loads were obtained using both models provided small displacement assumption is valid since
crack initiation occurs just before specimen final failure. Otherwise, the CC was found to provide
conservative failure loads compared to CDM.

Sapora, Efremidis, et al. (2021) confronted Gradient Elasticity (GE) model and CC to predict borehole crack initiation under uniform biaxial loading and pressure. The CC can be considered as local in the constitutive law and non-local in the failure criterion, since crack initiation occurs when stress and energy conditions are simultaneously met at a certain distance of the stress concentration or singular point. On the opposite, GE model is nonlocal in the constitutive law and local in the failure criterion, since it considers the stress concentration factor as the governing failure parameter. It is based on a characteristic internal length which quantifies the distance over which non-locality acts, thus smoothing high variations in the elastic stress field. It appears to be not applicable below a threshold size as the internal length becomes comparable to the hole radius. Sapora, Efremidis, et al. (2021) showed that almost identical failure stress predictions could be obtained provided the internal length in the GE model is properly chosen compared to the material characteristic length.

Doitrand, Henry, Lube, et al. (2021) assessed fracture size effect based on the CC or Weibull approaches. Whereas both approaches well reproduced the size effect in gypsum specimens, only the CC succeeded in correctly predicting the failure stress variation for ZnO specimens. Fracture surface observations actually revealed that the critical pore size range lied around 50–250 microns whatever the specimen size, not retrieving increasing critical pore size with increasing specimen size (Uhl et al. 2022). It thus questioned the basis assumption of increasing critical flaw size with increasing specimen size associated to Weibull’s approach. The CC and Weibull approach were combined by Leguillon, Martin, and Lafarie-Frenot (2015) to predict ceramic bending failure and rationalize the differences between the measured tensile and bending strength, concluding that only the tensile strength can be considered as a material parameter.

5 CC applications

The CC is particularly adapted to assess crack initiation in many configurations already described
by Weißgräuber, Leguillon, et al. (2016), such as in presence of pores, holes or cavities (Rosendahl
et al. 2016; Felger et al. 2017a; Sapora et al. 2018; Sapora and Cornetti 2018; Torabi et al. 2018;
Torabi et al. 2017; Carrère et al. 2021; Uhl et al. 2022; Correas et al. 2021; Doitrand and Leguillon
2021; Ferrian et al. 2022; Sapora, Spagnoli, et al. 2023; Sakha et al. 2023), cracks and U-notches
(Picard et al. 2006; Leguillon et al. 2007; Doitrand, Henry, Saad, et al. 2020; Aranda et al. 2023;
Baldassari et al. 2023; Sapora, Ferrian, et al. 2023; Ferrian et al. 2024) or V-notches (Felger and
Becker 2017; Martin et al. 2018; Roy Xu and Leguillon 2019), bonded joints or interfaces (Stein
et al. 2016a; Stein et al. 2016b; Muñoz-Reja et al. 2017; Dölling et al. 2019; Felger, Stein, et al. 2019;
Aranda et al. 2020; Birro et al. 2020; Birro et al. 2021; Frey et al. 2021; Dölling et al. 2021) or less
classical applications such as snow slab avalanches prediction (Rosendahl and Weißgräuber 2020).
We herein focus on two particular applications: multi-cracking and small scale failure.

5.1 Multi-cracking

The CC may be applied to predict multiple crack initiations, such as multiple transverse cracks
in laminates (Kashtalyan et al. 2016) or in a stiff inclusion embedded in a soft matrix under a
compressive loading (Quesada et al. 2009). This configuration results in multiple crack initiations
in the inclusion due to an excess of available energy at first crack initiation. A main difficulty that
arises when handling multiple cracks is related to the number of possible initiation configurations
(2^N for N potential crack locations). Actually, the number of possible initiation configurations
can be reduced by only considering potential interactions between two cracks that are close
to each other. For instance, Doitrand, Fagiano, Hild, et al. (2017) showed that it is necessary
to include the initiation and propagation of both cracks in the energy balance to consider the
interaction between two cracks that are close to each other. Nevertheless, they highlighted
that the first crack has a negligible influence on the second crack initiation if both cracks are
separated by more than 1 mm in a woven composite. Based on this observation, it was possible to
The CC predicts that force-control or displacement-control should lead to significant
differences in crack initiation failure load for specimens small with respect to the material
characteristic length. Experimental validation based on small scale specimen or in materials
exhibiting large material characteristic lengths is still missing.

So far, the CC has not been applied to time-dependent material behavior, the extension of
crack initiation in visco-elastic/plastic materials for instance is still awaited.
reduce the number of possible configurations to assess the initiation and propagation of 14 cracks in a woven composite representative volume element by considering the interactions between only 6 pairs of cracks.

Another strategy was employed by Leguillon et al. (2016) to predict multiple surface cracks in an oxidized polymer under bending. It consists in modeling a periodic array of cracks by a representative cell (RC) containing a single crack. As a consequence, the spacing between two cracks is determined by the RC length and the interaction between two neighbor cracks is considered through periodic boundary conditions. Crack density increase is then obtained by crack network subdivision through adding a second crack in the RC. The same approach was also used to assess multi-cracking in coatings or thin layers (Leguillon et al. 2017; Leguillon and Martin 2018; Coleman et al. 2020), inclined facet array initiation ahead of a parent crack front under mode I+III loading (Doitrand and Leguillon 2018c) or thermal shock-induced multi-cracking (Faria Ricardo et al. 2020).

## 5.2 Small scale fracture

There is no limitation to address small scale specimen fracture using the CC. In practice, fracture of small scale specimens may rather be driven by the energy criterion (Leguillon 2002) since the available stored energy in the system depends on the specimen volume. For instance, micron-scale alumina platelet apparent bending strength much larger than its tensile strength was measured experimentally (Feilden et al. 2017), due to failure mainly being driven by the energy criterion, and thus the material critical ERR (Doitrand, Henry, Chevalier, et al. 2020). Microscopic scale interface crack initiation in nacre-like composites made of similar alumina platelets embedded in a secondary glassy phase acting as an interface between the platelets was also addressed using the CC (Doitrand, Henry, Saad, et al. 2020; Duminy et al. 2023). Duminy et al. (2023) highlighted interface crack containment phenomenon that resulted in interface crack initiation being driven by the energy criterion.

Situations where the failure stress exceeds the critical stress were also encountered at the atomic scale by means of molecular simulations of graphene failure initiation (Brochard et al. 2016), the obtained failure behavior was consistent with the one predicted by the CC.

Gallo and Sapora (2020) implemented the CC to predict crack initiation of single crystal silicon notched cantilever beam tested in a transmission electron microscope. Whereas the CC correctly provided the experimentally measured failure loads, they highlighted a strong deviation of failure loads predicted by LEFM compared to experimentally measured loads due to the small studied scale. Crack initiation in micro-scale cantilever beam was also addressed by Doitrand, Henry, Zacharie-Aubrun, et al. (2020) and Jiménez-Alfaro and Leguillon (2021). Jiménez-Alfaro and Leguillon (2021) highlighted the limitation of the MA approach at small scales when the assumption for crack length smallness with respect to the studied structure is no longer valid. They also showed that small scale specimen fracture is actually weakly sensitive to the material tensile strength. Duminy et al. (2024) implemented the CC to predict crack initiation in millimetre-scale samples. The proposed implementation was based on boundary conditions taken from displacement fields measured by digital image correlation, which enabled the inverse identification of fracture properties.

