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Cited by 65Polymer composites and self-healingNumerical methods in engineeringMechanical Behavior of Composites

A cohesive-zone crack healing model for self-healing materials

Open access
Ponnusami, Sathiskumar A., Krishnasamy, Jayaprakash, Turteltaub, Sergio, van der Zwaag, Sybrand·2018·International Journal of Solids and Structures
DOI 10.1016/j.ijsolstr.2017.11.004
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AI snapshot

Written from the paper’s full text.

TL;DR

The paper extends a bilinear cohesive-zone fracture model with a healing variable to simulate crack healing and mechanical-property recovery in self-healing materials. It demonstrates single and multiple healing events, including application to a particle-based extrinsic self-healing unit cell under mode I loading.

Key findings

  • The model can simulate recovery after multiple healing events and allows different fracture properties for each healing material phase; simulations show load-carrying capacity can be partially recovered multiple times even when healing quality degrades, e.g., first healing at 75% and second at 50% of original fracture properties.
  • For a particle-based extrinsic self-healing unit cell, recovery depends on both healing-material fracture properties and filling efficiency: with healing strength/fracture-energy ratios σ⁽¹⁾c/σ⁽⁰⁾c and G⁽¹⁾c/G⁽⁰⁾c = 0.25, 0.5, 0.75, and 1, lower properties reduce post-healing load capacity.
  • Partial crack filling reduces recovery: filling ratios Vh/Vc = 1, 0.75, 0.5, and 0.25 show decreasing load-carrying capability, and the initial post-healing force-displacement slope decreases with lower filling efficiency.
  • Healing under constant load produces a more brittle post-healing response than healing under unloaded conditions, except when healing-material properties are relatively low; the paper notes this conclusion assumes the same healing-material fracture properties in both cases.

Methods

  • A cohesive-zone constitutive model is extended with a healing variable; the healed response is a composite/rule-of-mixtures (Voigt-like equal crack opening) weighted sum of original and healing material tractions, with energy-based damage parameters determining phase volume fractions.
  • The model is implemented in a finite element framework using cohesive elements or XFEM, with consistent tangent matrices for softening and unloading/reloading conditions.
  • Verification uses a three-element mesh with a zero-thickness cohesive element between two 20 μm × 20 μm continuum elements; application uses a 2D plane-strain unit cell of L = 75 μm with a circular particle of diameter d = 10 μm (nominal in-plane particle volume fraction 14%), matrix/particle properties E = 150 GPa, ν = 0.25, σc = 400 MPa, Gc = 100 J/m².

Limitations

  • The paper states that healing kinetics are not explicitly modeled; when healing is activated, the resting period is assumed sufficiently long for complete healing, and healing kinetics must be coupled separately through fracture properties and crack filling.
  • The paper states that the Voigt-like equal-strain assumption may overpredict tractions and the post-healing force peak; a model preserving both linear momentum and kinematic compatibility would likely predict a lower post-healing peak.
  • The paper states that crack-gap filling and healing are modeled only implicitly through shifts in crack opening displacements, and the new healing material is not explicitly modeled as additional material or mass entering the system.
  • The paper states that the unit cell is two-dimensional plane strain, so the particle is interpreted as prismatic rather than spherical, and matrix/particle elastic and fracture properties are kept equal for simplicity with a perfectly bonded interface and no interface fracture.
  • Evident from the text: the work is simulation-based and does not report experimental validation of the model.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1016/j.ijsolstr.2017.11.004

Cites

42 of 42 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

2 of 26 cited sources checked · 2 supported · 0 flagged

  • Premisecitation

    Some materials with intrinsic self-healing capacity (such as MAX phases) may undergo multiple healing events whereby a crack is healed on multiple occasions.

    “Some materials with intrinsic self-healing capacity (such as MAX phases), may undergo multiple healing events whereby a crack is healed on multiple occasions ( Li et al., 2012; Sloof et al., 2016 ).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Li et al., 2012

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Sloof et al., 2016 source
  • Findingnone given

    Complete failure occurs when the crack opening reaches the critical crack opening for failure of the original phase.

