Mechanical behavior of adhesive joints: A review on modeling techniques

Mechanical behavior of adhesive joints: A review on modeling techniques

Maximilian Ries

Institute of Applied Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany.

DOI:

https://doi.org/10.7494/cmms.2024.4.1010

Abstract:

In the pursuit of lighter designs, many industries are shifting from conventional fasteners to adhesive joints, which offer a better strength-to-weight ratio and facilitate the use of fiber-reinforced polymers. However, modeling adhesive joints presents major challenges due to the complex behavior of polymeric adhesives and the microstructural changes induced by the substrates. As a result, various simulation methods have been developed to capture the behavior of adhesive joints across different scales. Molecular dynamics studies address atomistic and nanoscale phenomena, while continuum approaches — such as the finite element method, cohesive zone models, and peridynamics — focus on meso and macro scales. Additionally, multiscale methods combine particle and continuum approaches to provide a more comprehensive understanding of the adhesive bond behavior. This review paper offers an overview of the most relevant numerical methods employed to examine the mechanical behavior of adhesive joints and illustrates the simulations’ applications through examples from the literature.

Cite as:

Ries, M. (2024). Mechanical behavior of adhesive joints: A review on modeling techniques. Computer Methods in Materials Science, 24(4), 5-35. https://doi.org/10.7494/cmms.2024.4.1010

Article (PDF):

Keywords:

Adhesive joint, Modeling techniques, Mechanical behavior

References:

Abdalla, A. M. A., Elmoghazy, Y. H., Sarkon, G. K., Gazioglu, A., Sabry, O. K., Sawelih, A. A., Al Sharif, A., Wehbi, H., AliAbd, A. Y., Sahmani, S., & Safaei, B. (2025). Exploring the impact of graphene nanoplatelets on adhesive mechanicalstrength: A comprehensive investigation into single-lap joint elastoplastic behavior via cohesive zone method. InternationalJournal of Adhesion and Adhesives, 138, 103908. https://doi.org/10.1016/j.ijadhadh.2024.103908.

 Adams, R. D., Cowap, J. W., Farquharson, G., Margary, G. M., & Vaughn, D. (2009). The relative merits of the Boeing wedgetest and the double cantilever beam test for assessing the durability of adhesively bonded joints, with particular referenceto the use of fracture mechanics. International Journal of Adhesion and Adhesives, 29(6), 609–620. https://doi.org/10.1016/j.ijadhadh.2009.02.010.

 Africa, P. C., Arndt, D., Bangerth, W., Blais, B., Fehling, M., Gassmöller, R., Heister, T., Heltai, L., Kinnewig, S., Kronbichler,M., Maier, M., Munch, P., Schreter-Fleischhacker, M., Thiele, J. P., Turcksin, B., Wells, D., & Yushutin, V.(2024). The deal.II library, version 9.6. Journal of Numerical Mathematics, 32(4), 369–380. https://doi.org/10.1515/jnma-2024-0137.

Alfano, G., & Crisfield, M. A. (2001). Finite element interface models for the delamination analysis of laminated composites:Mechanical and computational issues. International Journal for Numerical Methods in Engineering, 50(7), 1701–1736. https://doi.org/10.1002/nme.93.

Ali-Ahmad, M., Subramaniam, K., & Ghosn, M. (2006). Experimental investigation and fracture analysis of debonding betweenconcrete and frp sheets. Journal of Engineering Mechanics, 132(9), 914–923. https://doi.org/10.1061/(asce)0733-9399(2006)132:9(914).

Allen, M. P. (2004). Introduction to molecular dynamics simulation. In N. Attig, K. Binder, H. Grubmüller, K. Kremer (Eds.),Computational Soft Matter: From Synthetic Polymers to Proteins. Lecture Notes. John von Neumann Institute for Computing.

Allix, O., & Corigliano, A. (1996). Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens.International Journal of Fracture, 77, 111–140. https://doi.org/10.1007/BF00037233.

Aramoon, A., Breitzman, T. D., Woodward, Ch., & El-Awady, J. A. (2016). Coarse-grained molecular dynamics study of thecuring and properties of highly cross-linked epoxy polymers. The Journal of Physical Chemistry B, 120(35), 9495–9505. https://doi.org/10.1021/acs.jpcb.6b03809.

Armstrong, K. (1997). Long-term durability in water of aluminium alloy adhesive joints bonded with epoxy adhesives. InternationalJournal of Adhesion and Adhesives, 17(2), 89–105. https://doi.org/10.1016/s0143-7496(96)00038-3.

Ascione, F., & Mancusi, G. (2010). Failure criteria for FRP adhesive lap joints: A comparative analysis. Mechanics of AdvancedMaterials and Structures, 17(2), 157–164. https://doi.org/10.1080/15376490903556659.

Aufray, M., & Roche, A. A. (2007). Epoxy–amine/metal interphases: Influences from sharp needle-like crystal formation. InternationalJournal of Adhesion and Adhesives, 27(5), 387–393. https://doi.org/10.1016/j.ijadhadh.2006.09.009.

Badulescu, C., Cognard, J. Y., Créac’hcadec, R., & Vedrine, P. (2012). Analysis of the low temperature-dependent behaviour ofa ductile adhesive under monotonic tensile/compression–shear loads. International Journal of Adhesion and Adhesives,36, 56–64. https://doi.org/10.1016/j.ijadhadh.2012.03.009.

Baggioli, A., Casalegno, M., David, A., Pasquini, M., & Raos, G. (2020). Polymer-mediated adhesion: Nanoscale surfacemorphology and failure mechanisms. Macromolecules, 54(1), 195–202. https://doi.org/10.1021/acs.macromol.0c02343.

Bandyopadhyay, A., Valavala, P. K., Clancy, T. C., Wise, K. E., & Odegard, G. M. (2011). Molecular modeling of crosslinkedepoxy polymers: The effect of crosslink density on thermomechanical properties. Polymer, 52(11), 2445–2452. https://doi.org/10.1016/j.polymer.2011.03.052.

Banea, M. D., Silva, L. F. M., da, & Campilho, R. D. S. G. (2010). Temperature dependence of the fracture toughness ofadhesively bonded joints. Journal of Adhesion Science and Technology, 24(11–12), 2011–2026. https://doi.org/10.1163/016942410×507713.

Banea, M. D., Silva, L. F. M., da, & Campilho, R. D. S. G. (2011). Mode I fracture toughness of adhesively bonded joints asa function of temperature: Experimental and numerical study. International Journal of Adhesion and Adhesives, 31(5),273–279. https://doi.org/10.1016/j.ijadhadh.2010.09.005.

Barenblatt, G. I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7,55–129. https://doi.org/10.1016/S0065-2156(08)70121-2.

Behera, D., Roy, P., & Madenci, E. (2021). Peridynamic modeling of bonded-lap joints with viscoelastic adhesives in thepresence of finite deformation. Computer Methods in Applied Mechanics and Engineering, 374, 113584. https://doi.org/10.1016/j.cma.2020.113584.

Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International Journal for NumericalMethods in Engineering, 45(5), 601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3C601::AIDNME598%3E3.0.CO;2-S.

2-S.Berendsen, H. J. C., Postma, J. P. M., Gunsteren, W. F., van, DiNola, A., & Haak, J. R. (1984). Molecular dynamics with couplingto an external bath. The Journal of Chemical Physics, 81(8), 3684–3690. https://doi.org/10.1063/1.448118.

Bergström, J. S., & Bischoff, J. E. (2010). An advanced thermomechanical constitutive model for UHMWPE. The InternationalJournal of Structural Changes in Solids, 2(1), 31–39.

Berruet, R., Vinard, E., Calle, A., Tighzert, H., Chabert, B., Magloire, H., & Eloy, R. (1987). Mechanical properties and biocompatibilityof two polyepoxy matrices: DGEBA-DDM and DGEBA-IPD. Biomaterials, 8(3), 162–171. https://doi.org/10.1016/0142-9612(87)90058-5.

Bhardwaj, A., Sommer, J.-U., & Werner, M. (2024). Nucleation patterns of polymer crystals analyzed by machine learningmodels. Macromolecules, 57(20), 9711–9724. https://doi.org/10.1021/acs.macromol.4c00920.

Blackman, B. R. K., Kinloch, A. J., Rodriguez-Sanchez, F. S., & Teo, W. S. (2012). The fracture behaviour of adhesively-bondedcomposite joints: Effects of rate of test and mode of loading. International Journal of Solids and Structures, 49(13),1434–1452. https://doi.org/10.1016/j.ijsolstr.2012.02.022.

Bocharova, V., Genix, A.-C., Carrillo, J.-M. Y., Kumar, R., Carroll, B., Erwin, A., Voylov, D., Kisliuk, A., Wang, Y., Sumpter,B. G., & Sokolov, A. P. (2020). Addition of short polymer chains mechanically reinforces glassy poly (2-vinylpyridine)–silica nanoparticle nanocomposites. ACS Applied Nano Materials, 3(4), 3427–3438. https://doi.org/10.1021/acsanm.0c00180.

Bourdin, B., Francfort, G. A., & Marigo, J.-J. (2000). Numerical experiments in revisited brittle fracture. Journal of the Mechanicsand Physics of Solids, 48(4), 797–826. https://doi.org/10.1016/s0022-5096(99)00028-9.

Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S., & Karplus, M. (1983). CHARMM: A programfor macromolecular energy, minimization, and dynamics calculations. Journal of Computational Chemistry, 4(2),187–217. https://doi.org/10.1002/jcc.540040211.

Brown, D., & Clarke, J. H. R. (1991). Molecular dynamics simulation of an amorphous polymer under tension. 1. phenomenology.Macromolecules, 24(8), 2075–2082. https://doi.org/10.1021/ma00008a056.

Büyüköztürk, O., Buehler, M. J., Lau, D., & Tuakta, C. (2011). Structural solution using molecular dynamics: Fundamentalsand a case study of epoxy-silica interface. International Journal of Solids and Structures, 48(14–15), 2131–2140. https://doi.org/10.1016/j.ijsolstr.2011.03.018.

Cadenaro, M., Maravic, T., Comba, A., Mazzoni, A., Fanfoni, L., Hilton, T., Ferracane, J., & Breschi, L. (2019). The role ofpolymerization in adhesive dentistry. Dental Materials, 35(1), e1–e22. https://doi.org/10.1016/j.dental.2018.11.012.

Campilho, R. D. S. G., Moura, M. F. S. F., de, & Domingues, J. J. M. S. (2008). Using a cohesive damage model to predict thetensile behaviour of CFRP single-strap repairs. International Journal of Solids and Structures, 45(5), 1497–1512. https://doi.org/10.1016/j.ijsolstr.2007.10.003.

Campilho, R. D. S. G., Banea, M. D., Chaves, F. J. P., & Silva, L. F. M., da (2011a). eXtended Finite Element Method forfracture characterization of adhesive joints in pure mode I. Computational Materials Science, 50(4), 1543–1549. https://doi.org/10.1016/j.commatsci.2010.12.012.

Campilho, R. D. S. G., Banea, M. D., Pinto, A. M. G., Silva, L. F. M., da, & Jesus, A. M. P., de (2011b). Strength prediction ofsingle- and double-lap joints by standard and extended finite element modelling. International Journal of Adhesion andAdhesives, 31(5), 363–372. https://doi.org/10.1016/j.ijadhadh.2010.09.008.

Campilho, R. D. S. G., Banea, M. D., Neto, J. A. B. P., & Silva, L. F. M., da (2013). Modelling adhesive joints with cohesivezone models: Effect of the cohesive law shape of the adhesive layer. International Journal of Adhesion and Adhesives, 44,48–56. https://doi.org/10.1016/j.ijadhadh.2013.02.006.

Carlberger, T., Biel, A., & Stigh, U. (2009). Influence of temperature and strain rate on cohesive properties of a structural epoxyadhesive. International Journal of Fracture, 155, 155–166. https://doi.org/10.1007/s10704-009-9337-4.

Chandra, N., Li, H., Shet, C., & Ghonem, H. (2002). Some issues in the application of cohesive zone models for metal–ceramic interfaces. International Journal of Solids and Structures, 39(10), 2827–2855. https://doi.org/10.1016/S0020-7683(02)00149-X.

Chang, S.-H., & Kim, H.-S. (2011). Investigation of hygroscopic properties in electronic packages using molecular dynamicssimulation. Polymer, 52(15), 3437–3442. https://doi.org/10.1016/j.polymer.2011.05.056.

Chaouch, S., & Yvonnet, J. (2024). Unsupervised machine learning classification for accelerating FE2 multiscale fracturesimulations. Computer Methods in Applied Mechanics and Engineering, 432, 117278. https://doi.org/10.1016/j.cma.2024.117278.

Chen, J. (2002). Predicting progressive delamination of stiffened fibre-composite panel and repaired sandwich panel by decohesionmodels. Journal of Thermoplastic Composite Materials, 15(5), 429–442. https://doi.org/10.1177/0892705702015005736.

Chiang, M. Y. M., & Fernandez-Garcia, M. (2002). Relation of swelling and tg depression to the apparent free volume ofa particle- filled, epoxy-based adhesive. Journal of Applied Polymer Science, 87(9), 1436–1444. https://doi.org/10.1002/app.11576.

Chowdhury, S. C., & Gillespie, J. W. (2022). Strain-rate dependent mode i cohesive traction laws for glass fiber-epoxy interphaseusing molecular dynamics simulations. Composites Part B: Engineering, 237, 109877. https://doi.org/10.1016/j.compositesb.2022.109877.

Chowdhury, S. C., & Gillespie, J. W. (2024). Strain-rate dependent mixed-mode traction laws for glass fiber-epoxy interphaseusing molecular dynamics simulations. Composites Part B: Engineering, 275, 111351. https://doi.org/10.1016/j.compositesb.2024.111351.

Clancy, T. C., Frankland, S. J. V., Hinkley, J. A., & Gates, T. S. (2009). Molecular modeling for calculation of mechanicalproperties of epoxies with moisture ingress. Polymer, 50(12), 2736–2742. https://doi.org/10.1016/j.polymer.2009.04.021.

De Carvalho, N. V., Mabson, G. E., Krueger, R., & Deobald, L. R. (2019). A new approach to model delamination growth infatigue using the virtual crack closure technique without re-meshing. Engineering Fracture Mechanics, 222, 106614. https://doi.org/10.1016/j.engfracmech.2019.106614.

De Nograro, F. F., Guerrero, P., Corcuera, M. A., & Mondragon, I. (1995). Effects of chemical structure of hardener on curingevolution and on the dynamic mechanical behavior of epoxy resins. Journal of Applied Polymer Science, 56(2), 177–192. https://doi.org/10.1002/app.1995.070560208.

Deng, J., Song, Y., Lan, Z., Xu, Z., Chen, Y., Yang, B., & Hao, H. (2022). The surface modification effect on the interfacialproperties of glass fiber-reinforced epoxy: A molecular dynamics study. Nanotechnology Reviews, 11(1), 1143–1157. https://doi.org/10.1515/ntrev-2022-0068.

Dietz, J. D., Nan, K., & Hoy, R. S. (2022). Unexpected ductility in semiflexible polymer glasses with entanglementlength equal to their kuhn length. Physical Review Letters, 129(12), 127801. https://doi.org/10.1103/PhysRev-Lett.129.127801.

Dorduncu, M. (2020). Peridynamic modeling of adhesively bonded beams with modulus graded adhesives using refined zigzagtheory. International Journal of Mechanical Sciences, 185, 105866. https://doi.org/10.1016/j.ijmecsci.2020.105866.

Dugdale, D. S. (1960). Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 8(2), 100–104. https://doi.org/10.1016/0022-5096(60)90013-2.

Duin, A. C. T., van, Dasgupta, S., Lorant, F., & Goddard, W. A. (2001). ReaxFF: A reactive force field for hydrocarbons. TheJournal of Physical Chemistry A, 105(41), 9396–9409. https://doi.org/10.1021/jp004368u.

Esmaeili, A., Steinmann, P., & Javili, A. (2017). Non-coherent energetic interfaces accounting for degradation. ComputationalMechanics, 59, 361–383. https://doi.org/10.1007/s00466-016-1342-7.

Español, P., & Warren, P. (1995). Statistical mechanics of dissipative particle dynamics. Europhysics Letters, 30(4), 191. https://doi.org/10.1209/0295-5075/30/4/001.

Evans, D. J., & Holian, B. L. (1985). The nose–hoover thermostat. The Journal of Chemical Physics, 83(8), 4069–4074. https://doi.org/10.1063/1.449071.

Everaers, R., Karimi-Varzaneh, H. A., Fleck, F., Hojdis, N., & Svaneborg, C. (2020). Kremer–grest models for commoditypolymer melts: Linking theory, experiment, and simulation at the kuhn scale. Macromolecules, 53(6), 1901–1916. https://doi.org/10.1021/acs.macromol.9b02428.

Faller, R., Kolb, A., & Müller-Plathe, F. (1999). Local chain ordering in amorphous polymer melts: Influence of chain stiffness.Physical Chemistry Chemical Physics, 1(9), 2071–2076. https://doi.org/10.1039/A809796H.

Fata, D., Bockenheimer, C., & Possart, W. (2005). Chapter 30. Epoxies on stainless steel-curing and aging. In W. Possart (Ed.),Adhesion: Current Research and Application (pp. 479–506). Wiley‐VCH. https://doi.org/10.1002/3527607307.

Fernandes, T. A. B., Campilho, R. D. S. G., Banea, M. D., & Silva, L. F. M., da (2015). Adhesive selection for single lap bondedjoints: Experimentation and advanced techniques for strength prediction. The Journal of Adhesion, 91(10–11), 841–862. https://doi.org/10.1080/00218464.2014.994703.

Feyel, F. (1999). Multiscale FE2 elastoviscoplastic analysis of composite structures. Computational Materials Science, 16(1–4),344–354. https://doi.org/10.1016/S0927-0256(99)00077-4.

Firooz, S., & Javili, A. (2019). Understanding the role of general interfaces in the overall behavior of composites and size effects.Computational Materials Science, 162, 245–254. https://doi.org/10.1016/j.commatsci.2019.02.042.

Floros, I. S., Tserpes, K. I., & Löbel, T. (2015). Mode-I, mode-II and mixed-mode I+II fracture behavior of composite bondedjoints: Experimental characterization and numerical simulation. Composites Part B: Engineering, 78, 459–468. https://doi.org/10.1016/j.compositesb.2015.04.006.