## 6 Conclusion and perspectives

Among the challenges mentioned in a previous review paper by Weißgraeber, Leguillon, et al. (2016), several major advances have been proposed such as the CC application in 3D, extension to non linearities and fatigue, or considering dynamic loading or kinetic energy variation during crack initiation. The CC has also been successfully confronted to other fracture approaches, thus enabling using them in a complementary manner. Some questions are nevertheless still awaiting answers or further analysis.

If the energy balance, from which the energy criterion derives, seems difficult to refute, there are more possibilities for the stress criterion. Beyond the classical discussion about averaging or not the stress, the use of a strain criterion instead of a stress criterion could also be discussed.
References

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Campagnolo, A., F. Berto, and D. Leguillon (2016). "Fracture assessment of sharp V-notched components under Mode II loading: a comparison among some recent criteria". *Theoretical and Applied Fracture Mechanics* 85, pp. 217–226. doi: https://doi.org/10.1016/j.tafmec.2016.02.001

Campagnolo, A., F. Berto, S. Razavi, and M. Ayatollahi (2017). "Some recent criteria for brittle fracture prediction under in-plane shear loading". *Procedia Structural Integrity* 3, pp. 110–118. doi: https://doi.org/10.1016/j.prostr.2017.04.019
Although similar results can be expected with respect to stress criterion for linear elastic materials, it could bring significant differences in case of nonlinear material behavior, for instance metals exhibiting plasticity or 3D printed materials.

How to define the crack shapes in configurations where failure is controlled by the energy criterion? Are the stress isocontour-based crack shapes still valid in such configurations? The definition of crack shapes remains a crucial point to further develop 3D CC applications. Further experimental confrontation of the 3D crack shapes based on stress isovalues would be necessary, which requires determining stable crack initiation configurations with no unstable crack propagation after initiation.

Experimental evidences of sudden crack jumps at initiation have been given, which supports the CC results that a crack initiates over a finite length. Nevertheless, in many situations this jump includes both crack initiation and subsequent unstable crack propagation. Even with a rapid camera, it seems difficult to separate both phases experimentally. Therefore, experimental results in stable crack initiation configurations, driven by the energy criterion, are awaited to definitely confirm the existence of a crack jump solely corresponding to crack initiation.

Regarding the crack jump, despite the recent advances to consider the dynamic crack formation resulting in a kinetic energy increase, the dynamic extension of the CC requires the knowledge of the crack velocity profile. A challenge will consist in either determining it experimentally or predicting it numerically, which seems unavoidable to make this approach applicable without adding another parameter to identify.

The CC predicts that force-control or displacement-control should lead to significant differences in crack initiation failure load for specimens small with respect to the material characteristic length. Experimental validation based on small scale specimen or in materials exhibiting large material characteristic lengths is still missing.

So far, the CC has not been applied to time-dependent material behavior, the extension of crack initiation in visco-elastic/plastic materials for instance is still awaited.

Finally, there is a need for computational implementations of the coupled criterion. Even if some tools are already existing and available (Doitrand, Martin, et al. 2020), a more general implementation tool would allow extending the application of the coupled criterion to many complex problems and widen the user community.

## References

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Acary, V. and Y. Monerie (2006). *Nonsmooth fracture dynamics using a cohesive zone approach*. Research Report RR-6032. INRIA. 56 pp. [HAL].

Ambati, M., T. Gerasimov, and L. De Lorenzis (2015). Phase-field modeling of ductile fracture. *Computational Mechanics* 55(5):1017–1040. [DOI].

Aranda, M., I. G. García, A. Quintanas-Corominas, and J. Reinoso (2023). Crack impinging on a curved weak interface: Penetration or deflection? *Journal of the Mechanics and Physics of Solids* 178:105326. [DOI], [OA].

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Bourdin, B., G. Francfort, and J.-J. Marigo (2000). Numerical experiments in revisited brittle fracture. *Journal of the Mechanics and Physics of Solids* 48(4):797-826. [DOI].

Brochard, L., I. G. Tejada, and K. Sab (2016). From yield to fracture, failure initiation captured by molecular simulation. *Journal of the Mechanics and Physics of Solids* 95:632-646. [DOI], [HAL].

Campagnolo, A., F. Berto, and D. Leguillon (2016). Fracture assessment of sharp V-notched components under Mode II loading: a comparison among some recent criteria. *Theoretical and Applied Fracture Mechanics* 85:217-226. [DOI].

Campagnolo, A. and A. Sapora (2021). A FFM analysis on mode III static and fatigue crack initiation from sharp V-notches. *Engineering Fracture Mechanics* 258:108063. [DOI].

Carpinteri, A., P. Cornetti, N. Pugno, and A. Sapora (2011). The problem of the critical angle for edge and center V-notched structures. *European Journal of Mechanics - A/Solids* 30(3):281-285. [DOI], [HAL].

Carrère, N., A. Doitrand, É. Martin, and D. Leguillon (2021). Theoretical study based on 2D assumptions of the influence of small pores on crack initiation in adhesively bonded joints. *International Journal of Adhesion and Adhesives* 111:102979. [DOI], [OA].

Carrère, N., É. Martin, and D. Leguillon (2015). Comparison between models based on a coupled criterion for the prediction of the failure of adhesively bonded joints. *Engineering Fracture Mechanics* 138:185-201. [DOI].

Catalanotti, G. and P. Camanho (2013). A semi-analytical method to predict net-tension failure of mechanically fastened joints in composite laminates. *Composites Science and Technology* 76:69-76. [DOI], [OA].

Chao Correas, A., P. Cornetti, M. Corrado, and A. Sapora (2022). Finite Fracture Mechanics extension to dynamic loading scenarios. *International Journal of Fracture* 239(2):149-165. [DOI], [OA].

Chao Correas, A., M. Corrado, A. Sapora, and P. Cornetti (2021). Size-effect on the apparent tensile strength of brittle materials with spherical cavities. en. *Theoretical and Applied Fracture Mechanics* 116:103120. [DOI], [OA].

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Coleman, K., R. Bermejo, D. Leguillon, and S. Trolier-McKinstry (2020). Thickness Dependence of crack initiation and propagation in stacks for piezoelectric microelectromechanical systems. *Acta Materialia* 191:245-252. [DOI], [OA].

Cornetti, P., V. Mantič, and A. Carpinteri (2012). Finite Fracture Mechanics at elastic interfaces. *International Journal of Solids and Structures* 49(7-8):1022-1032. [DOI], [OA].

Cornetti, P., M. Muñoz-Reja, A. Sapora, and A. Carpinteri (2019). Finite Fracture Mechanics and cohesive crack model: weight functions vs. cohesive laws. *International Journal of Solids and Structures* 156-157:126-136. [DOI], [OA].

Cornetti, P. and A. Sapora (2019). Penny-shaped cracks by Finite Fracture Mechanics. *International Journal of Fracture* 219(1):153-159. [DOI].

Cornetti, P., A. Sapora, and A. Carpinteri (2016). Short cracks and V-notches: Finite Fracture Mechanics vs. Cohesive Crack Model. *Engineering Fracture Mechanics* 168:2-12. [DOI], [OA].

Cornetti, P., M. Corrado, L. D. Lorenzis, and A. Carpinteri (2015). An analytical cohesive crack modeling approach to the edge debonding failure of FRP-plated beams. *International Journal of Solids and Structures* 53:92-106. [DOI], [OA].