    “Complete failure occurs when the crack opening reaches the critical crack opening for failure (0) f of the original phase.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).
  • Findingown data

    After complete failure, the crack opening continues to grow due to the externally imposed deformation at essentially zero stress.

    “Afterwards, the crack opening continues to grow due to the externally-imposed deformation at essentially zero stress.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).
  • Findingnone given

    During the first stage of loading, the damage variable D(0) of the original material increases from 0 to 1, indicating that the original material undergoes full damage.

    “During the first stage of loading, the damage variable D (0) of the original material increases from 0 to 1, which indicates that the original material undergoes full damage.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).
  • Findingown data

    In the simulation, the traction in the cohesive element initially increases up to the cohesive strength of the original material and then decreases as a result of damage evolution.

    “the traction in the cohesive element initially increases up to the value equal to cohesive strength σ (0) c of the original material and then decreases as a result of damage evolution.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).
  • Classified as probably not a substantial claim. 22
  • May combine two claims. 18

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In Alsheghri and Al-Rub (2015), a thermodynamics-based cohesive zone methodology is used to model crack healing behavior by extending previous work on continuum damage-healing mechanics.

    “In Alsheghri and Al-Rub (2015) a thermodynamics-based cohesive zone methodology is used to model crack healing behavior by extending previous work on continuum damage-healing mechanics ( Darabi et al., 2012 ).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Alsheghri and Al-Rub (2015) source
    • cites Darabi et al., 2012 source

  • Classified as probably not a substantial claim. May combine two claims.

    Findingnone given

    During the healing process, the damage variable D(0) of the original material remains at 1 while the damage variable D(1) of the healing material becomes active with an initial value equal to zero.

    “During that process, the damage variable D (0) of the original material remains at 1 while the damage variable D (1) of the healing material becomes active with an initial value equal to zero (no damage).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).

  • May combine two claims.

    Findingreasoning

    During the third stage, the damage variable D(1) of the healing material increases from 0 to 1, so at the end of the loading process the healing material is also fully damaged.

    “During the third stage of the process, the damage variable D (1) of the healing material increases from 0 to 1, hence at the end of the loading process the healing material is also fully damaged.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).

  • May combine two claims.

    Findingown data

    Some points undergo healing from a fully-failed state, some from a partially-failed state, and some cracked points experienced no healing because they had not failed at the instant healing was activated.

    “some points undergo healing from a fully-failed state, some from a partially-failed state and some points that are cracked at the end of the loading process experienced no healing since they had not failed at the instant at which healing was activated.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The rate of damage per phase decreases as the number of active phases increases, with the largest rate corresponding to the most recently created phase.

    “the rate of damage per phase decreases as the number of active phases increases (i.e., the damage gets distributed among the different phases, with the largest rate corresponding to the most recently created phase).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    A decrease in filling efficiency decreases the initial slope of the post-healed behavior, whereas a decrease in fracture properties for fixed filling efficiency leaves the initial slope the same.

    “in the latter case the initial slope of the post-healed behavior remains the same for distinct fracture properties whereas in the former case the initial slope decreases with decreasing filling efficiency (compare Figs. 9 b and 11 b).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Findingnone given

    Other loading cases indicate that the model is able to predict the behavior under complex sequences of mixed-mode loading, unloading and healing.

    “Other loading cases, not shown here for conciseness, indicate that the model is able to predict the behavior under complex sequences of mixed-mode loading, unloading and healing.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    The second peak lies between the original material's fracture strength and the healed material's fracture strength because the original material was not fully damaged before healing and partly contributes to the effective composite fracture strength.

    “The second peak lies between the one of the original material and the healed material since the original material was not fully damaged before healing was activated, hence it partly contributes to the effective (composite) fracture strength.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The characteristics of the initial post-healing response in a force-displacement diagram may be used as an indicator of the filling efficiency of a healing event; an initial response similar to that of the original material corresponds to maximum crack filling efficiency regardless of the fracture properties of the healing material.