Frenkel, D., & Smit, B. (2023). Understanding Molecular Simulation: From Algorithms to Applications (3rd ed.). Elsevier.Fritz, D., Koschke, K., Harmandaris, V. A., Vegt, N. F. A., van der, & Kremer, K. (2011). Multiscale modeling of soft matter:Scaling of dynamics. Physical Chemistry Chemical Physics, 13(22), 10412. https://doi.org/10.1039/c1cp20247b.

Garcia, F. G., Soares, B. G., Pita, V. J. R. R., Sánchez, R., & Rieumont, J. (2007). Mechanical properties of epoxy networksbased on DGEBA and aliphatic amines. Journal of Applied Polymer Science, 106(3), 2047–2055. https://doi.org/10.1002/app.24895.

Gavrilov, A. A., Komarov, P. V., & Khalatur, P. G. (2014). Thermal properties and topology of epoxy networks: A multiscalesimulation methodology. Macromolecules, 48(1), 206–212. https://doi.org/10.1021/ma502220k.

Ghareeb, A., & Elbanna, A. (2020). An adaptive quasicontinuum approach for modeling fracture in networked materials: Applicationto modeling of polymer networks. Journal of the Mechanics and Physics of Solids, 137, 103819. https://doi.org/10.1016/j.jmps.2019.103819.

Giuntoli, A., Hansoge, N. K., Beek, A., van, Meng, Z., Chen, W., & Keten, S. (2021). Systematic coarse-graining of epoxyresins with machine learning-informed energy renormalization. npj Computational Materials, 7(1), 168. https://doi.org/10.1038/s41524-021-00634-1.

González, M. (2011). Force fields and molecular dynamics simulations. JDN, 12, 169–200. https://doi.org/10.1051/sfn/201112009.

Griffith, A. A. (1921). VI. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society A,221(582–593), 163–198. https://doi.org/10.1098/rsta.1921.0006.

Groot, R. D., & Warren, P. B. (1997). Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation.The Journal of Chemical Physics, 107(11), 4423–4435. https://doi.org/10.1063/1.474784.

Gusev, A. A., Zehnder, M. M., & Suter, U. W. (1996). Fluctuation formula for elastic constants. Physical Review B, 54(1).https://doi.org/10.1103/PhysRevB.54.1.

Haba, D., Brunner, A. J., Barbezat, M., Spetter, D., Tremel, W., & Pinter, G. (2016). Correlation of epoxy material propertieswith the toughening effect of fullerene-like WS2 nanoparticles. European Polymer Journal, 84, 125–136. https://doi.org/10.1016/j.eurpolymj.2016.09.022.

Han, X., Crocombe, A. D., Anwar, S. N. R., & Hu, P. (2014). The strength prediction of adhesive single lap joints exposed tolong term loading in a hostile environment. International Journal of Adhesion and Adhesives, 55, 1–11. https://doi.org/10.1016/j.ijadhadh.2014.06.013.

Hasheminia, S. M., Park, B. Ch., Chun, H.-J., Park, J.-Ch., & Chang, H. S. (2019). Failure mechanism of bonded jointswith similar and dissimilar material. Composites Part B: Engineering, 161, 702–709. https://doi.org/10.1016/j.compositesb.2018.11.016.

Häßler, R., & Mühlen, E., zur (2000). An introduction to μta and its application to the study of interfaces. Thermochimica Acta,361(1–2), 113–120. https://doi.org/10.1016/s0040-6031(00)00552-9.

Hiemenz, P. C., & Lodge, T. P. (2007). Polymer Chemistry (2nd ed.). CRC Press. https://doi.org/10.1201/9781420018271.

Hillerborg, A., Modéer, M., & Petersson, P.-E. (1976). Analysis of crack formation and crack growth in concrete by means offracture mechanics and finite elements. Cement and Concrete Research, 6(6), 773–781. https://doi.org/10.1016/0008-8846(76)90007-7.

Holzapfel, G. A. (2000). Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science. Wiley.Hutchinson, J. W., & Suo, Z. (1991). Mixed mode cracking in layered materials. In J. W. Hutchinson, T. Y. Wu (Eds.), Advancesin Applied Mechanics (vol. 29, pp. 63–191). Elsevier. https://doi.org/10.1016/s0065-2156(08)70164-9.

Izrailev, S., Stepaniants, S., Isralewitz, B., Kosztin, D., Lu, H., Molnar, F., Wriggers, W., & Schulten, K. (1999). Steeredmolecular dynamics. In Computational molecular dynamics: Challenges, methods, ideas (pp. 39–65). Springer BerlinHeidelberg. https://doi.org/10.1007/978-3-642-58360-5_2.

Jahani, Y., Baena, M., Barris, C., Perera, R., & Torres, L. (2022). Influence of curing, post-curing and testing temperatureson mechanical properties of a structural adhesive. Construction and Building Materials, 324, 126698. https://doi.org/10.1016/j.conbuildmat.2022.126698.

Jaillon, A., Jumel, J., Paroissien, E., & Lachaud, F. (2019). Mode I cohesive zone model parameters identification and comparisonof measurement techniques for robustness to the law shape evaluation. The Journal of Adhesion, 96(1–4), 272–299. https://doi.org/10.1080/00218464.2019.1669450.

Jang, C. W., Mullinax, J. W., & Lawson, J. W. (2022). Mechanical properties and failure of aerospace-grade epoxy resins fromreactive molecular dynamics simulations with nanoscale defects. ACS Applied Polymer Materials, 4(8), 5269–5274. https://doi.org/10.1021/acsapm.2c00503.

Javili, A., McBride, A. T., & Steinmann, P. (2019). Continuum-kinematics-inspired peridynamics. Mechanical problems. Journalof the Mechanics and Physics of Solids, 131, 125–146. https://doi.org/10.1016/j.jmps.2019.06.016.

Jeyranpour, F., Alahyarizadeh, G., & Arab, B. (2015). Comparative investigation of thermal and mechanical properties of crosslinkedepoxy polymers with different curing agents by molecular dynamics simulation. Journal of Molecular Graphicsand Modelling, 62, 157–164. https://doi.org/10.1016/j.jmgm.2015.09.012.

Ji, G., Ouyang, Z., Li, G., Ibekwe, S., & Pang, S.-S. (2010). Effects of adhesive thickness on global and local Mode-I interfacialfracture of bonded joints. International Journal of Solids and Structures, 47(18–19), 2445–2458. https://doi.org/10.1016/j.ijsolstr.2010.05.006.

Jia, Z., Yuan, G., Hui, D., Feng, X., & Zou, Y. (2018). Effect of high loading rate and low temperature on mode i fracture toughnessof ductile polyurethane adhesive. Journal of Adhesion Science and Technology, 33(1), 79–92. https://doi.org/10.1080/01694243.2018.1546364.

Jin, F.-L., Li, X., & Park, S.-J. (2015). Synthesis and application of epoxy resins: A review. Journal of Industrial and EngineeringChemistry, 29, 1–11. https://doi.org/10.1016/j.jiec.2015.03.026.

Jin, K., López Barreiro, D., Martin-Martinez, F. J., Qin, Z., Hamm, M., Paul, Ch. W., & Buehler, M. J. (2018). Improving theperformance of pressure sensitive adhesives by tuning the crosslinking density and locations. Polymer, 154, 164–171. https://doi.org/10.1016/j.polymer.2018.08.065.

Jokinen, J., Wallin, M., & Saarela, O. (2015). Applicability of VCCT in mode I loading of yielding adhesively bonded joints –a case study. International Journal of Adhesion and Adhesives, 62, 85–91. https://doi.org/10.1016/j.ijadhadh.2015.07.004.

Joshi, S. Y., & Deshmukh, S. A. (2021). A review of advancements in coarse-grained molecular dynamics simulations. MolecularSimulation, 47(10–11), 786–803. https://doi.org/10.1080/08927022.2020.1828583.

Kacar, G., Peters, E. A. J. F., & With, G., de (2013). Mesoscopic simulations for the molecular and network structure of a thermosetpolymer. Soft Matter, 9(24), 5785. https://doi.org/10.1039/c3sm50304f.

Kaczmarczyk, Ł., Ullah, Z., Lewandowski, K., Meng, X., Zhou, X.-Y., Athanasiadis, I., Nguyen, H., Chalons-Mouriesse, C.-A.,Richardson, E., Miur, E., Shvarts, A., Wakeni, M., & Pearce, C. (2020). MoFEM: an open source, parallel finite elementlibrary. The Journal of Open Source Software, 5(45), 1441. https://doi.org/10.21105/joss.01441.

Kanamori, K., Kimoto, Y., Toriumi, S., & Yonezu, A. (2021). On the cyclic fatigue of adhesively bonded aluminium: Experimentsand molecular dynamics simulation. International Journal of Adhesion and Adhesives, 107, 102848. https://doi.org/10.1016/j.ijadhadh.2021.102848.

Kanzow, J., Faupel, F., Egger, W., Sperr, P., Kögel, G., Wehlack, C., Meiser, A., & Possart, W. (2005). Chapter 29. Depthresolvedanalysis of the aging behavior of epoxy thin films by positron spectroscopy. In W. Possart (Ed.), Adhesion: CurrentResearch and Application (pp. 465–477). Wiley‐VCH. https://doi.org/10.1002/3527607307.ch29.

Karac, A., Blackman, B. R. K., Cooper, V., Kinloch, A. J., Rodriguez Sanchez, S., Teo, W. S., & Ivankovic, A. (2011). Modellingthe fracture behaviour of adhesively-bonded joints as a function of test rate. Engineering Fracture Mechanics, 78(6),973–989. https://doi.org/10.1016/j.engfracmech.2010.11.014.