Cornetti, P., N. Pugno, A. Carpinteri, and D. Taylor (2006). Finite fracture mechanics: A coupled stress and energy failure criterion. *Engineering Fracture Mechanics* 73(14):2021-2033. [DOI].

Correas, A. C., M. Corrado, A. Sapora, and P. Cornetti (2021). Spherical voids by finite fracture mechanics. *Procedia Structural Integrity* 33:788-794. [DOI], [OA].

Dally, J., W. Fourney, and G. Irwin (1985). On the uniqueness of the stress intensity factor-crack velocity relationship. *International Journal of Fracture* 27(3):159-168. [DOI].

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Doitrand, A., R. Estevez, and D. Leguillon (2019b). "Experimental characterization and numerical modeling of crack initiation in rhombus hole PMMA specimens under compression". *European Journal of Mechanics A/Solids* 76, pp. 290-299. DOI: https://doi.org/10.1016/j.euromechsol.2019.04.013

Doitrand, A., C. Fagiano, N. Carrére, V. Chiaruttini, and M. Hirsekorn (2017a). "Damage onset modeling in woven composites based on a coupled stress and energy criterion". *Engineering Fracture Mechanics* 169, 189-200. DOI: https://doi.org/10.1016/j.engfracmech.2016.11.021

Doitrand, A., C. Fagiano, F. Hild, V. Chiaruttini, A. Mavel, and M. Hirsekorn (2017b). "Mesoscale analysis of damage growth in woven composites". *Composites: Part A* 96, 77-88. DOI: https://doi.org/10.1016/j.compositesa.2017.02.018

Doitrand, A., R. Henry, J. Chevalier, and S. Meille (2020a). "Revisiting the strength of micron-scale ceramic platelets". *Journal of the American Ceramic Society* 103, 6991-7000. DOI: https://doi.org/10.1111/jace.17148

Doitrand, A., R. Henry, T. Lube, and S. Meille (2021b). "Size effect assessment by Weibull's approach and the coupled criterion". *Engineering Fracture Mechanics* 256, p. 107979. DOI: https://doi.org/10.1016/j.engfracmech.2021.107979

Doitrand, A., R. Henry, and S. Meille (2021c). "Brittle material strength and fracture toughness estimation from four-point bending test". *Journal of Theoretical, Computational, and Applied Mechanics*. DOI: https://doi.org/10.46298/jtcam.6753

Doitrand, A., R. Henry, H. Saad, S. Deville, and S. Meille (2020b). "Determination of interface fracture properties by micro- and macro-scale experiments in nacre-like alumina". *Journal of the Mechanics and Physics of Solids* 145, p. 104143. DOI: https://doi.org/10.1016/j.jmps.2020.104143

Doitrand, A., R. Henry, I. Zacharie-Aubrun, J. Gatt, and S. Meille (2020c). "UO₂ micron scale specimen fracture: Parameter identification and influence of porosities". *Theoretical and Applied Fracture Mechanics* 108, p. 102665. DOI: https://doi.org/10.1016/j.tafmec.2020.102665

Doitrand, A. and D. Leguillon (2018a). "3D application of the coupled criterion to crack initiation prediction in epoxy/aluminum specimens under four point bending". *International Journal of Solids and Structures* 143, pp. 175-182. DOI: https://doi.org/10.1016/j.ijsolstr.2018.03.005

Doitrand, A. and D. Leguillon (2018b). "Comparison between 2D and 3D applications of the coupled criterion to crack initiation prediction in scarf adhesive joints". *International Journal of Adhesion and Adhesives* 85, pp. 69-76. DOI: https://doi.org/10.1016/j.ijadhadh.2018.05.022

Doitrand, A. and D. Leguillon (2018c). "Numerical modeling of the nucleation of facets ahead of a primary crack under modeI+III". *International Journal of Fracture* 123(1), pp. 37-50. DOI: https://doi.org/10.1007/s10704-018-0305-8
double cantilever beam: A comparison between cohesive crack modeling and finite fracture mechanics. *International Journal of Solids and Structures* 124:57–72. [DOI].

Djeumen, E., G. Molnár, N. Tardif, M. Coret, J. Desquines, T. Taurines, and M.-C. Baietto (2022). Modeling diffusive phase transformation and fracture in viscoplastic materials. *International Journal of Solids and Structures* 252:111757. [DOI], [OA].

Doitrand, A., R. Henry, T. Lube, and S. Meille (2021). Size effect assessment by Weibull's approach and the coupled criterion. *Engineering Fracture Mechanics* 256:107979. [DOI], [OA].

Doitrand, A., R. Henry, H. Saad, S. Deville, and S. Meille (2020). Determination of interface fracture properties by micro- and macro-scale experiments in nacre-like alumina. *Journal of the Mechanics and Physics of Solids* 145:104143. [DOI], [OA].

Doitrand, A., R. Henry, I. Zacharie-Aubrun, J.-M. Gatt, and S. Meille (2020). UO₂ micron scale specimen fracture: Parameter identification and influence of porosities. *Theoretical and Applied Fracture Mechanics* 108:102665. [DOI], [OA].

Doitrand, A., D. Leguillon, and R. Estevez (2020). Experimental determination of generalized stress intensity factors from full-field measurements. *Engineering Fracture Mechanics* 230:106980. [DOI], [OA].

Doitrand, A., P. Cornetti, A. Sapora, and R. Estevez (2021). Experimental and theoretical characterization of mixed mode brittle failure from square holes. *International Journal of Fracture* 228(1):33–43. [DOI], [HAL].

Doitrand, A., R. Estevez, and D. Leguillon (2019a). Comparison between cohesive zone and coupled criterion modeling of crack initiation in rhombus hole specimens under quasi-static compression. *Theoretical and Applied Fracture Mechanics* 99:51–59. [DOI], [HAL].

Doitrand, A., R. Estevez, and D. Leguillon (2019b). Experimental characterization and numerical modeling of crack initiation in rhombus hole PMMA specimens under compression. *European Journal of Mechanics - A/Solids* 76:290–299. [DOI], [OA].

Doitrand, A., C. Fagiano, N. Carrère, V. Chiaruttini, and M. Hirsekorn (2017). Damage onset modeling in woven composites based on a coupled stress and energy criterion. *Engineering Fracture Mechanics* 169:189–200. [DOI], [HAL].

Doitrand, A., C. Fagiano, F. Hild, V. Chiaruttini, A. Mavel, and M. Hirsekorn (2017). Mesoscale analysis of damage growth in woven composites. *Composites Part A: Applied Science and Manufacturing* 96:77–88. [DOI], [HAL].

Doitrand, A., R. Henry, J. Chevalier, and S. Meille (2020). Revisiting the strength of micron-scale ceramic platelets. *Journal of the American Ceramic Society* 103(12):6991–7000. [DOI], [HAL].

Doitrand, A., R. Henry, and S. Meille (2021). Brittle material strength and fracture toughness estimation from four-point bending test. *Journal of Theoretical, Computational and Applied Mechanics*. [DOI], [OA].

Doitrand, A. and D. Leguillon (2018a). 3D application of the coupled criterion to crack initiation prediction in epoxy/aluminum specimens under four point bending. *International Journal of Solids and Structures* 143:175–182. [DOI], [HAL].