    “The simulations also indicate that the characteristics of the initial post-healing response in a forcedisplacement diagram may be used as an indicator of the filling efficiency of a healing event whereby an initial response similar to that of the original material corresponds to maximum crack filling efficiency regardless of the fracture properties of the healing material.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The approach can be extended to account for multiple healing events and is capable of dealing with a complex history of partial crackings and healings.

    “The approach presented in the previous section can be extended to account for multiple healing events.This generalization is capable of dealing with a complex history of (partial) crackings and healings.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The volume fraction w[m](p) of the pth material phase is related to the energy-based damage parameter of that phase prior to the mth healing event, recursively as in Eq. (18).

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    Detailed healing kinetics of a material can be coupled to the present model through fracture properties and crack filling behavior to simulate specific materials.

    “Nonetheless, detailed healing kinetics of a material can be coupled to the present model through fracture properties and crack filling behavior to simulate specific materials.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The model is suitable for analyzing and optimizing existing self-healing materials or for designing new self-healing materials with improved lifetime characteristics based on multiple healing events.

    “It is shown that the model is suitable for analyzing and optimizing existing self-healing materials or for designing new self-healing materials with improved lifetime characteristics based on multiple healing events.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In an extrinsic self-healing system, the healing process is typically activated by cracks that interact with the capsules.

    “In an extrinsic system, the healing process is typically activated by cracks that interact with the capsules ( White et al., 2001; Kessler et al., 2003; Carabat et al., 2015 ).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites White et al., 2001 source
    • cites Kessler et al., 2003 source
    • cites Carabat et al., 2015 source

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given

    The material that fills the crack is typically different from the matrix material for both extrinsic and intrinsic self-healing cases.

    “The material that fills the crack is typically different than the matrix material for both the extrinsic and intrinsic cases.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given

    The proposed crack healing model is a composite-based constitutive model for simulating recovery of fracture properties upon activation of crack healing.

    “The proposed crack healing model is a composite-based constitutive model for simulating the recovery of fracture properties upon activation of crack healing.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: A partially damaged area that has been healed contains contributions from both the original material and the healing material.

  • May combine two claims.

    Interpretationnone given

    The model can simulate property recovery after multiple healing events and can handle different fracture properties for the healing material compared to the original material.

    “The model is capable of simulating property recovery after multiple healing events and is also able to handle different fracture properties for the healing material as compared to that of the original material.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Recovery of load-carrying capability as a function of healing parameters, crack length and capsule properties has not received adequate attention in the literature yet.

  • Classified as probably not a substantial claim.

    Interpretationnone given

    The proposed cohesive relation is a composite-type material model that accounts for the properties of both the original and the healing material, which are typically different.

    “The proposed cohesive relation is a composite-type material model that accounts for the properties of both the original and the healing material, which are typically different.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    A bilinear relation captures the essential ingredients of most cohesive relations, namely cohesive strength and fracture energy, which are viewed as variable material properties in the present healing model.

    “a bilinear relation captures the essential ingredients of most cohesive relations, namely the cohesive strength σ c and the fracture energy G c , which are viewed as variable material properties in the present healing model.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationnone given

    The model does not explicitly aim to capture actual healing kinetics, but to simulate recovery of overall load bearing capacity as a function of crack filling and fracture properties of the filling material.

    “It is noted that the model developed here does not explicitly aim to capture the actual healing kinetics, but to simulate the recovery of the overall load bearing capacity as a function of crack filling and fracture properties of the filling material.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The crack healing model does not include healing kinetics explicitly; its focus is to develop a methodology to simulate cracking and recovery of mechanical integrity upon healing.

    “Firstly, the crack healing model does not include healing kinetics explicitly, rather the focus is to develop a methodology to simulate cracking and the recovery of mechanical integrity upon healing.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Study design and conductnone given

    The finite element mesh is sufficiently resolved so that proper discretization of the cohesive zone is ensured.