Karachalios, E. F., Adams, R. D., & Silva, L. F. M., da (2013). Single lap joints loaded in tension with ductile steel adherends.International Journal of Adhesion and Adhesives, 43, 96–108. https://doi.org/10.1016/j.ijadhadh.2013.01.017.

Karimi-Varzaneh, H. A., Vegt, N. F. A., van der, Müller-Plathe, F., & Carbone, P. (2012). How good are coarse-grainedpolymer models? A comparison for atactic polystyrene. ChemPhysChem, 13(15), 3428–3439. https://doi.org/10.1002/cphc.201200111.

Katnam, K. B., Sargent, J. P., Crocombe, A. D., Khoramishad, H., & Ashcroft, I. A. (2010). Characterisation of moisture-dependentcohesive zone properties for adhesively bonded joints. Engineering Fracture Mechanics, 77(16), 3105–3119. https://doi.org/10.1016/j.engfracmech.2010.08.023.

Keten, S., & Buehler, M. J. (2008). Asymptotic strength limit of hydrogen-bond assemblies in proteins at vanishing pullingrates. Physical Review Letters, 100(19). https://doi.org/10.1103/physrevlett.100.198301.

Khoramishad, H., Crocombe, A. D., Katnam, K. B., & Ashcroft, I. A. (2010). Predicting fatigue damage in adhesively bondedjoints using a cohesive zone model. International Journal of Fatigue, 32(7), 1146–1158. https://doi.org/10.1016/j.ijfatigue.2009.12.013.

Konrad, J., & Zahn, D. (2023). Interfaces in reinforced epoxy resins: From molecular scale understanding towards mechanicalproperties. Journal of Molecular Modeling, 29(8), 243. https://doi.org/10.1007/s00894-023-05654-w.

Konrad, J., Meißner, R. H., Bitzek, E., & Zahn, D. (2021). A molecular simulation approach to bond reorganization in epoxyresins: From curing to deformation and fracture. ACS Polymers Au, 1(3), 165–174. https://doi.org/10.1021/acspolymersau.1c00016.

Kremer, K., & Grest, G. S. (1990). Dynamics of entangled linear polymer melts: A molecular-dynamics simulation. The Journalof Chemical Physics, 92(8), 5057–5086. https://doi.org/10.1063/1.458541.

Kröger, M. (2004). Simple models for complex nonequilibrium fluids. Physics Reports, 390(6), 453–551. https://doi.org/10.1016/j.physrep.2003.10.014.

Kröger, M., Dietz, J. D., Hoy, R. S., & Luap, C. (2023). The Z1+ package: Shortest multiple disconnected path for the analysisof entanglements in macromolecular systems. Computer Physics Communications, 283, 108567. https://doi.org/10.1016/j.cpc.2022.108567.

Krueger, R. (2015). 1 – The virtual crack closure technique for modeling interlaminar failure and delamination in advancedcomposite materials. In P. P. Camanho, S. R. Hallett (Eds.), Numerical Modelling of Failure in Advanced Composite Materials(pp. 3–53). Elsevier. https://doi.org/10.1016/b978-0-08-100332-9.00001-3.

Laio, A., & Gervasio, F. L. (2008). Metadynamics: A method to simulate rare events and reconstruct the free energy in biophysics,chemistry and material science. Reports on Progress in Physics, 71(12), 126601. https://doi.org/10.1088/0034-4885/71/12/126601.

Langeloth, M., Sugii, T., Böhm, M. C., & Müller-Plathe, F. (2015). The glass transition in cured epoxy thermosets: A comparativemolecular dynamics study in coarse-grained and atomistic resolution. The Journal of Chemical Physics, 143(24),243158. https://doi.org/10.1063/1.4937627.

Lapique, F., & Redford, K. (2002). Curing effects on viscosity and mechanical properties of a commercial epoxy resin adhesive.International Journal of Adhesion and Adhesives, 22(4), 337–346. https://doi.org/10.1016/s0143-7496(02)00013-1.

Lau, D., Büyüköztürk, O., & Buehler, M. J. (2012). Characterization of the intrinsic strength between epoxy and silica usinga multiscale approach. Journal of Materials Research, 27(14), 1787–1796. https://doi.org/10.1557/jmr.2012.96.

Laurien, M., Javili, A., & Steinmann, P. (2023). Peridynamic modeling of nonlocal degrading interfaces in composites. Forcesin Mechanics, 10, 100124. https://doi.org/10.1016/j.finmec.2022.100124.

Laurien, M., Javili, A., & Steinmann, P. (2024). Nonlocal interfaces accounting for progressive damage within continuum-kinematics-inspired peridynamics. International Journal of Solids and Structures, 290, 112641. https://doi.org/10.1016/j.ijsolstr.2023.112641.

Li, Ch., & Strachan, A. (2016). Free volume evolution in the process of epoxy curing and its effect on mechanical properties.Polymer, 97, 456–464. https://doi.org/10.1016/j.polymer.2016.05.059.

Li, Ch., Ke, L., He, J., Chen, Z., & Jiao, Y. (2019). Effects of mechanical properties of adhesive and CFRP on the bondbehavior in CFRP-strengthened steel structures. Composite Structures, 211, 163–174. https://doi.org/10.1016/j.compstruct.2018.12.020.

Li, K., Li, Y., Lian, Q., Cheng, J., & Zhang, J. (2016a). Influence of cross-linking density on the structure and properties ofthe interphase within supported ultrathin epoxy films. Journal of Materials Science, 51(19), 9019–9030. https://doi.org/10.1007/s10853-016-0155-6.

Li, K., Huo, N., Liu, X., Cheng, J., & Zhang, J. (2016b). Effects of the furan ring in epoxy resin on the thermomechanicalproperties of highly cross-linked epoxy networks: A molecular simulation study. RSC Advances, 6(1), 769–777. https://doi.org/10.1039/C5RA22955C.

Li, M., Gu, Y.-Z., Liu, H., Li, Y.-X., Wang, S.-K., Wu, Q., & Zhang, Z.-G. (2013). Investigation the interphase formation processof carbon fiber/epoxy composites using a multiscale simulation method. Composites Science and Technology, 86,117–121. https://doi.org/10.1016/j.compscitech.2013.07.008.

Li, P., Li, W., Li, B., Yang, S., Shen, Y., Wang, Q., & Zhou, K. (2023). A review on phase field models for fracture and fatigue.Engineering Fracture Mechanics, 289, 109419. https://doi.org/10.1016/j.engfracmech.2023.109419.

Liao, L., Huang, C., & Sawa, T. (2013). Effect of adhesive thickness, adhesive type and scarf angle on the mechanical propertiesof scarf adhesive joints. International Journal of Solids and Structures, 50(25–26), 4333–4340. https://doi.org/10.1016/j.ijsolstr.2013.09.005.

Lin, K., & Wang, Z. (2023). Multiscale mechanics and molecular dynamics simulations of the durability of fiber-reinforcedpolymer composites. Communications Materials, 4(1), 66. https://doi.org/10.1038/s43246-023-00391-2.

Liu, H., Uhlherr, A., Varley, R. J., & Bannister, M. K. (2004). Influence of substituents on the kinetics of epoxy/aromatic diamineresin systems. Journal of Polymer Science Part A: Polymer Chemistry, 42(13), 3143–3156. https://doi.org/10.1002/pola.20169.

Livraghi, M., Höllring, K., Wick, Ch. R., Smith, D. M., & Smith, A.-S. (2021). An exact algorithm to detect the percolationtransition in molecular dynamics simulations of cross-linking polymer networks. Journal of Chemical Theory and Computation,17(10), 6449–6457. https://doi.org/10.1021/acs.jctc.1c00423.

Livraghi, M., Pahi, S., Nowakowski, P., Smith, D. M., Wick, Ch. R., & Smith, A.-S. (2023). Block chemistry for accuratemodeling of epoxy resins. The Journal of Physical Chemistry B, 127(35), 7648–7662. https://doi.org/10.1021/acs.jpcb.3c04724.

Loh, W. K., Crocombe, A. D., Abdel Wahab, M. M., & Ashcroft, I. A. (2002). Environmental degradation of the interfacial fractureenergy in an adhesively bonded joint. Engineering Fracture Mechanics, 69(18), 2113–2128. https://doi.org/10.1016/s0013-7944(02)00004-8.

Lu, X., Giovanis, D. G., Yvonnet, J., Papadopoulos, V., Detrez, F., & Bai, J. (2018). A data-driven computational homogenizationmethod based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites.Computational Mechanics, 64(2), 307–321. https://doi.org/10.1007/s00466-018-1643-0.

Ma, Q., Huang, D., Wu, L., & Xu, Y. (2023). An extended peridynamic model for analyzing interfacial failure of compositematerials with non-uniform discretization. Theoretical and Applied Fracture Mechanics, 125, 103854. https://doi.org/10.1016/j.tafmec.2023.103854.

Maguire, J. F., Talley, P. L., & Lupkowski, M. (1994). The interphase in adhesion: Bridging the gap. The Journal of Adhesion,45(1–4), 269–290. http://doi.org/10.1080/00218469408026643.

Mancusi, G., & Ascione, F. (2013). Performance at collapse of adhesive bonding. Composite Structures, 96, 256–261. https://doi.org/10.1016/j.compstruct.2012.09.027.