Doitrand, A. and D. Leguillon (2018b). Comparison between 2D and 3D applications of the coupled criterion to crack initiation prediction in scarf adhesive joints. *International Journal of Adhesion and Adhesives* 85:69–76. [DOI], [HAL].

Doitrand, A. and D. Leguillon (2018c). Numerical modeling of the nucleation of facets ahead of a primary crack under mode I+III. *International Journal of Fracture* 213(1):37–50. [DOI], [HAL].

Doitrand, A. and D. Leguillon (2021). Asymptotic analysis of pore crack initiation near a free edge. *Theoretical and Applied Fracture Mechanics* 116:103125. [DOI], [OA].

Doitrand, A., D. Leguillon, and É. Martin (2020). Computation of generalized stress intensity factors of 3D singularities. *International Journal of Solids and Structures* 190:271–280. [DOI], [OA].

Doitrand, A., D. Leguillon, G. Molnár, and V. Lazarus (2023). Revisiting facet nucleation under mixed mode I+III loading with T-stress and mode-dependent fracture properties. *International Journal of Fracture* 242(1):85–106. [DOI], [HAL].

Doitrand, A., É. Martin, and D. Leguillon (2020). Numerical implementation of the coupled criterion: Matched asymptotic and full finite element approaches. *Finite Elements in Analysis and Design* 168:103344. [DOI], [OA].
Doitrand, A. and D. Leguillon (2021d). "Asymptotic analysis of pore crack initiation near a free edge". *Theoretical and Applied Fracture Mechanics* 116, p. 103125. doi: https://doi.org/10.1016/j.tafmec.2021.103125

Doitrand, A., D. Leguillon, and R. Estevez (2020d). "Experimental determination of generalized stress intensity factors from full-field measurements". *Engineering Fracture Mechanics* 230, p. 106980. doi: https://doi.org/10.1016/j.engfracmech.2020.106980

Doitrand, A., D. Leguillon, and E. Martin (2020e). "Computation of generalized stress intensity factors of 3D singularities". *International Journal of Solids and Structures* 190, 271–280. doi: https://doi.org/10.1016/j.ijsolstr.2019.11.019

Doitrand, A, D Leguillon, G Molnár, and V Lazarus (2023a). "Revisiting facet nucleation under mixed mode I+III loading with T-stress and mode-dependent fracture properties". *To be published*

Doitrand, A., E. Martin, and D. Leguillon (2020f). "Numerical implementation of the coupled criterion: Matched asymptotic and full finite element approaches". *Finite Element in Analysis and Design* 168, p. 103344. doi: https://doi.org/10.1016/j.finel.2019.103344

Doitrand, A., G. Molnár, R. Estevez, and A. Gravouil (2023b). "Strength-based regularization length in phase field fracture". *Theoretical and Applied Fracture Mechanics* 124, p. 103728. doi: https://doi.org/10.1016/j.tafmec.2022.103728

Doitrand, A., G. Molnár, D. Leguillon, E. Martin, and N. Carrère (2022). "Dynamic crack initiation assessment with the coupled criterion". *European Journal of Mechanics - A/Solids* 93, p. 104483. doi: https://doi.org/10.1016/j.euromechsol.2021.104483

Doitrand, A. and A. Sapora (2020g). "Nonlinear implementation of Finite Fracture Mechanics: A case study on notched Brazilian disk samples". *International Journal of Non-Linear Mechanics* 119, p. 103245. doi: https://doi.org/10.1016/j.ijnonlinmec.2019.103245

Dolling, S., S. Bremm, A. Kohlstetter, J. Felger, and W. Becker (2021). "Predicting thermally induced edge-crack initiation using finite fracture mechanics". *Engineering Fracture Mechanics* 252, p. 107808. doi: https://doi.org/10.1016/j.engfracmech.2021.107808

Dolling, S., S. Bremm, S. Hell, and W. Becker (2019). "A finite fracture mechanics approach for interlaminar crack initiation using the scaled boundary finite element method". *PAMM* 19.1, e201900163. doi: https://doi.org/10.1002/pamm.201900163

Duminy, T., R. Henry, J. Adrien, A. Doitrand, and S. Meille (2023). "Anisotropic fracture in nacre-like alumina". *Theoretical and Applied Fracture Mechanics* 123, p. 103710. doi: https://doi.org/10.1016/j.tafmec.2022.103710

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Ernesto Mendoza-Navarro, L., A. Diaz-Diaz, R. Castañeda-Balderas, S. Hunkeler, and R. Noret (2013). "Interfacial failure in adhesive joints: Experiments and predictions". *International Journal of Adhesion and Adhesives* 44, pp. 36–47. doi: https://doi.org/10.1016/j.ijadhadh.2013.02.004

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Felger, J., P. Rosendahl, D. Leguillon, and W. Becker (2019a). "Predicting crack patterns at bi-material junctions: A coupled stress and energy approach". *International Journal of Solids and Structures* 164, pp. 191–201. doi: https://doi.org/10.1016/j.ijsolstr.2019.01.015

Felger, J., N. Stein, and W. Becker (2017a). "Asymptotic finite fracture mechanics solution for crack onset at elliptical holes in composite plates of finite-width". *Engineering Fracture Mechanics* 182, pp. 621–634. doi: https://doi.org/10.1016/j.engfracmech.2017.05.048

Felger, J., N. Stein, and W. Becker (2017b). "Mixed-mode fracture in open-hole composite plates of finite-width: An asymptotic coupled stress and energy approach". *International Journal of Solids and Structures* 122-123, pp. 14–24. doi: https://doi.org/10.1016/j.ijsolstr.2017.05.039
Doitrand, A., G. Molnár, R. Estevez, and A. Gravouil (2023). Strength-based regularization length in phase field fracture. *Theoretical and Applied Fracture Mechanics* 124:103728. [DOI], [OA].

Doitrand, A., G. Molnár, D. Leguillon, É. Martin, and N. Carrère (2022). Dynamic crack initiation assessment with the coupled criterion. *European Journal of Mechanics - A/Solids* 93:104483. [DOI], [OA].

Doitrand, A. and A. Sapora (2020). Nonlinear implementation of Finite Fracture Mechanics: A case study on notched Brazilian disk samples. *International Journal of Non-Linear Mechanics* 119:103245. [DOI], [OA].

Dölling, S., S. Bremm, A. Kohlstetter, J. Felger, and W. Becker (2021). Predicting thermally induced edge-crack initiation using finite fracture mechanics. *Engineering Fracture Mechanics* 252:107808. [DOI].

Dölling, S., S. Bremm, S. Hell, and W. Becker (2019). A finite fracture mechanics approach for interlaminar crack initiation using the scaled boundary finite element method. *PAMM* 19(1):e201900163. [DOI], [OA].

Duminy, T., A. Doitrand, and S. Meille (2024). Fracture parameter identification by Digital Image Correlation and Finite Fracture Mechanics for millimeter-scale samples. *Engineering Fracture Mechanics* 295:109770. [DOI], [HAL].

Duminy, T., R. Henry, J. Adrien, A. Doitrand, and S. Meille (2023). Anisotropic fracture in nacre-like alumina. *Theoretical and Applied Fracture Mechanics* 123:103710. [DOI], [OA].

Erdogan, F. and G. C. Sih (1963). On the crack extension in plates under plane loading and transverse shear. *Journal of Basic Engineering* 85(4):519-525. [DOI].