    “The finite element mesh is sufficiently resolved so that proper discretization of the cohesive zone is ensured.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Other modeling approaches explored in the literature to simulate crack healing behavior are based on the theory of porous media or the discrete element method.

    “Other modeling approaches explored in the literature to simulate crack healing behavior are based on the theory of porous media ( Bluhm et al., 2015 ) or the discrete element method ( Luding and Suiker, 2008; Herbst and Luding, 2008 ).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Bluhm et al., 2015 source
    • cites Luding and Suiker, 2008 source
    • cites Herbst and Luding, 2008 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In general, the elastic and fracture properties of the healing particle and the matrix are different, which decide whether a matrix crack would break the healing particle or not.

    “in general the elastic and fracture properties of the healing particle and the matrix are different, which in fact decide whether a matrix crack would break the healing particle or not.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ponnusami et al. (2015b)

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Crack-particle interaction has been analyzed parametrically in Ponnusami et al. (2015a, 2015b) to generate design guidelines for selecting healing particles in terms of their mechanical properties.

    “Crackparticle interaction, which is a crucial aspect to successfully trigger the healing mechanism, has been analyzed parametrically in Ponnusami et al. (2015a , 2015b) to generate design guidelines for the selection of the healing particles in terms of their mechanical properties.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ponnusami et al. (2015a , 2015b)

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationnone given

    Modeling of the crack gap filling and healing is only done implicitly through the shift in crack opening displacements; the new material is not explicitly modeled as an additional material or mass entering the system.

    “modeling of the crack gap filling and healing is only done implicitly through the shift in crack opening displacements, whereby the new material is not explicitly modeled as an additional material (or mass) entering the system.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisenone given

    In these continuum damage models, the internal variables describing degradation and healing refer to effective behavior of unresolved cracking and healing events, and details at the level of individual cracks are not explicitly taken into account.

    “The common feature of these models is that the internal variables describing the continuum degradation and healing of the material refer to the effective behavior of (unresolved) cracking and healing events.Correspondingly, details at the level of individual cracks are not explicitly taken into account.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    The Schimmel and Remmers model has limitations regarding multiple healing events and one-dimensionality.

    “Some limitations of the model are with regard to the multiple healing events and their one-dimensionality.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Schimmel and Remmers (2006)

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In Schimmel and Remmers (2006), a Mode I exponential cohesive zone model is proposed to simulate crack healing by introducing a jump in crack opening displacement.

    “In Schimmel and Remmers (2006) a Mode I exponential cohesive zone model is proposed to simulate crack healing by introducing a jump in crack opening displacement.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Schimmel and Remmers (2006)

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In Maiti and Geubelle (2006), crack healing is simulated through an artificial crack closure technique by introducing a wedge into the crack.

    “In Maiti and Geubelle (2006) , crack healing is simulated through an artificial crack closure technique by introducing a wedge into the crack.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Maiti and Geubelle (2006) source

  • May combine two claims.

    Interpretationreasoning

    If the crack propagates along the original material because the healing material is stronger, the recovered load-displacement response would be similar to the one with the same fracture properties.

    “However, the recovered load-displacement response would be similar to the one with the same fracture properties, as the crack is traversing along the original material.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In Ural et al. (2009), a cohesive zone model for fatigue crack growth is developed that also considers crack retardation during unloading regimes.

    “In Ural et al. (2009) , a cohesive zone model for fatigue crack growth is developed, which also considers crack retardation during unloading regimes.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ural et al. (2009) source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The Alsheghri and Al-Rub model takes into account the effect of temperature, resting time and crack closure on healing behavior.

    “The model takes into account the effect of various parameters such as temperature, resting time and crack closure on the healing behavior.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Alsheghri and Al-Rub (2015) source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In one extrinsic self-healing system reported in the literature, the healing agent within the particle produces healing material through increase in volume by oxidation under high temperature conditions.