Maple, J. R., Hwang, M.-J., Stockfisch, T. P., Dinur, U., Waldman, M., Ewig, C. S., & Hagler, A. T. (1994). Derivation ofclass II force fields. I. methodology and quantum force field for the alkyl functional group and alkane molecules. Journalof Computational Chemistry, 15(2), 162–182. https://doi.org/10.1002/jcc.540150207.

Marques, E. A. S., Silva, L. F. M., da, Banea, M. D., & Carbas, R. J. C. (2014). Adhesive joints for low- and high-temperatureuse: An overview. The Journal of Adhesion, 91(7), 556–585. https://doi.org/10.1080/00218464.2014.943395.

Martyna, G. J., Tobias, D. J., & Klein, M. L. (1994). Constant pressure molecular dynamics algorithms. The Journal of ChemicalPhysics, 101(5), 4177–4189. https://doi.org/10.1063/1.467468.

Mayo, S. L., Olafson, B. D., & Goddard, W. A. (1990). Dreiding: A generic force field for molecular simulations. The Journalof Physical Chemistry, 94(26), 8897–8909. https://doi.org/10.1021/j100389a010.

Meiser, A., & Possart, W. (2011). Epoxy-metal interphases: Chemical and mechanical aging. The Journal of Adhesion, 87(4),313–330. https://doi.org/10.1080/00218464.2011.562105.

Meiser, A., Willstrand, K., Fehling, P., & Possart, W. (2008). Chemical aging in epoxies: A local study of the interphases to airand to metals. The Journal of Adhesion, 84(4), 299–321. https://doi.org/10.1080/00218460802004360.

Meiser, A., Kübel, C., Schäfer, H., & Possart, W. (2010). Electron microscopic studies on the diffusion of metal ions in epoxy–metal interphases. International Journal of Adhesion and Adhesives, 30(3), 170–177. https://doi.org/10.1016/j.ijadhadh.2009.12.001.

Meng, L., Zhang, H., Liu, Z., Shu, X., & Li, P. (2024). A direct FE2 method for concurrent multilevel modeling of a coupledthermoelectric problem – joule heating effect – in multiscale materials and structures. Thin-Walled Structures, 203,112166. https://doi.org/10.1016/j.tws.2024.112166.

Mészáros, L., Horváth, A., Vas, L. M., & Petrény, R. (2023). Investigation of the correlations between the microstructure andthe tensile properties multi-scale composites with a polylactic acid matrix, reinforced with carbon nanotubes and carbonfibers, with the use of the fiber bundle cell theory. Composites Science and Technology, 242, 110154. https://doi.org/10.1016/j.compscitech.2023.110154.

Miehe, C., Welschinger, F., & Hofacker, M. (2010). Thermodynamically consistent phase-field models of fracture: Variationalprinciples and multi-field fe implementations. International Journal for Numerical Methods in Engineering, 83(10),1273–1311. https://doi.org/10.1002/nme.2861.

Min, K., Rammohan, A. R., Lee, H. S., Shin, J., Lee, S. H., Goyal, S., Park, H., Mauro, J. C., Stewart, R., Botu, V., Kim, H.,& Cho, E. (2017). Computational approaches for investigating interfacial adhesion phenomena of polyimide on silicaglass. Scientific Reports, 7(1), 10475. https://doi.org/10.1038/s41598-017-10994-8.

Moës, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. InternationalJournal for Numerical Methods in Engineering, 46(1), 131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J.

Moghimikheirabadi, A., Karatrantos, A. V., & Kröger, M. (2021). Ionic polymer nanocomposites subjected to uniaxialextension: A nonequilibrium molecular dynamics study. Polymers, 13(22), 4001. https://doi.org/10.3390/polym13224001.

Mohapatra, P. C., & Smith, L. V. (2019). Characterization of adhesive yield criteria usingmixed-mode loading. Journal of AdhesionScience and Technology, 33(11), 1248–1260. https://doi.org/10.1080/01694243.2019.1585058.

Moya-Sanz, E. M., Ivañez, I., & Garcia-Castillo, S. K. (2017). Effect of the geometry in the strength of single-lap adhesivejoints of composite laminates under uniaxial tensile load. International Journal of Adhesion and Adhesives, 72, 23–29. https://doi.org/10.1016/j.ijadhadh.2016.10.009.

Nemati Giv, A., Ayatollahi, M. R., Ghaffari, S. H., & Silva, L. F., da (2018). Effect of reinforcements at different scales onmechanical properties of epoxy adhesives and adhesive joints: A review. The Journal of Adhesion, 94(13), 1082–1121. https://doi.org/10.1080/00218464.2018.1452736.

Neto, J. A. B. P., Campilho, R. D. S. G., & Silva, L. F. M., da (2012). Parametric study of adhesive joints with composites.International Journal of Adhesion and Adhesives, 37, 96–101. https://doi.org/10.1016/j.ijadhadh.2012.01.019.

Noid, W. G., Chu, J.-W., Ayton, G. S., Krishna, V., Izvekov, S., Voth, G. A., Das, A., & Andersen, H. C. (2008a). The multiscalecoarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. The Journal of ChemicalPhysics, 128(24), 244114. https://doi.org/10.1063/1.2938860.

Noid, W. G., Liu, P., Wang, Y., Chu, J.-W., Ayton, G. S., Izvekov, S., Andersen, H. C., & Voth, G. A. (2008b). The multiscalecoarse-graining method. II. Numerical implementation for coarse-grained molecular models. The Journal of ChemicalPhysics, 128(24), 244115. https://doi.org/10.1063/1.2938857.

Nunes, S. L. S., Campilho, R. D. S. G., Silva, F. J. G., da, Sousa, C. C. R. G., de, Fernandes, T. A. B., Banea, M. D., & Silva,L. F. M., da (2015). Comparative failure assessment of single and double lap joints with varying adhesive systems.The Journal of Adhesion, 92(7–9), 610–634. https://doi.org/10.1080/00218464.2015.1103227.

Pal, S., Dansuk, K., Giuntoli, A., Sirk, T. W., & Keten, S. (2023). Predicting the effect of hardener composition on the mechanicaland fracture properties of epoxy resins using molecular modeling. Macromolecules, 56(12), 4447–4456. https://doi.org/10.1021/acs.macromol.2c02577.

Park, H., & Cho, M. (2020). A multiscale framework for the elasto-plastic constitutive equations of crosslinked epoxy polymersconsidering the effects of temperature, strain rate, hydrostatic pressure, and crosslinking density. Journal of the Mechanicsand Physics of Solids, 142, 103962. https://doi.org/10.1016/j.jmps.2020.103962.

Park, H., Choi, J., Kim, B., Yang, S., Shin, H., & Cho, M. (2018). Toward the constitutive modeling of epoxy matrix: Temperature-accelerated quasi-static molecular simulations consistent with the experimental test. Composites Part B: Engineering,142, 131–141. https://doi.org/10.1016/j.compositesb.2018.01.018.

Parrinello, M., & Rahman, A. (1982). Strain fluctuations and elastic constants. The Journal of Chemical Physics, 76(5), 2662–2666. https://doi.org/10.1063/1.443248.

Passlack, S., Brodyanski, A., Bock, W., Kopnarski, M., Presser, M., Geiß, P. L., Possart, G., & Steinmann, P. (2009). Chemicaland structural characterisation of DGEBA-based epoxies by time of flight secondary ion mass spectrometry (ToF-SIMS)as a preliminary to polymer interphase characterisation. Analytical and Bioanalytical Chemistry, 393(8), 1879–1888. https://doi.org/10.1007/s00216-009-2639-6.

Pfaller, S. (2022). Discrete and continuous methods for modelling and simulation of polymer materials [Habilitation thesis,Friedrich-Alexander-Universität Erlangen-Nürnberg]. OPEN FAU. https://doi.org/10.25593/OPUS4-FAU-18036.

Plimpton, S. (1995). Fast parallel algorithms for short-range molecular dynamics. Journal of Computational Physics, 117(1),1–19. https://doi.org/10.1006/jcph.1995.1039.

Pocius, A. V. (2012). Adhesion and Adhesives Technology: An Introduction. Hanser Publications.Possart, G. (2014). Mechanical Interphases in Adhesives: Experiments, Modelling and Simulation [Doctoral thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg].

Possart, G., Presser, M., Passlack, S., Geiß, P. L., Kopnarski, M., Brodyanski, A., & Steinmann, P. (2009). Micro–macro characterisationof DGEBA-based epoxies as a preliminary to polymer interphase modelling. International Journal of Adhesionand Adhesives, 29(5), 478–487. https://doi.org/10.1016/j.ijadhadh.2008.10.001.

Possart, W., Krüger, J. K., Wehlack, C., Müller, U., Petersen, Ch., Bactavatchalou, R., & Meiser, A. (2006). Formation andstructure of epoxy network interphases at the contact to native metal surfaces. Comptes Rendus. Chimie, 9(1), 60–79. https://doi.org/10.1016/j.crci.2005.04.009.

Pramanik, A., Basak, A. K., Dong, Y., Sarker, P. K., Uddin, M. S., Littlefair, G., Dixit, A. R., & Chattopadhyaya, S. (2017).Joining of carbon fibre reinforced polymer (CFRP) composites and aluminium alloys – a review. Composites Part A:Applied Science and Manufacturing, 101, 1–29. https://doi.org/10.1016/j.compositesa.2017.06.007.