Ernesto Mendoza-Navarro, L., A. Diaz-Diaz, R. Castañeda-Balderas, S. Hunkeler, and R. Noret (2013). Interfacial failure in adhesive joints: Experiments and predictions. *International Journal of Adhesion and Adhesives* 44:36-47. [DOI].

Faria Ricardo, L. F., D. Leguillon, G. Parry, and A. Doitrand (2020). Modeling the thermal shock induced cracking in ceramics. *Journal of the European Ceramic Society* 40(4):1513-1521. [DOI], [OA].

Feilden, E., T. Giovannini, N. Ni, C. Ferraro, E. Saiz, L. Vandeperre, and F. Giuliani (2017). Micromechanical strength of individual Al₂O₃ platelets. *Scripta Materialia* 131:55-58. [DOI].

Felger, J., P. L. Rosendahl, D. Leguillon, and W. Becker (2019). Predicting crack patterns at bi-material junctions: A coupled stress and energy approach. *International Journal of Solids and Structures* 164:191-201. [DOI], [OA].

Felger, J., N. Stein, and W. Becker (2017a). Asymptotic finite fracture mechanics solution for crack onset at elliptical holes in composite plates of finite-width. *Engineering Fracture Mechanics* 182:621-634. [DOI].

Felger, J., N. Stein, and W. Becker (2017b). Mixed-mode fracture in open-hole composite plates of finite-width: An asymptotic coupled stress and energy approach. *International Journal of Solids and Structures* 122:123-14-24. [DOI].

Felger, J., N. Stein, C. Frey, and W. Becker (2019). Scaling laws for the adhesive composite butt joint strength derived by finite fracture mechanics. *Composite Structures* 208:546-556. [DOI].

Felger, J. and W. Becker (2017). Asymptotic analysis of notch induced crack nucleation. *PAMM* 17(1):239-240. [DOI], [OA].

Ferrian, F., A. Chao Correas, P. Cornetti, and A. Sapora (2022). Size effects on spheroidal voids by Finite Fracture Mechanics and application to corrosion pits. *Fatigue & Fracture of Engineering Materials & Structures* 46(3):875-885. [DOI], [OA].

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Hamam, Z., N. Godin, P. Reynaud, C. Fusco, N. Carrére, and A. Doitrand (2022). "Transverse Cracking Induced Acoustic Emission in Carbon Fiber-Epoxy Matrix Composite Laminates". *Materials* 15, p. 394. DOI: https://doi.org/10.3390/ma15010394
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García, I. G., B. Carter, A. Ingraffea, and V. Mantič (2016). A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics. *Composites Part B: Engineering* 95:475-487. [DOI].

García, I. G. and D. Leguillon (2012). Mixed-mode crack initiation at a V-notch in presence of an adhesive joint. *International Journal of Solids and Structures* 49(15-16):2138-2149. [DOI], [OA].

García, I. G., V. Mantič, and A. Blázquez (2018). The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics. *International Journal of Fracture* 211(1-2):61-74. [DOI].

García, I. G., V. Mantič, and E. Graciani (2015). Debonding at the fibre-matrix interface under remote transverse tension. One debond or two symmetric debonds? *European Journal of Mechanics - A/Solids* 53:75-88. [DOI].

García, I. G., M. Paggi, and V. Mantič (2014). Fiber-size effects on the onset of fiber-matrix debonding under transverse tension: A comparison between cohesive zone and finite fracture mechanics models. *Engineering Fracture Mechanics* 115:96-110. [DOI].

Gentieu, T., J. Jumel, A. Catapano, and J. Broughton (2018). Size effect in particle debonding: comparisons between finite fracture mechanics and cohesive zone model. *Journal of Composite Materials* 53(14):1941-1954. [DOI], [OA].

Girard, H., A. Doitrand, B. Koohbor, R. Rinaldi, N. Godin, and J. Bikard (2024). "Comparison between 2D and 3D fiber-matrix debonding simulation for inverse identification of interface fracture properties". Preprint. [HAL].

Girard, H., A. Doitrand, B. Koohbor, R. Rinaldi, N. Godin, D. Long, and J. Bikard (2024). Influence of nearby fiber on fiber-matrix debonding: Coupled Criterion prediction and debonding shape determination. *Journal of the Mechanics and Physics of Solids* 183:105498. [DOI], [HAL].

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Hamam, Z., N. Godin, P. Reynaud, C. Fusco, N. Carrère, and A. Doitrand (2022). Transverse Cracking Induced Acoustic Emission in Carbon Fiber-Epoxy Matrix Composite Laminates. *Materials* 15(1):394. [DOI], [OA].

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Jiménez-Alfaro, S. and D. Leguillon (2021). "Finite fracture Mechanics at the micro-scale. Application to bending tests of micro cantilever beams". *Engineering Fracture Mechanics* 258, p. 108012. doi: https://doi.org/10.1016/j.engfracmech.2021.108012

Jiménez-Alfaro, S. and D. Leguillon (2022a). "Modelling of glass matrix composites by the Coupled Criterion and the Matched Asymptotics approach. The role of a single platelet". *Theoretical and Applied Fracture Mechanics* 122, p. 103650. doi: https://doi.org/10.1016/j.tafmec.2022.103650

Jiménez-Alfaro, S., J. Reinoso, D. Leguillon, and C. Maurini (2022b). "Finite Fracture Mechanics from the macro- to the micro-scale. Comparison with the Phase Field model". *Procedia Structural Integrity* 42. 23 European Conference on Fracture, pp. 553-560. doi: https://doi.org/10.1016/j.prostr.2022.12.070

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Kashtalyan, M., I. García, and V. Mantič (2018). "Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates". *International Journal of Solids and Structures* 139-140, pp. 189-199. doi: https://doi.org/10.1016/j.ijsolstr.2018.01.033

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Laschuetza, T. and T. Seelig (2021). "Remarks on dynamic cohesive fracture under static pre-stress - with a comparison to finite fracture mechanics". *Engineering Fracture Mechanics* 242, p. 107466. doi: https://doi.org/10.1016/j.engfracmech.2020.107466
Irwin, G. (1958). Fracture. *Elasticity and Plasticity*. Berlin Heidelberg: Springer, pp 551–590. [DOI].

Jiménez-Alfaro, S. and D. Leguillon (2022). Modelling of glass matrix composites by the Coupled Criterion and the Matched Asymptotics approach. The role of a single platelet. *Theoretical and Applied Fracture Mechanics* 122:103650. [DOI], [OA].

Jiménez-Alfaro, S. and D. Leguillon (2023). Modelling of glass matrix composites by the Coupled Criterion and the Matched Asymptotic Approach. The effect of residual stresses and volume fraction. *Theoretical and Applied Fracture Mechanics* 128:104112. [DOI], [OA].

Jiménez-Alfaro, S., J. Reinoso, D. Leguillon, and C. Maurini (2022). Finite Fracture Mechanics from the macro- to the micro-scale. Comparison with the Phase Field model. *Procedia Structural Integrity* 42:553–560. [DOI], [OA].

Jiménez-Alfaro, S. and D. Leguillon (2021). Finite fracture Mechanics at the micro-scale. Application to bending tests of micro cantilever beams. *Engineering Fracture Mechanics* 258:108012. [DOI], [OA].

Kanninen, M. and C. Popelar (1987). *Advanced Fracture Mechanics*. Vol. 15. Oxford Engineering Science Series. Oxford University Press. ISBN: 9780195035322.