    “in one of the extrinsic self-healing systems reported in the literature, the healing agent within the particle produces healing material through increase in volume by oxidation under high temperature conditions ( Sloof et al., 2015; Ponnusami et al., 2015a ).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Sloof et al., 2015 source
    • cites Ponnusami et al., 2015a

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationnone given

    Distinct cohesive relations can be used at different spatial locations, allowing phase-specific fracture properties for the healing agent and the healing material.

    “Distinct cohesive relations can be used at different spatial locations (matrix, particle, matrix-particle interface), hence phase-specific fracture properties can be specified for the healing agent inside the particle and the healing material that appears in the cracks after activation of the healing mechanism.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The developed framework does not explicitly model the crack healing kinetics; the results of the healing process are provided as input parameters to the model.

    “The developed framework does not explicitly model the crack healing kinetics, rather the results of the healing process are provided as input parameters to the model.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    The model can be applied for either extrinsic or intrinsic self-healing material systems with an appropriate coupling to healing kinetics in each case.

    “The model can be applied for either extrinsic or intrinsic self-healing material systems with an appropriate coupling to healing kinetics in each case.”
    Quote in the paperNot a substantial claim
36 of 36

  • The authors state this as an assumption.

    Whenever the healing process is activated at a location within the cohesive crack, the resting period is sufficiently long that complete healing occurs.

    “whenever the healing process is activated at a location within the cohesive crack, the resting period is assumed to be sufficiently long such that complete healing occurs.”

  • The authors state this as an assumption.

    A partially damaged area that has been healed contains contributions from both the original material and the healing material.

    “it is assumed that a partially damaged area that has been healed contains contributions from both the original material and the healing material.”

  • The authors state this as an assumption.

    The factor w(1) is given by the value of the energy-based damage parameter at the instance of healing activation, D(0)*.

    “the proposed constitutive model assumes that the factor w (1) is given by the value of the energy-based damage parameter at the instance of healing activation, D (0) *”

  • The authors state this as an assumption.

    If healing is activated in a partially damaged surface, the process occurs at constant stress provided there is no change in the external loading.

    “it is assumed that the process occurs at constant stress provided there is no change in the external loading.”

  • The authors state this as an assumption.

    The healing material transmits zero load at the instant of healing activation.

    “the healing material is assumed to transmit zero load at the instant of healing activation.”

  • The authors state this as an assumption.

    The volume fraction w[m](p) of the pth material phase is related to the energy-based damage parameter of that phase prior to the mth healing event, recursively as in Eq. (18).

    “it is assumed that the volume fraction w [ m ]( p ) of the p th material phase is related to the energy-based damage parameter of that phase prior to the m th healing event, which can be expressed recursively as”

  • The authors state this as an assumption.

    In all simulations, complete healing occurs at the end of the zero loading-rate time period (rest period).

    “In all the simulations, it is assumed that complete healing occurs at the end of the zero loading-rate time period (rest period).”

  • The paper relies on this without support.

    Recovery of load-carrying capability as a function of healing parameters, crack length and capsule properties has not received adequate attention in the literature yet.

    “recovery of load-carrying capability as a function of healing parameters, crack length and capsule properties is a subject of importance but has not received adequate attention in the literature yet.”

  • The paper relies on this without support.

    The capability of simulating multiple healing events is not demonstrated in many of the abovementioned studies.

    “the capability of simulating multiple healing events is not demonstrated in many of the abovementioned studies”

  • The authors state this as an assumption.

    Any additional substance required for the healing process is readily available in the matrix material.

    “The present simulation assumes that any additional substance required for the process is readily available in the matrix material (e.g., free oxygen transported by diffusion required for oxidation as found in self-healing thermal barrier coatings Sloof et al., 2015 ).”

  • The authors state this as an assumption.

    The two-dimensional plane strain model is qualitatively representative of a spherical particle albeit with a different volume fraction.

    “Despite this interpretation, the model is assumed to be qualitatively representative of a spherical particle albeit with a different volume fraction.”