Qi, B., Zhang, Q. X., Bannister, M., & Mai, Y.-W. (2006). Investigation of the mechanical properties of DGEBA-basedepoxy resin with nanoclay additives. Composite Structures, 75(1–4), 514–519. https://doi.org/10.1016/j.compstruct.2006.04.032.

Raghava, R., Caddell, R. M., & Yeh, G. S. Y. (1973). The macroscopic yield behaviour of polymers. Journal of Materials Science,8, 225–232. https://doi.org/10.1007/BF00550671.

Ramalho, L. D. C., Sánchez-Arce, I. J., Gonçalves, D. C., Belinha, J., & Campilho, R. D. S. G. (2022). Numerical analysisof the dynamic behaviour of adhesive joints: A review. International Journal of Adhesion and Adhesives, 118, 103219. https://doi.org/10.1016/j.ijadhadh.2022.103219.

Raos, G., & Zappone, B. (2024). Tuning adhesion and energy dissipation in polymer films between solid surfaces via graftingand cross-linking. Macromolecules, 57(14), 6502–6513. https://doi.org/10.1021/acs.macromol.4c00062.

Reith, D., Pütz, M., & Müller-Plathe, F. (2003). Deriving effective mesoscale potentials from atomistic simulations. Journal of Computational Chemistry, 24(13), 1624–1636. https://doi.org/10.1002/jcc.10307.

Ribeiro, T. E. A., Campilho, R. D. S. G., Silva, L. F. M., da & Goglio, L. (2016). Damage analysis of composite–aluminiumadhesively-bonded single-lap joints. Composite Structures, 136, 25–33. https://doi.org/10.1016/j.compstruct.2015.09.054.

Ries, M. (2023). Characterization and Modeling of Polymer Nanocomposites Across the Scales – A Comprehensive ApproachCovering the Mechanical Behavior of Matrix, Filler, and Interphase [Doctoral thesis, Friedrich-Alexander-UniversitätErlangen-Nürnberg]. OPEN FAU. https://doi.org/10.25593/opus4-fau-23638.

Ries, M., Possart, G., Steinmann, P., & Pfaller, S. (2021). A coupled MD-FE methodology to characterize mechanical interphasesin polymeric nanocomposites. International Journal of Mechanical Sciences, 204, 106564. https://doi.org/10.1016/j.ijmecsci.2021.106564.

Ries, M., Seibert, J., Steinmann, P., & Pfaller, S. (2022). Applying a generic and fast coarse-grained molecular dynamics modelto extensively study the mechanical behavior of polymer nanocomposites. Express Polymer Letters, 16(12), 1304–1321. https://doi.org/10.3144/expresspolymlett.2022.94.

Ritter, J., Shegufta, S., & Zaiser, M. (2023). Effects of disorder on deformation and failure of brittle porous materials. Journalof Statistical Mechanics: Theory and Experiment, 2023(5), 053301. https://doi.org/10.1088/1742-5468/acccdf.

Roche, A. A., Dole, P., & Bouzziri, M. (1994). Measurement of the practical adhesion of paint coatings to metallic sheets bythe pull-off and three-point flexure tests. Journal of Adhesion Science and Technology, 8(6), 587–609. https://doi.org/10.1163/156856194×00366.

Rudawska, A. (2019). Comparison of the adhesive joints’ strength of the similar and dissimilar systems of metal alloy/polymercomposite. Applied Adhesion Science, 7(1), 7. https://doi.org/10.1186/s40563-019-0123-x.

Rybicki, E. F., & Kanninen, M. F. (1977). A finite element calculation of stress intensity factors by a modified crack closureintegral. Engineering Fracture Mechanics, 9(4), 931–938. https://doi.org/10.1016/0013-7944(77)90013-3.

Saeb, S., Firooz, S., Steinmann, P., & Javili, A. (2021). Generalized interfaces via weighted averages for application to gradedinterphases at large deformations. Journal of the Mechanics and Physics of Solids, 149, 104234. https://doi.org/10.1016/j.jmps.2020.104234.

Saikia, P. J., & Muthu, N. (2024). Estimation of CZM parameters for investigating the interface fracture of adhesively bondedjoints under mode I, mode II, and mixed-mode (I/II) loading. Fatigue and Fracture of Engineering Materials and Structures,47(12), 4636–4649. https://doi.org/10.1111/ffe.14457.

Santos, J. P. J. R., Correia, D. S., Marques, E. A. S., Carbas, R. J. C., Gilbert, F., & Silva, L. F. M., da (2023). Extended finiteelement method (XFEM) model for the damage mechanisms present in joints bonded using adhesives doped with inorganicfillers. Materials, 16(23), 7499. https://doi.org/10.3390/ma16237499.

Savitzky, A., & Golay, M. J. E. (1964). Smoothing and differentiation of data by simplified least squares procedures. AnalyticalChemistry, 36(8), 1627–1639. https://doi.org/10.1021/ac60214a047.

Scattina, A., Peroni, L., Peroni, M., & Avalle, M. (2011). Numerical analysis of hybrid joining in car body applications. Journalof Adhesion Science and Technology, 25(18), 2409–2433. https://doi.org/10.1163/016942411X580117.

Schaller, E., Javili, A., Schmidt, I., Papastavrou, A., & Steinmann, P. (2022). A peridynamic formulation for nonlocal bone remodelling.Computer Methods in Biomechanics and Biomedical Engineering, 25(16), 1835–1851. https://doi.org/10.1080/10255842.2022.2039641.

Schmandt, Ch., & Marzi, S. (2025). A strain-rate-dependent cohesive zone model for peel-loaded thick and flexible adhesivelayers of various geometries prone to stick–slip failure. Theoretical and Applied Fracture Mechanics, 136, 104755. https://doi.org/10.1016/j.tafmec.2024.104755.

Schmelzle, L., Striewe, M., Mergheim, J., Meschut, G., Possart, G., Teutenberg, D., Hein, D., & Steinmann, P. (2023). Testing,modelling, and parameter identification for adhesively bonded joints under the influence of temperature. Journal of AdhesionScience and Technology, 37(16), 2285–2316. https://doi.org/10.1080/01694243.2022.2125714.

Senthil, K., Arockiarajan, A., & Palaninathan, R. (2018). Numerical study on the onset of initiation of debond growth in adhesivelybonded composite joints. International Journal of Adhesion and Adhesives, 84, 202–219. https://doi.org/10.1016/j.ijadhadh.2018.03.009.

Shell, M. S. (2016). Coarse-graining with the relative entropy. In S. A. Rice, A. R. Dinner (Eds.), Advances in Chemical Physics(vol. 161, pp. 395–441). John Wiley & Sons. https://doi.org/10.1002/9781119290971.ch5.

Shi, T., & Zhang, Y. (2024). A length-free phase field model for epoxy adhesive materials based on modified drucker–pragercriterion. Composite Structures, 346, 118450. https://doi.org/10.1016/j.compstruct.2024.118450.

Shi, T., Livi, S., Duchet-Rumeau, J., & Gérard, J.-F. (2021). Enhanced mechanical and thermal properties of ionic liquidcore/silica shell microcapsules-filled epoxy microcomposites. Polymer, 233, 124182. https://doi.org/10.1016/j.polymer.2021.124182.

Shim, M.-J., & Kim, S.-W. (1997). Cure reaction and mechanical properties of DGEBA/MDA/nitrile system. Materials Chemistryand Physics, 47(2–3), 198–202. https://doi.org/10.1016/S0254-0584(97)80051-X.

Shin, K. Ch., & Lee, J. J. (2003). Bond parameters to improve tensile load bearing capacities of co-cured single and double lapjoints with steel and carbon fiber-epoxy composite adherends. Journal of Composite Materials, 37(5), 401–420. https://doi.org/10.1177/0021998303037005040.

Shishesaz, M., & Hosseini, M. (2018). Effects of joint geometry and material on stress distribution, strength and failure ofbonded composite joints: An overview. The Journal of Adhesion, 96(12), 1053–1121. https://doi.org/10.1080/00218464.2018.1554483.

Shokuhfar, A., & Arab, B. (2013). The effect of cross linking density on the mechanical properties and structure of the epoxypolymers: Molecular dynamics simulation. Journal of Molecular Modeling, 19(9), 3719–3731. https://doi.org/10.1007/s00894-013-1906-9.

Silling, S. A. (2000). Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics andPhysics of Solids, 48(1), 175–209. https://doi.org/10.1016/s0022-5096(99)00029-0.

Silling, S. A., Epton, M., Weckner, O., Xu, J., & Askari, E. (2007). Peridynamic states and constitutive modeling. Journal ofElasticity, 88(2), 151–184. https://doi.org/10.1007/s10659-007-9125-1.

Silva, L. F. M., da, & Campilho, R. D. S. G. (2011). Advances in Numerical Modeling of Adhesive Joints. Springer Berlin,Heidelberg. https://doi.org/10.1007/978-3-642-23608-2.

Silva, L. F. M., da, Rodrigues, T. N. S. S., Figueiredo, M. A. V., Moura, M. F. S. F., de, & Chousal, J. A. G. (2006). Effectof adhesive type and thickness on the lap shear strength. The Journal of Adhesion, 82(11), 1091–1115. https://doi.org/10.1080/00218460600948511.

