagation in periodic microstructured materials o rr, A. C., de Borst, R., Hennig, P., K \

Reference 42

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Observation 2417e852-2fa9-4b2d-8c84-251dc9bbc885 · outbound

This paper cites S., González, C., LLorca, J., 2015.

A phase field approach for damage propagation in periodic microstructured materials S., González, C., LLorca, J., 2015

Reference 43

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Observation 027757dd-6ac7-4ac8-b929-0cd49617cf3a · outbound

This paper cites S., Palencia, E.

A phase field approach for damage propagation in periodic microstructured materials S., Palencia, E

Reference 44

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Observation 6d9508ca-b7da-4531-b230-777bdb1565df · outbound

This paper cites J., Bi \'c ani \'c , N., 2008.

A phase field approach for damage propagation in periodic microstructured materials J., Bi \'c ani \'c , N., 2008

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.834126Z

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Observation b8e6db3d-a764-4fbc-b06e-a8c0aa15b9e0 · outbound

This paper cites Variational approach to interface element modeling of brittle fracture propagation.

A phase field approach for damage propagation in periodic microstructured materials Variational approach to interface element modeling of brittle fracture propagation

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.827376Z

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Observation 78e6dd03-f2c8-44eb-b543-08c57053e6ed · outbound

This paper cites Advanced constitutive modeling of heterogeneous materials with a gradient-enhanced computational homogenization scheme.

A phase field approach for damage propagation in periodic microstructured materials Advanced constitutive modeling of heterogeneous materials with a gradient-enhanced computational homogenization scheme

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.820565Z

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Observation 19c73e98-ceee-4c15-b722-2cac7004f645 · outbound

This paper cites Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy.

A phase field approach for damage propagation in periodic microstructured materials Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.813403Z

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Observation 68125f16-82b0-4719-ac73-c7588ef612de · outbound

This paper cites Simulation of size effects by a phase field model for fracture.

A phase field approach for damage propagation in periodic microstructured materials Simulation of size effects by a phase field model for fracture

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.806359Z

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Observation fc24735d-b293-485a-88fe-fead483db2d0 · outbound

This paper cites Finite elements with embedded strong discontinuities for the modeling of failure in solids.

A phase field approach for damage propagation in periodic microstructured materials Finite elements with embedded strong discontinuities for the modeling of failure in solids

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.799356Z

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Observation 7740d674-7f48-455e-bd04-f70e16ad0dd8 · outbound

This paper cites A convergence study of phase-field models for brittle fracture.

A phase field approach for damage propagation in periodic microstructured materials A convergence study of phase-field models for brittle fracture

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.792278Z

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Observation c302f1a7-d868-4d31-98e6-0f0f54eaf9f8 · outbound

This paper cites A continuum damage model for composite laminates: Part \ I\ – constitutive model.

A phase field approach for damage propagation in periodic microstructured materials A continuum damage model for composite laminates: Part \ I\ – constitutive model

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.785357Z

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Observation 3fc7a0d1-17cd-4e19-81f8-86cb7e73002b · outbound

This paper cites G., 2012.

A phase field approach for damage propagation in periodic microstructured materials G., 2012

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.778281Z

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Observation a934baea-13e4-4321-a53f-056eca5ea79a · outbound

This paper cites F., 2018.

A phase field approach for damage propagation in periodic microstructured materials F., 2018

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.771360Z

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Observation dc3c3204-0d5f-4f4c-90ee-67e6aba6d195 · outbound

This paper cites Asymptotic homogenization of elastic composite materials with a regular structure.

A phase field approach for damage propagation in periodic microstructured materials Asymptotic homogenization of elastic composite materials with a regular structure

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.764794Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation dff3d8df-0aff-4fc7-b8cc-a1a1735b7822 · outbound

This paper cites Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory.

A phase field approach for damage propagation in periodic microstructured materials Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.757771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 49020b96-f53f-44ba-8470-ded5901b1667 · outbound

This paper cites Phase field modeling of fracture in multi-physics problems.

A phase field approach for damage propagation in periodic microstructured materials Phase field modeling of fracture in multi-physics problems

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.750896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 73ae8836-02df-4e44-bfe0-a37a6754de5d · outbound

This paper cites A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits.

A phase field approach for damage propagation in periodic microstructured materials A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.743833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2086970e-cb78-4dc8-89c3-09c3b451703a · outbound

This paper cites A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits.

A phase field approach for damage propagation in periodic microstructured materials A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.737029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a472eb53-a120-431a-b5b7-fd6d9f0bd932 · outbound

This paper cites Formulation and numerical exploitation of mixed variational principles for coupled problems of cahn-hilliard-type and standard diffusion in elastic solids.

A phase field approach for damage propagation in periodic microstructured materials Formulation and numerical exploitation of mixed variational principles for coupled problems of cahn-hilliard-type and standard diffusion in elastic solids

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.730038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b1f0f6b0-5b62-42ba-a25d-fa998d7385de · outbound

This paper cites Phase field modeling of fracture in multi-physics problems.