Kashtalyan, M., I. G. García, and V. Mantič (2016). Evolution of Crack Density in Cross-Ply Laminates - Application of a Coupled Stress and Energy Criterion. *Key Engineering Materials* 713:262–265. [DOI].

Kumar, A., B. Bourdin, G. A. Francfort, and O. Lopez-Pamies (2020). Revisiting nucleation in the phase-field approach to brittle fracture. *Journal of the Mechanics and Physics of Solids* 142:104027. [DOI], [OA].

Labossiere, P. E. W. and M. L. Dunn (1999). Stress intensities at interface corners in anisotropic bimaterials. *Engineering Fracture Mechanics* 62(6):555–576. [DOI], [OA].

Labossiere, P. E. W. and M. L. Dunn (2001). Fracture initiation at three-dimensional bimaterial interface corners. *Journal of the Mechanics and Physics of Solids* 49(3):609–634. [DOI].

Laschuetza, T. and T. Seelig (2021). Remarks on dynamic cohesive fracture under static pre-stress – with a comparison to finite fracture mechanics. *Engineering Fracture Mechanics* 242:107466. [DOI].

Le Pavic, J., T. Bonnemains, É. Lolive, G. Stamoulis, D. D. Silva, and D. Thévenet (2020). Failure load prediction of a tubular bonded structures using a coupled criterion. *Theoretical and Applied Fracture Mechanics* 108:102531. [DOI], [OA].

Le Pavic, J., G. Stamoulis, T. Bonnemains, D. Da Silva, and D. Thévenet (2018). Fast failure prediction of adhesively bonded structures using a coupled stress-energetic failure criterion. *Fatigue & Fracture of Engineering Materials & Structures* 42(3):627–639. [DOI], [HAL].

Leguillon, D. (1995). Computation of 3D-Singularities in Elasticity. *Boundary Value Problems and Integral Equations in Nonsmooth Domains* 167:161–170. [HAL].

Leguillon, D. (2011). Determination of the length of a short crack at a V-notch from a full field measurement. *International Journal of Solids and Structures* 48(6):884–892. [DOI].

Leguillon, D. (2014). An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case. *Theoretical and Applied Fracture Mechanics* 74:7–17. [DOI], [HAL].

Leguillon, D., O. Haddad, M. Adamowska, and P. Da Costa (2014). Cracks Pattern Formation and Spalling in Functionalized Thin Films. *Procedia Materials Science* 3:104–109. [DOI], [OA].

Leguillon, D., C. Lacroix, and É. Martin (2000). Interface debonding ahead of a primary crack. *Journal of the Mechanics and Physics of Solids* 48(10):2137–2161. [DOI], [HAL].

Leguillon, D., C. Lacroix, and É. Martin (2001). Crack deflection by an interface - asymptotics of the residual thermal stresses. *International Journal of Solids and Structures* 38(42-43):7423–7445. [DOI], [HAL].

Leguillon, D., M. Lafarie-Frenot, Y. Pannier, and É. Martin (2016). Prediction of the surface cracking pattern of an oxidized polymer induced by residual and bending stresses. *International Journal of Solids and Structures* 91:89–101. [DOI], [OA].

Leguillon, D., J. Laurencin, and M. Dupeux (2003). Failure initiation in an epoxy joint between two steel plates. *European Journal of Mechanics - A/Solids* 22(4):509–524. [DOI], [HAL].

Leguillon, D., É. Martin, O. Ševeček, and R. Bermejo (2015). Application of the coupled stress-energy criterion to predict the fracture behaviour of layered ceramics designed with internal compressive stresses. *European Journal of Mechanics - A/Solids* 54:94–104. [DOI], [HAL].
Le Pavic, J., T. Bonnemains, E. Lolive, G. Stamoulis, D. Da Silva, and D. Thévenet (2020). "Failure load prediction of a tubular bonded structures using a coupled criterion". *Theoretical and Applied Fracture Mechanics* 108, p. 102531. doi: https://doi.org/10.1016/j.tafmec.2020.102531

Le Pavic, J., G. Stamoulis, T. Bonnemains, D. Da Silva, and D. Thévenet (2018). "Fast failure prediction of adhesively bonded structures using a coupled stress-energetic failure criterion". *Fatigue & Fracture of Engineering Materials & Structures* 42.3, pp. 627-639. doi: https://doi.org/10.1111/ffe.12938

Leguillon, D. (1995). "Computation of 3d-singularities in elasticity". *Boundary value problems and integral equations in nonsmooth domains* 167, pp. 161-170

Leguillon, D. (2002). "Strength or toughness? A criterion for crack onset at a notch". *European Journal of Mechanics - A/Solids* 21(1), pp. 61-72. doi: https://doi.org/10.1016/S0997-7538(01)01184-6

Leguillon, D. (2011). "Determination of the length of a short crack at a v-notch from a full field measurement". *International Journal of Solids and Structures* 48.6, pp. 884-892. doi: https://doi.org/10.1016/j.ijsolstr.2010.11.020

Leguillon, D. (2014). "An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case". *Theoretical and Applied Fracture Mechanics* 74, pp. 7-17. doi: https://doi.org/10.1016/j.tafmec.2014.05.004

Leguillon, D., O. Haddad, M. Adamowska, and P. Da Costa (2014). "Cracks Pattern Formation and Spalling in Functionalized Thin Films". *Procedia Materials Science* 3. 20th European Conference on Fracture, pp. 104-109. doi: https://doi.org/10.1016/j.mspro.2014.06.020

Leguillon, D., C. Lacroix, and E. Martin (2000). "Interface debonding ahead of a primary crack". *Journal of the Mechanics and Physics of Solids* 48.10, pp. 2137-2161. doi: https://doi.org/10.1016/S0022-5096(99)00101-5

Leguillon, D., C. Lacroix, and E. Martin (2001). "Crack deflection by an interface – asymptotics of the residual thermal stresses". *International Journal of Solids and Structures* 38.42, pp. 7423-7445. doi: https://doi.org/10.1016/S0020-7683(01)00013-0

Leguillon, D., M. Lafarie-Frenot, Y. Pannier, and E. Martin (2016). "Prediction of the surface cracking pattern of an oxidized polymer induced by residual and bending stresses". *International Journal of Solids and Structures* 91, pp. 89-101. doi: https://doi.org/10.1016/j.ijsolstr.2016.04.019

Leguillon, D., J. Laurencin, and M. Dupeux (2003a). "Failure initiation in an epoxy joint between two steel plates". *European Journal of Mechanics - A/Solids* 22.4, pp. 509-524. doi: https://doi.org/10.1016/S0997-7538(03)00066-4

Leguillon, D., J. Li, and E. Martin (2017a). "Multi-cracking in brittle thin layers and coatings using a FFM model". *European Journal of Mechanics - A/Solids* 63, 14-21. doi: http://dx.doi.org/10.1016/j.euromechsol.2016.12.003

Leguillon, D. and E. Martin (2012a). "Crack nucleation at stress concentration points in composite materials - application to crack deflection by an interface". *Mathematical Methods and Models in Composites*, pp. 401-424. doi: 10.1142/9781848167858_0010

Leguillon, D. and E. Martin (2013a). "The strengthening effect caused by an elastic contrast—part I: the bimaterial case". *International Journal of Fracture* 179, pp. 157-167. doi: https://doi.org/10.1007/s10704-012-9787-y