Silva, L. F. M., da, Neves, P. J., das, Adams, R., & Spelt, J. (2009a). Analytical models of adhesively bonded joints – Part I:Literature survey. International Journal of Adhesion and Adhesives, 29(3), 319–330. https://doi.org/10.1016/j.ijadhadh.2008.06.005.

Silva, L. F. M., da, Neves, P. J., das, Adams, R., Wang, A., & Spelt, J. (2009b). Analytical models of adhesively bonded joints –Part II: Comparative study. International Journal of Adhesion and Adhesives, 29(3), 331–341. https://doi.org/10.1016/j.ijadhadh.2008.06.007.

Sluis, O., van der, Iwamoto, N., Qu, J., Yang, S., Yuan, C., Driel, W. D., van, & Zhang, G. Q. (2018). Advances in delaminationmodeling of metal/polymer systems: Atomistic aspects. In J. E. Morris (Ed.), Nanopackaging: Nanotechnologies andElectronics Packaging (pp. 129–183).

Springer Cham.Smit, R. J. M., Brekelmans, W. A. M., & Meijer, H. E. H. (1998). Prediction of the mechanical behavior of nonlinear heterogeneoussystems by multi-level finite element modeling. Computer Methods in Applied Mechanics and Engineering,155(1–2), 181–192. https://doi.org/10.1016/S0045-7825(97)00139-4.

Solar, M., Qin, Z., & Buehler, M. J. (2014). Molecular mechanics and performance of crosslinked amorphous polymer adhesives.Journal of Materials Research, 29(9), 1077–1085. https://doi.org/10.1557/jmr.2014.82.

Soliman, S. M. A., Abdelhakim, M., & Sabaa, M. W. (2024). Study curing of epoxy resin by Isophoronediamine/Triethylenetetramineand reinforced with montmorillonite and effect on compressive strength. BMC Chemistry, 18(1), 211. https://doi.org/10.1186/s13065-024-01319-8.

Soutis, C. (2005). Carbon fiber reinforced plastics in aircraft construction. Materials Science and Engineering: A, 412(1–2),171–176. https://doi.org/10.1016/j.msea.2005.08.064.

Spannraft, L., Possart, G., Steinmann, P., & Mergheim, J. (2022). Generalized interfaces enabling macroscopic modeling ofstructural adhesives and their failure. Forces in Mechanics, 9, 100137. https://doi.org/10.1016/j.finmec.2022.100137.

Spannraft, L., Steinmann, P., & Mergheim, J. (2023). A generalized anisotropic damage interface model for finite strains.Journal of the Mechanics and Physics of Solids, 174, 105255. https://doi.org/10.1016/j.jmps.2023.105255.

Steinmann, P., & Runesson, K. (2021). The Catalogue of Computational Material Models: Basic Geometrically Linear Modelsin 1D. Springer Cham. https://doi.org/10.1007/978-3-030-63684-5.

Stevens, M. J. (2001). Interfacial fracture between highly cross-linked polymer networks and a solid surface: Effect of interfacialbond density. Macromolecules, 34(8), 2710–2718. https://doi.org/10.1021/ma000553u.

Stewart, I., Chambers, A., & Gordon, T. (2007). The cohesive mechanical properties of a toughened epoxy adhesive as a functionof cure level. International Journal of Adhesion and Adhesives, 27(4), 277–287. https://doi.org/10.1016/j.ijadhadh.2006.05.003.

Subramaniyan, A. K., & Sun, C. T. (2008). Continuum interpretation of virial stress in molecular simulations. InternationalJournal of Solids and Structures, 45(14–15), 4340–4346. https://doi.org/10.1016/j.ijsolstr.2008.03.016.

Sugiman, S., Crocombe, A. D., & Aschroft, I. A. (2013). Experimental and numerical investigation of the static response ofenvironmentally aged adhesively bonded joints. International Journal of Adhesion and Adhesives, 40, 224–237. https://doi.org/10.1016/j.ijadhadh.2012.08.007.

Sun, H. (1998). COMPASS: An ab initio force-field optimized for condensed-phase applications overview with details on alkaneand benzene compounds. The Journal of Physical Chemistry B, 102(38), 7338–7364. https://doi.org/10.1021/jp980939v.

Sundararaghavan, V., & Kumar, A. (2013). Molecular dynamics simulations of compressive yielding in cross-linked epoxiesin the context of argon theory. International Journal of Plasticity, 47, 111–125. https://doi.org/10.1016/j.ijplas.2013.01.004.

Tadmor, E. B., & Miller, R. E. (2011). Modeling Materials: Continuum, Atomistic and Multiscale Techniques. Cambridge UniversityPress. https://doi.org/10.1017/CBO9781139003582.

Tadmor, E. B., Ortiz, M., & Phillips, R. (1996). Quasicontinuum analysis of defects in solids. Philosophical Magazine A, 73(6),1529–1563. https://doi.org/10.1080/01418619608243000.

Tadmor, E. B., Miller, R. E., & Elliott, R. S. (2012). Continuum Mechanics and Thermodynamics: From Fundamental Conceptsto Governing Equations. Cambridge University Press.Taib, A. A., Boukhili, R., Achiou, S., Gordon, S., & Boukehili, H. (2006). Bonded joints with composite adherends. Part I.effect of specimen configuration, adhesive thickness, spew fillet and adherend stiffness on fracture. International Journalof Adhesion and Adhesives, 26(4), 226–236. https://doi.org/10.1016/j.ijadhadh.2005.03.015.

Tam, L.-h., & Lau, D. (2014). A molecular dynamics investigation on the cross-linking and physical properties of epoxy-basedmaterials. RSC Advsnces, 4(62), 33074–33081. https://doi.org/10.1039/C4RA04298K.

Tam, L.-h., & Lau, D. (2015). Moisture effect on the mechanical and interfacial properties of epoxy-bonded material system:An atomistic and experimental investigation. Polymer, 57, 132–142. https://doi.org/10.1016/j.polymer.2014.12.026.

Tam, L.-h., & Lau, D. (2016). Effect of structural voids on mesoscale mechanics of epoxy-based materials. Coupled SystemsMechanics, 5(4), 355–369. https://doi.org/10.12989/csm.2016.5.4.355.

Tavares, M. I. B., D’almeida, J. R. M., & Monteiro, S. N. (2000). 13C solid-state NMR analysis of the DGEBA/TETA epoxy system. Journal of Applied Polymer Science, 78(13), 2358–2362. https://doi.org/10.1002/1097-4628(20001220)78:13%3C2358::AID-APP120%3E3.0.CO;2-T.

Theodorou, D. N., & Suter, U. W. (1986). Atomistic modeling of mechanical properties of polymeric glasses. Macromolecules,19(1), 139–154. https://doi.org/10.1021/ma00155a022.

Thompson, A. P., Plimpton, S. J., & Mattson, W. (2009). General formulation of pressure and stress tensor for arbitrary manybodyinteraction potentials under periodic boundary conditions. The Journal of Chemical Physics, 131(15), 154107. https://doi.org/10.1063/1.3245303.

Thompson, A. P., Aktulga, H. M., Berger, R., Bolintineanu, D. S., Brown, W. M., Crozier, P. S., Veld, P. J., in’t, Kohlmeyer, A.,Moore, S. G., Nguyen, T. D., Shan, R., Stevens, M. J., Tranchida, J., Trott, Ch., & Plimpton, S. J. (2022). LAMMPS –a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. ComputerPhysics Communications, 271, 108171. https://doi.org/10.1016/j.cpc.2021.108171.

Tkachuk, A. I., Zagora, A. G., Terekhov, I. V., & Mukhametov, R. R. (2022). Isophorone diamine – a curing agent for epoxyresins: Production, application, prospects. A review. Polymer Science, Series D, 15(2), 171–176. https://doi.org/10.1134/S1995421222020289.

Treloar, L. R. G. (1975). The Physics of Rubber Elasticity (3rd ed.). Clarendon Press.Tserpes, K., Barroso-Caro, A., Carraro, P. A., Beber, V. C., Floros, I., Gamon, W., Kozłowski, M., Santandrea, F., Shahverdi,M., Skejić, D., Bedon, Ch., & Rajčić, V. (2021). A review on failure theories and simulation models for adhesive joints.The Journal of Adhesion, 98(12), 1855–1915. https://doi.org/10.1080/00218464.2021.1941903.

Vakhrushev, A. V. (2018). Introductory chapter: Molecular dynamics: Basic tool of nanotechnology simulations for “Production4.0” revolution. In A. V. Vakhrushev (Ed.), Molecular Dynamics. InTech. https://doi.org/10.5772/intechopen.79045.

Vallée, T., Correia, J. R., & Keller, T. (2006). Probabilistic strength prediction for double lap joints composed of pultrudedGFRP profiles part I: Experimental and numerical investigations. Composites Science and Technology, 66(13), 1903–1914. https://doi.org/10.1016/j.compscitech.2006.04.007.

Varshney, V., Patnaik, S. S., Roy, A. K., & Farmer, B. L. (2008). A molecular dynamics study of epoxy-based networks: Crosslinkingprocedure and prediction of molecular and material properties. Macromolecules, 41(18), 6837–6842. https://doi.org/10.1021/ma801153e.

Verlet, L. (1967). Computer “experiments” on classical fluids. I. thermodynamical properties of Lennard-Jones molecules.Physical Review, 159(1), 98–103. https://doi.org/10.1103/physrev.159.98.