A phase field approach for damage propagation in periodic microstructured materials Phase field modeling of fracture in multi-physics problems

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.722620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 31f26c63-7645-4b54-aee2-6c4960bea418 · outbound

This paper cites Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field fe implementations.

A phase field approach for damage propagation in periodic microstructured materials Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field fe implementations

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.714869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 12bde69a-fc72-4f9d-8d6f-193e4e64d1e3 · outbound

This paper cites A finite element method for crack growth without remeshing.

A phase field approach for damage propagation in periodic microstructured materials A finite element method for crack growth without remeshing

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.707999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ac5d3c05-f949-4516-9161-0f612ae40145 · outbound

This paper cites On the choice of parameters in the phase field method for simulating crack initiation with experimental validation.

A phase field approach for damage propagation in periodic microstructured materials On the choice of parameters in the phase field method for simulating crack initiation with experimental validation

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.700846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 627e81e0-2226-4dff-ab6d-6daf843e2f96 · outbound

This paper cites T., Yvonnet, J., Bornert, M., Chateau, C., Sab, K., Romani, R., Le Roy, R., 2016 b.

A phase field approach for damage propagation in periodic microstructured materials T., Yvonnet, J., Bornert, M., Chateau, C., Sab, K., Romani, R., Le Roy, R., 2016 b

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.693566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c7c1add2-3b56-4c43-ad03-854dbd93981c · outbound

This paper cites A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography.

A phase field approach for damage propagation in periodic microstructured materials A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.686471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a991638f-3ac0-4ab0-9580-df57ac81d830 · outbound

This paper cites Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach.

A phase field approach for damage propagation in periodic microstructured materials Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.679550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7869fc2d-a925-4791-9d49-c2903423a9b0 · outbound

This paper cites Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis.

A phase field approach for damage propagation in periodic microstructured materials Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.672809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 49066af6-fee6-424a-9515-81f01da35aad · outbound

This paper cites D., Jasiuk, I., 1999.

A phase field approach for damage propagation in periodic microstructured materials D., Jasiuk, I., 1999

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.666014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 88e6cdfd-5264-488d-be2f-d77012038b60 · outbound

This paper cites Multiscale computational homogenization: review and proposal of a new enhanced-first-order method.

A phase field approach for damage propagation in periodic microstructured materials Multiscale computational homogenization: review and proposal of a new enhanced-first-order method

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.659501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 05d8db05-ba0a-4aea-bccd-68a2158cef41 · outbound

This paper cites Fracture of solar-grade anisotropic polycrystalline silicon: A combined phase field–cohesive zone model approach.

A phase field approach for damage propagation in periodic microstructured materials Fracture of solar-grade anisotropic polycrystalline silicon: A combined phase field–cohesive zone model approach

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.652348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a1cdca8a-a9f4-400f-b2d8-7508e115b232 · outbound

This paper cites an unresolved cited work.

A phase field approach for damage propagation in periodic microstructured materials Unresolved cited work

Reference 72

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:32:36.644891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c9776e52-f8e7-44a8-8df8-2e7177c00868 · outbound

This paper cites Stiffness and strength of hierarchical polycrystalline materials with imperfect interfaces.

A phase field approach for damage propagation in periodic microstructured materials Stiffness and strength of hierarchical polycrystalline materials with imperfect interfaces

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.637087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ad6edd1d-0735-4412-a6c6-3ab8b62798f8 · outbound

This paper cites Boundary conditions for the high order homogenized equation: laminated rods, plates and composites.

A phase field approach for damage propagation in periodic microstructured materials Boundary conditions for the high order homogenized equation: laminated rods, plates and composites

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.629994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 31c76741-fac3-47e1-986b-b0e1f1967d19 · outbound

This paper cites A critical comparison of nonlocal and gradient-enhanced softening continua.

A phase field approach for damage propagation in periodic microstructured materials A critical comparison of nonlocal and gradient-enhanced softening continua

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.622929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0024d5fb-b6ec-486d-8940-84105776e291 · outbound

This paper cites Gradient damage models and their use to approximate brittle fracture.

A phase field approach for damage propagation in periodic microstructured materials Gradient damage models and their use to approximate brittle fracture

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.616021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 67849d9b-2494-4e6d-8ebc-4da57bd376b8 · outbound

This paper cites From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models.

A phase field approach for damage propagation in periodic microstructured materials From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.609012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8228eece-0cd6-4cf0-93ca-1752e06c9a51 · outbound

This paper cites A phase field approach to simulate intralaminar and translaminar fracture in long fiber composite materials.

A phase field approach for damage propagation in periodic microstructured materials A phase field approach to simulate intralaminar and translaminar fracture in long fiber composite materials

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.602196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e4549f81-49fc-4300-8c71-428924591a1f · outbound

This paper cites A consistent anisotropic damage model for laminated fiber-reinforced composites using the 3d-version of the puck failure criterion.

A phase field approach for damage propagation in periodic microstructured materials A consistent anisotropic damage model for laminated fiber-reinforced composites using the 3d-version of the puck failure criterion

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.594986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f8e02e5e-a8f9-47ad-ad12-7700332bfef3 · outbound

This paper cites Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation.