Leguillon, D. and E. Martin (2013b). "The strengthening effect caused by an elastic contrast—part II: stratification by a thin stiff layer". *International Journal of Fracture* 179(1-2), 169-178. doi: https://doi.org/10.1007/s10704-012-9785-0

Leguillon, D. and E. Martin (2018a). "Prediction of multi-cracking in sub-micron films using the coupled criterion". *International Journal of Fracture* 209 (1), pp. 187-202. doi: https://doi.org/10.1007/s10704-017-0255-6

Leguillon, D., E. Martin, and M. Lafarie-Frenot (2015a). "Flexural vs. tensile strength in brittle materials". *Comptes Rendus Mécanique* 343.4, pp. 275-281. doi: https://doi.org/10.1016/j.crme.2015.02.003

Leguillon, D., E. Martin, O. Sevecek, and R. Bermejo (2018b). "What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation?" *International Journal of Fracture* 212, pp. 86-103. doi: https://doi.org/10.1007/s10704-018-0294-7
Leguillon, D. and S. Murer (2012). Fatigue crack nucleation at a stress concentration point. *CP2012 Conference Proceedings*. Vol. 46. [HAL].

Leguillon, D. and R. Piat (2008). Fracture of porous materials - Influence of the pore size. *Engineering Fracture Mechanics* 75(7):1840-1853. [DOI], [HAL].

Leguillon, D., D. Quesada, C. Putot, and É. Martin (2007). Prediction of crack initiation at blunt notches and cavities - size effects. *Engineering Fracture Mechanics* 74(15):2420-2436. [DOI], [HAL].

Leguillon, D. and E. Sanchez-Palencia (1987). *Computation of Singular Solutions in Elliptic Problems and Elasticity*. Wiley. ISBN: 9780471917571.

Leguillon, D. and Z. Yosibash (2017). Failure initiation at V-notch tips in quasi-brittle materials. *International Journal of Solids and Structures* 122-123:1-13. [DOI], [OA].

Leguillon, D. (2002). Strength or toughness? A criterion for crack onset at a notch. *European Journal of Mechanics - A/Solids* 21(1):61-72. [DOI], [HAL].

Leguillon, D., J. Li, and É. Martin (2017). Multi-cracking in brittle thin layers and coatings using a FFM model. *European Journal of Mechanics - A/Solids* 63:14-21. [DOI], [HAL].

Leguillon, D. and É. Martin (2012). Crack nucleation at stress concentration points in composite materials - application to crack deflection by an interface. *Mathematical Methods and Models in Composites*. World Scientific, pp 401-424. [DOI], [HAL].

Leguillon, D. and É. Martin (2013a). The strengthening effect caused by an elastic contrast—part I: the bimaterial case. *International Journal of Fracture* 179(1-2):157-167. [DOI], [HAL].

Leguillon, D. and É. Martin (2013b). The strengthening effect caused by an elastic contrast—part II: stratification by a thin stiff layer. *International Journal of Fracture* 179(1-2):169-178. [DOI], [HAL].

Leguillon, D. and É. Martin (2018). Prediction of multi-cracking in sub-micron films using the coupled criterion. *International Journal of Fracture* 209 (1):187-202. [DOI], [HAL].

Leguillon, D., É. Martin, and M.-C. Lafarie-Frenot (2015). Flexural vs. tensile strength in brittle materials. *Comptes Rendus. Mécanique* 343(4):275-281. [DOI], [OA].

Leguillon, D., É. Martin, O. Sevecek, and R. Bermejo (2018). What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation? *International Journal of Fracture* 212(1):89-103. [DOI], [HAL].

Leguillon, D. and S. Murer (2008). A Criterion for Crack Kinking Out of an Interface. *Key Engineering Materials* 385-387:9-12. [DOI], [HAL].

Leguillon, D., O. Sevecek, É. Martin, and R. Bermejo (2015). Edge cracking due to a compressive residual stress in ceramic laminates. *Comptes Rendus. Mécanique* 343(3):192-198. [DOI], [OA].

Leguillon, D. and Z. Yosibash (2003). Crack onset at a v-notch. Influence of the notch tip radius. *International Journal of Fracture* 122(1/2):1-21. [DOI], [HAL].

Leite, A., V. Mantič, and F. París (2021). Crack onset in stretched open hole PMMA plates considering linear and non-linear elastic behaviours. *Theoretical and Applied Fracture Mechanics* 114:102931. [DOI].

Li, J., É. Martin, D. Leguillon, and C. Dupin (2018). A finite fracture model for the analysis of multi-cracking in woven ceramic matrix composites. *Composites Part B: Engineering* 139:75-83. [DOI], [HAL].

Li, J. and X.-B. Zhang (2006). A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials. *Engineering Fracture Mechanics* 73(4):505-523. [DOI].

Li, J. and D. Leguillon (2018). Finite element implementation of the coupled criterion for numerical simulations of crack initiation and propagation in brittle or quasi-brittle materials. *Theoretical and Applied Fracture Mechanics* 93:105-115. [DOI], [HAL].

Li, J., D. Leguillon, É. Martin, and X.-B. Zhang (2019). Numerical implementation of the coupled criterion for damaged materials. *International Journal of Solids and Structures* 165:93-103. [DOI], [OA].

Liu, Y., C. Deng, and B. Gong (2020). Discussion on equivalence of the theory of critical distances and the coupled stress and energy criterion for fatigue limit prediction of notched specimens. *International Journal of Fatigue* 131:105326. [DOI].

Lo, Y.-S., M. J. Borden, K. Ravi-Chandar, and C. M. Landis (2019). A phase-field model for fatigue crack growth. *Journal of the Mechanics and Physics of Solids* 132:103684. [DOI], [OA].
Leguillon, D., E. Martin, O. Ševeček, and R. Bermejo (2015b). "Application of the coupled stress-energy criterion to predict the fracture behaviour of layered ceramics designed with internal compressive stresses". *European Journal of Mechanics - A/Solids* 54, pp. 94-104. doi: https://doi.org/10.1016/j.euromechsol.2015.06.008

Leguillon, D. and S. Murer (2012b). "Fatigue crack nucleation at a stress concentration point". *CP2012 Conference Proceedings*. Vol. 46. https://www.gruppofrattura.it/ocs/index.php/esis/CP2012/paper/viewFile/92

Leguillon, D. and R. Piat (2008a). "Fracture of porous materials – Influence of the pore size". *Engineering Fracture Mechanics* 75.7. Critical Distance Theories of Fracture, pp. 1840–1853. doi: https://doi.org/10.1016/j.engfracmech.2006.12.002

Leguillon, D., D. Quesada, C. Putot, and E. Martin (2007). "Prediction of crack initiation at blunt notches and cavities – size effects". *Engineering Fracture Mechanics* 74.15, pp. 2420–2436. doi: https://doi.org/10.1016/j.engfracmech.2006.11.008

Leguillon, D. and E. Sanchez-Palencia (1987). *Computation of Singular Solutions in Elliptic Problems and Elasticity*. Wiley, USA

Leguillon, D. and Z Yosibash (2003b). "Crack onset at a v-notch. Influence of the notch tip radius". *International Journal of Fracture* 122, 1–21. doi: https://doi.org/10.1023/B:FRAC.0000005372.68959.1d