Viana, G., Machado, J., Carbas, R., Costa, M., Silva, L. M. F., da, Vaz, M., & Banea, M. D. (2018). Strain rate dependence ofadhesive joints for the automotive industry at low and high temperatures. Journal of Adhesion Science and Technology,32(19), 2162–2179. https://doi.org/10.1080/01694243.2018.1464635.

Vu-Bac, N., Bessa, M. A., Rabczuk, T., & Liu, W. K. (2015). A multiscale model for the quasi-static thermo-plastic behaviorof highly cross-linked glassy polymers. Macromolecules, 48(18), 6713–6723. https://doi.org/10.1021/acs.macromol.5b01236.

Wang, Ch., Li, Y., Tao, L., Li, Y., Hu, L., & Feng, Z. (2025). Isogeometric analysis of adhesion between visco-hyperelasticmaterial based on modified exponential cohesive zone model. Computer Methods in Applied Mechanics and Engineering,434, 117562. https://doi.org/10.1016/j.cma.2024.117562.

Wang, H.-T., & Wu, G. (2018). Bond-slip models for CFRP plates externally bonded to steel substrates. Composite Structures,184, 1204–1214. https://doi.org/10.1016/j.compstruct.2017.10.033.

Wang, J., Wolf, R. M., Caldwell, J. W., Kollman, P. A., & Case, D. A. (2004). Development and testing of a general amber force field. Journal of Computational Chemistry, 25(9), 1157–1174. https://doi.org/10.1002/jcc.20035.

Ward, I. M., & Sweeney, J. (2012). Mechanical Properties of Solid Polymers (3rd ed.). John Wiley & Sons.Weber, F., Ries, M., Bauer, Ch., Wick, Ch. R., & Pfaller, S. (2023). On equilibrating non-periodic molecular dynamics samplesfor coupled particle-continuum simulations of amorphous polymers. Forces in Mechanics, 10, 100159. https://doi.org/10.1016/j.finmec.2022.100159.

Weber, F., Dötschel, V., Steinmann, P., Pfaller, S., & Ries, M. (2024). Evaluating the impact of filler size and filler content onthe stiffness, strength, and toughness of polymer nanocomposites using coarse-grained molecular dynamics. EngineeringFracture Mechanics, 307, 110270. https://doi.org/10.1016/j.engfracmech.2024.110270.

Weber, F., Vassaux, M., Laubert, L., & Pfaller, S. (2025). How to properly measure the fracture properties of brittle materialsusing molecular simulations? Application to mode I and mode III in silica glass. arXiv. https://doi.org/10.48550/arXiv.2501.16537.

Wehlack, C., & Possart, W. (2005). Chapter 6. Chemical structure formation and morphology in ultrathin polyurethane filmson metals. In W. Possart (Ed.), Adhesion: Current Research and Applications (pp. 71–88). Wiley-VCH. https://doi.org/10.1002/3527607307.ch6.

Wei, Y., Jin, X., Luo, Q., Li, Q., & Sun, G. (2024). Adhesively bonded joints – a review on design, manufacturing, experiments,modeling and challenges. Composites Part B: Engineering, 276, 111225. https://doi.org/10.1016/j.compositesb.2024.111225.

Weiner, S. J., Kollman, P. A., Nguyen, D. T., & Case, D. A. (1986). An all atom force field for simulations of proteins and nucleicacids. Journal of Computational Chemistry, 7(2), 230–252. https://doi.org/10.1002/jcc.540070216.

White, S. R., Mather, P. T., & Smith, M. J. (2002). Characterization of the cure-state of DGEBA-DDS epoxy using ultrasonic,dynamic mechanical, and thermal probes. Polymer Engineering & Science, 42(1), 51–67. https://doi.org/10.1002/pen.10927.

Wu, Ch., & Xu, W. (2006). Atomistic molecular modelling of crosslinked epoxy resin. Polymer, 47(16), 6004–6009. https://doi.org/10.1016/j.polymer.2006.06.025.

Wu, Ch., & Xu, W. (2007). Atomistic molecular simulations of structure and dynamics of crosslinked epoxy resin. Polymer,48(19), 5802–5812. https://doi.org/10.1016/j.polymer.2007.07.019.

Wu, Y., Liu, J., Liu, H., Zhang, Z., Chen, P., & Huang, X. (2025). Mechanical analysis of bone fracture treatment withhydrogel adhesives. International Journal of Adhesion and Adhesives, 136, 103873. https://doi.org/10.1016/j.ijadhadh.2024.103873.

Xia, W., Song, J., Jeong, C., Hsu, D. D., Phelan Jr., F. R., Douglas, J. F., & Keten, S. (2017). Energy-renormalization forachieving temperature transferable coarse-graining of polymer dynamics. Macromolecules, 50(21), 8787–8796. https://doi.org/10.1021/acs.macromol.7b01717.

Xia, W., Hansoge, N. K., Xu, W.-S., Phelan Jr., F. R., Keten, S., & Douglas, J. F. (2019). Energy renormalization for coarse-grainingpolymers having different segmental structures. Science Advances, 5(4). https://doi.org/10.1126/sciadv.aav4683.

Xia, W., Oterkus, E., & Oterkus, S. (2021). Ordinary state-based peridynamic homogenization of periodic micro-structuredmaterials. Theoretical and Applied Fracture Mechanics, 113, 102960. https://doi.org/10.1016/j.tafmec.2021.102960.

Xiao, G. Z., Delamar, M., & Shanahan, M. (1997). Irreversible interactions between water and dgeba/dda epoxy resinduring hygrothermal aging. Journal of Applied Polymer Science, 65(3), 449–458. https://doi.org/10.1002/(sici)1097-4628(19970718)65:3<449::aid-app4>3.0.co;2-h.

Xu, W., & Wei, Y. (2013). Influence of adhesive thickness on local interface fracture and overall strength of metallic adhesivebonding structures. International Journal of Adhesion and Adhesives, 40, 158–167. https://doi.org/10.1016/j.ijadhadh.2012.07.012.

Yagyu, H., Hirai, Y., Uesugi, A., Makino, Y., Sugano, K., Tsuchiya, T., & Tabata, O. (2012). Simulation of mechanical propertiesof epoxy-based chemically amplified resist by coarse-grained molecular dynamics. Polymer, 53(21), 4834–4842. https://doi.org/10.1016/j.polymer.2012.08.050.

Yang, S., & Qu, J. (2014a). An investigation of the tensile deformation and failure of an epoxy/Cu interface using coarse-grainedmolecular dynamics simulations. Modelling and Simulation in Materials Science and Engineering, 22(6), 065011. https://doi.org/10.1088/0965-0393/22/6/065011.

Yang, S., & Qu, J. (2014b). Coarse-grained molecular dynamics simulations of the tensile behavior of a thermosetting polymer.Physical Review E, 90(1), 012601. https://doi.org/10.1103/physreve.90.012601.

Yang, S., Gao, F., & Qu, J. (2013). A molecular dynamics study of tensile strength between a highly-crosslinked epoxy moldingcompound and a copper substrate. Polymer, 54(18), 5064–5074. https://doi.org/10.1016/j.polymer.2013.07.019.

Yang, S., Cui, Z., & Qu, J. (2014). A coarse-grained model for epoxy molding compound. The Journal of Physical Chemistry B,118(6), 1660–1669. https://doi.org/10.1021/jp409297t.

Yarovsky, I., & Evans, E. (2002). Computer simulation of structure and properties of crosslinked polymers: Application toepoxy resins. Polymer, 43(3), 963–969. https://doi.org/10.1016/S0032-3861(01)00634-6.

Yudhanto, A., Alfano, M., & Lubineau, G. (2021). Surface preparation strategies in secondary bonded thermoset-based compositematerials: A review. Composites Part A: Applied Science and Manufacturing, 147, 106443. https://doi.org/10.1016/j.compositesa.2021.106443.

Zernsdorf, K., Mechtcherine, V., Curbach, M., & Bösche, T. (2024). Numerical material testing of mineral-impregnated carbonfiber reinforcement for concrete. Materials, 17(3), 737. https://doi.org/10.3390/ma17030737.

Zhang, S., Yu, T., & Chen, G. (2017). Reinforced concrete beams strengthened in flexure with near-surface mounted (NSM)CFRP strips: Current status and research needs. Composites Part B: Engineering, 131, 30–42. https://doi.org/10.1016/j.compositesb.2017.07.072.

Zhao, W., Steinmann, P., & Pfaller, S. (2021). A particle-continuum coupling method for multiscale simulations of viscoelas-tic–viscoplastic amorphous glassy polymers. International Journal for Numerical Methods in Engineering, 122(24),7431–7451. https://doi.org/10.1002/nme.6836.

Zhou, M. (2003). A new look at the atomic level virial stress: On continuum-molecular system equivalence. Proceedings ofthe Royal Society A: Mathematical, Physical and Engineering Sciences, 459(2037), 2347–2392. https://doi.org/10.1098/rspa.2003.1127.

Zienkiewicz, O. C., Taylor, R. L., & Zhu, J. Z. (2005). The Finite Element Method Set. Elsevier.Zimmerman, J. A., Webb III, E. B., Hoyt, J. J., Jones, R. E., Klein, P. A., & Bammann, D. J. (2004). Calculation of stress inatomistic simulation. Modelling and Simulation in Materials Science and Engineering, 12(4), S319. https://www.doi.org/10.1088/0965-0393/12/4/S03.