  • The authors state this as an assumption.

    Both the matrix and the healing particle are isotropic and linearly elastic up to fracture.

    “Both the matrix and the healing particle are assumed to be isotropic and linearly elastic up to fracture.”

  • The authors state this as an assumption.

    The interface between the particle and the matrix is perfectly bonded and interface fracture does not occur.

    “The interface between the particle and the matrix is assumed to be perfectly bonded and interface fracture is taken not to occur.”

  • The authors state this as an assumption.

    In the previous subsection, the healing particle upon fracture releases an amount of healing agent sufficient for complete filling of the crack opening volume.

    “In the previous subsection, it was assumed that the healing particle, upon fracture, releases an amount of healing agent (denoted as V h ) that is sufficient for complete filling of the crack opening volume (or crack opening area in two dimension, denoted as V c ).”

  • The authors state this as an assumption.

    Filling takes place in the zone adjacent to the healing particle.

    “As indicated in the figure, filling is assumed to take place in the zone adjacent to the healing particle.”

  • The authors state this as an assumption.

    The particle in the unit cell is capable of providing sufficient healing material for two healing events.

    “In this section, it is assumed that the particle in the unit cell shown in Fig. 7 is capable of providing sufficient healing material for two healing events.”

  • The authors state this as an assumption.

    The ratio of crack opening volume to available healing material volume is 1 for both healing events, resulting in complete filling of the crack.

    “The ratio of crack opening volume (or area) to the available healing material volume is assumed to be 1 for both healing events, resulting in complete filling of the crack.”

  • The authors state this as an assumption.

    The healing material has the same fracture properties in both loaded and unloaded healing conditions.

    “although this conclusion is based on the assumption that the healing material has the same fracture properties in both cases, which may not be necessarily the case in some self-healing materials.”
18 of 18

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

  • Particle area fraction is reported as 14% instead of about 1.4%

    Major

    For a circular particle of diameter 10 μm in a 75 μm × 75 μm cell, the in-plane area fraction is π(10/2)2/752 ≈ 1.4%, not 14%. Even the diameter-to-cell-length percentage is only 13.33%; it is not an area fraction.

    Reported 14 · recomputed 13.333333

1 of 1

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Authors
Ponnusami, S. A., Krishnasamy, J., Turteltaub, S., & van der Zwaag, S.
Affiliations
Delft University of Technology (NL)
Corresponding author
Turteltaub, Sergio
ORCID
Venue
International Journal of Solids and Structures
Publisher
Elsevier BV
Published
2018-03
Volume
134
Pages
249-263
ISSN
0020-7683 (ISSN-L)
DOI
10.1016/j.ijsolstr.2017.11.004
OpenAlex
W2767961421
Semantic Scholar
3e6ba443f63e4332dad01abb4a67f20ead7394c8
Cited by
63
References
42
Citations by year
2026: 2 · 2025: 9 · 2024: 4 · 2023: 8 · 2022: 9 · 2021: 6 · 2020: 12 · 2019: 6 · 2018: 7
FWCI
3.82
Type
journal article
Language
en
Open access
Licence
Locations
  • International Journal of Solids and Structures (publishedVersion)
  • City Research Online (City University London) (acceptedVersion)
  • Research Repository (Delft University of Technology) (submittedVersion, cc-by-nc-nd)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
Funders
  • Rijksdienst voor Ondernemend Nederland (SHM01021)
  • Agentschap NL
  • Seventh Framework Programme (309849)
Topics
  • Physical Sciences › Materials Science › Polymers and Plastics › Polymer composites and self-healing
  • Physical Sciences › Engineering › Mechanics of Materials › Numerical methods in engineering
  • Physical Sciences › Engineering › Mechanics of Materials › Mechanical Behavior of Composites
Keywords
self-healing materials, crack healing, cohesive zone model, composite model, extended finite element method, fracture mechanics, constitutive modeling

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-09.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-09.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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