Leguillon, D. and Z. Yosibash (2017b). "Failure initiation at V-notch tips in quasi-brittle materials". *International Journal of Solids and Structures* 122-123, 1–13. doi: https://doi.org/10.1016/j.ijsolstr.2017.05.036

Leguillon, D. and S. Murer (2008b). "A Criterion for Crack Kinking Out of an Interface". *Key Engineering Materials* 385-387, pp. 9–12. doi: https://doi.org/10.4028/www.scientific.net/KEM.385-387.9

Leguillon, D., O. Sevecek, E. Martin, and R. Bermejo (2015c). "Edge cracking due to a compressive residual stress in ceramic laminates". *Comptes Rendus Mécanique* 343.3, pp. 192–198. doi: https://doi.org/10.1016/j.crme.2014.11.001

Leite, A., V. Mantič, and F. París (Aug. 2021). "Crack onset in stretched open hole PMMA plates considering linear and non-linear elastic behaviours". *Theoretical and Applied Fracture Mechanics* 114, p. 102931. doi: https://doi.org/10.1016/j.tafmec.2021.102931

Li, J. and D. Leguillon (2018a). "Finite element implementation of the coupled criterion for numerical simulations of crack initiation and propagation in brittle or quasi-brittle materials". *Theoretical and Applied Fracture Mechanics* 93, pp. 105–115. doi: https://doi.org/10.1016/j.compositesb.2017.11.050

Li, J., D. Leguillon, E. Martin, and X. Zhang (2019). "Numerical implementation of the coupled criterion for damaged materials". *International Journal of Solids and Structures* 165, pp. 93–103. doi: https://doi.org/10.1016/j.ijsolstr.2019.01.025

Li, J., E. Martin, D. Leguillon, and C. Dupin (2018b). "A finite fracture model for the analysis of multi-cracking in woven ceramic matrix composites". *Composites part B* 139, pp. 75–83. doi: https://doi.org/10.1016/j.compositesb.2017.11.050

Li, J. and X. Zhang (2006). "A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials". *Engineering Fracture Mechanics* 73, pp. 505–523. doi: https://doi.org/10.1016/j.engfracmech.2005.09.001

Liu, Y., C. Deng, and B. Gong (2020). "Discussion on equivalence of the theory of critical distances and the coupled stress and energy criterion for fatigue limit prediction of notched specimens". *International Journal of Fatigue* 131, p. 105236. doi: https://doi.org/10.1016/j.ijfatigue.2019.105326

Lo, Y., M. Borden, K. Ravi-Chandar, and C. Landis (2019). "A phase-field model for fatigue crack growth". *Journal of the Mechanics and Physics of Solids* 132, p. 103684. doi: https://doi.org/10.1016/j.jmps.2019.103684

Mantič, V. (2009). "Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion". *International Journal of Solids and Structures* 46.6, pp. 1287–1304. doi: https://doi.org/10.1016/j.ijsolstr.2008.10.036

París, F., ed. (2014). *Prediction of initiation and growth of cracks in composites. Coupled stress and energy criterion of the finite fracture mechanics*
Mantič, V. (2009). Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion. *International Journal of Solids and Structures* 46(6):1287-1304. [DOI], [OA].

Mantič, V. (2014). Prediction of initiation and growth of cracks in composites. Coupled stress and energy criterion of the finite fracture mechanics. *16th European Conference on Composite Materials (ECCM16)* (Sevilla, Spain, July 22-26, 2014). [HAL].

Martin, É. and N. Carrère (2023). A fast procedure to predict the notch strength with the coupled criterion. *Engineering Fracture Mechanics* 284:109257. [DOI].

Martin, É., D. Leguillon, and N. Carrère (2010). A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates. *International Journal of Solids and Structures* 47(9):1297-1305. [DOI], [OA].

Martin, É., D. Leguillon, and N. Carrère (2012). A coupled strength and toughness criterion for the prediction of the open hole tensile strength of a composite plate. *International Journal of Solids and Structures* 49(26):3915-3922. [DOI], [OA].

Martin, É., D. Leguillon, A. Catapano, and N. Carrère (2020). Prediction of interfacial debonding between stiff spherical particles and a soft matrix with the coupled criterion. *Theoretical and Applied Fracture Mechanics* 109:102749. [DOI], [OA].

Martin, É., D. Leguillon, O. Sevecek, and R. Bermejo (2018). Understanding the tensile strength of ceramics in the presence of small critical flaws. *Engineering Fracture Mechanics* 201:167-175. [DOI], [HAL].

Martin, É. and D. Leguillon (2004). Energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites. *International Journal of Solids and Structures* 41(24-25):6937-6948. [DOI], [HAL].

Martin, É., B. Poitou, D. Leguillon, and J. M. Gatt (2008). Competition between deflection and penetration at an interface in the vicinity of a main crack. *International Journal of Fracture* 151(2):247-268. [DOI], [HAL].

Martin, É., T. Vandellos, D. Leguillon, and N. Carrère (2016). Initiation of edge debonding: coupled criterion versus cohesive zone model. *International Journal of Fracture* 199(2):157-168. [DOI], [HAL].

Methfessel, T., C. El Yaakoubi-Mesbah, and W. Becker (2024). Failure analysis of crack-prone joints with Finite Fracture Mechanics using an advanced modeling approach for the adhesive layer. *International Journal of Adhesion and Adhesives* 130:103608. [DOI].

Mirzaei, A., P. Cornetti, and A. Sapora (2023). A novel Finite Fracture Mechanics approach to assess the lifetime of notched components. *International Journal of Fatigue* 173:107659. [DOI], [OA].

Mirzaei, A., A. Mirzaei, M. Shokrieh, A. Sapora, and P. Cornetti (2024). Fatigue life assessment of notched laminated composites: Experiments and modelling by Finite Fracture Mechanics. *Composites Science and Technology* 246:110376. [DOI], [OA].

Mittelman, B. and Z. Yosibash (2014). Asymptotic analysis of the potential energy difference because of a crack at a V-notch edge in a 3D domain. *Engineering Fracture Mechanics* 131:232-256. [DOI].

Mittelman, B. and Z. Yosibash (2015). Energy release rate cannot predict crack initiation orientation in domains with a sharp V-notch under mode III loading. *Engineering Fracture Mechanics* 141:230-241. [DOI].

Modniks, J., E. Spārniņš, J. Andersons, and W. Becker (2015). Analysis of the effect of a stress raiser on the strength of a UD flax/epoxy composite in off-axis tension. *Journal of Composite Materials* 49(9):1071-1080. [DOI].

Molnár, G., A. Doitrand, R. Estevez, and A. Gravouil (2020). Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion. *Theoretical and Applied Fracture Mechanics* 109:102736. [DOI], [OA].

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**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the authors—the copyright holder. To view a copy of this license, visit creativecommons.org/licenses/by/4.0.

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**Authors' contributions** All authors conceived of the study and participated in its design, coordination, and critical review of the manuscript. All authors read and approved the final manuscript.

**Competing interests** The authors declare that they have no competing interests.

**Journal's Note** JTCAM remains neutral with regard to the content of the publication and institutional affiliations.
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**Authors' contributions** All authors conceived of the study and participated in its design, coordination, and critical review of the manuscript. All authors read and approved the final manuscript.

**Competing interests** The authors declare that they have no competing interests.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a full copy of this license, visit http://creativecommons.org/licenses/by/4.0/.