A phase field approach for damage propagation in periodic microstructured materials Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.587726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 16d84eef-efc1-409c-a036-7fd1723f2d3b · outbound

This paper cites Identification of second-gradient elastic materials from planar hexagonal lattices.

A phase field approach for damage propagation in periodic microstructured materials Identification of second-gradient elastic materials from planar hexagonal lattices

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.580582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8b4837be-db5f-40f9-b8cf-440dd1a199d1 · outbound

This paper cites Identification of second-gradient elastic materials from planar hexagonal lattices.

A phase field approach for damage propagation in periodic microstructured materials Identification of second-gradient elastic materials from planar hexagonal lattices

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.573560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 763f0497-433b-4a5a-bd09-1af7586a1353 · outbound

This paper cites an unresolved cited work.

A phase field approach for damage propagation in periodic microstructured materials Unresolved cited work

Reference 83

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:32:36.566519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 88be4665-fa99-4215-affa-07853fec52ac · outbound

This paper cites Fracture propagation in brittle materials as a standard dissipative process: Effective crack tracking algorithms based on a viscous regularization.

A phase field approach for damage propagation in periodic microstructured materials Fracture propagation in brittle materials as a standard dissipative process: Effective crack tracking algorithms based on a viscous regularization

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.559413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 72af80b8-4ebf-4351-982b-e92f9f4ec3eb · outbound

This paper cites High-accuracy phase-field models for brittle fracture based on a new family of degradation functions.

A phase field approach for damage propagation in periodic microstructured materials High-accuracy phase-field models for brittle fracture based on a new family of degradation functions

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.552222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 25f7299b-9b7a-4e96-8bd6-647f3c418b14 · outbound

This paper cites Generalization of maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape.

A phase field approach for damage propagation in periodic microstructured materials Generalization of maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.544893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9e97605c-60b8-4e2d-a92f-60c698e9624b · outbound

This paper cites Effective elastic properties of matrix composites with transversely-isotropic phases.

A phase field approach for damage propagation in periodic microstructured materials Effective elastic properties of matrix composites with transversely-isotropic phases

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.537737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 893eeab6-76f2-40b3-b7da-730ab74ca2a8 · outbound

This paper cites Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization.

A phase field approach for damage propagation in periodic microstructured materials Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.530509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 287fd295-47bb-4d10-b400-2c9805026f57 · outbound

This paper cites On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media.

A phase field approach for damage propagation in periodic microstructured materials On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.523247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ee065ac9-14bd-4e65-9dcc-76fe5c7bd71d · outbound

This paper cites Crack nucleation in variational phase-field models of brittle fracture.

A phase field approach for damage propagation in periodic microstructured materials Crack nucleation in variational phase-field models of brittle fracture

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.515524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0355c5c8-1d6c-44eb-b543-aa8072f3fecd · outbound

This paper cites Phase field modeling of fracture in anisotropic brittle solids.

A phase field approach for damage propagation in periodic microstructured materials Phase field modeling of fracture in anisotropic brittle solids

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.507262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 33e90684-ce82-4b03-9f94-1b8bb61f9743 · outbound

This paper cites A micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media.

A phase field approach for damage propagation in periodic microstructured materials A micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.498452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 42d44b5b-3f43-411b-996d-c627e01552bd · outbound

This paper cites L., Murrali, A., 2015.

A phase field approach for damage propagation in periodic microstructured materials L., Murrali, A., 2015

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.414446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ee522515-d82e-4314-bf46-fc02c95fccbc · outbound

This paper cites Accurate simulation of delamination under mixed-mode loading using a cohesive model with a mode-dependent penalty stiffness.

A phase field approach for damage propagation in periodic microstructured materials Accurate simulation of delamination under mixed-mode loading using a cohesive model with a mode-dependent penalty stiffness

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.406833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0e6e7a41-aae9-47f9-ae52-214778b869fd · outbound

This paper cites V., de Borst, R., 2013.

A phase field approach for damage propagation in periodic microstructured materials V., de Borst, R., 2013

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.398118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation bf70a20a-86a0-42f9-ada3-cd632a501a9d · outbound

This paper cites R., 1981.

A phase field approach for damage propagation in periodic microstructured materials R., 1981

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.390408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0879630a-591a-4e5d-9936-4928350c3649 · outbound

This paper cites Y., 2017.

A phase field approach for damage propagation in periodic microstructured materials Y., 2017

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.381271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 27d7f28f-3e7c-43da-a29d-ff12154556f0 · outbound

This paper cites A micromechanical approach of nonlocal modeling for media with periodic microstructures.

A phase field approach for damage propagation in periodic microstructured materials A micromechanical approach of nonlocal modeling for media with periodic microstructures

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.373563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 52f6fcb0-7b5b-4e83-9e74-c141080b628a · outbound

This paper cites The finite element method.

A phase field approach for damage propagation in periodic microstructured materials The finite element method

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:32:36.364476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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