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All issues Volume 26 (2025) Mechanics & Industry, 26 (2025) 10 References
Open Access
Issue
Mechanics & Industry
Volume 26, 2025
Article Number 10
Number of page(s) 16
DOI https://doi.org/10.1051/meca/2025004
Published online 12 March 2025
  1. J. Boussinesq, Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques, Gauthier-Villars, Paris, 1885 [Google Scholar]
  2. V. Cerruti, Ricerche Intorno All’equilibrio de’corpi Elastici Isotropi. Reale Accaemia dei Lincei, Roma, 1882 [Google Scholar]
  3. H. Hertz, Über die Berührung fester elastischer Körper, Zeitung Reine Angew. Math. 92, 156-171 (1882) [CrossRef] [Google Scholar]
  4. D.A. Hills, D. Nowell, A. Sackfield, Mechanics of Elastic Contacts. Butterworth-Heinemann, Oxford [England]; Boston, 1993 [Google Scholar]
  5. N.R. Paulson, J.A.R. Bomidi, F. Sadeghi, R.D. Evans, Effects of crystal elasticity on rolling contact fatigue, Int. J. Fatigue 61, 67-75 (2014) [Google Scholar]
  6. J.-P. Noyel, F. Ville, P. Jacquet, A. Gravouil, C. Changenet, Development of a granular cohesive model for rolling contact fatigue analysis: crystal anisotropy modeling, Tribol. Trans. 59, 469-479 (2016) [CrossRef] [Google Scholar]
  7. H. Boffy, C.H. Venner, Multigrid solution of the 3D stress field in strongly heterogeneous materials, Tribol. Int. 74, 121-129 (2014) [CrossRef] [Google Scholar]
  8. B. Zhang, H. Boffy, C.H. Venner, Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials, Tribol. Int. 149, 105636 (2020) [CrossRef] [Google Scholar]
  9. R.A. Lebensohn, A.D. Rollett, Spectral methods for fullfield micromechanical modelling of polycrystalline materials, Computat. Mater. Sci. 173, 109336 (2020) [CrossRef] [Google Scholar]
  10. J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. Lond. Ser. A Math. Phys. Sci. 241, 376-396 (1957) [Google Scholar]
  11. J.D. Eshelby, The elastic field outside an ellipsoidal inclusion, Proc. Roy. Soc. Lond. Ser. A Math. Phys. Sci. 252, 561-569 (1959) [Google Scholar]
  12. T. Mura, Micromechanics of Defects in Solids. No. 3 in Mechanics of Elastic and Inelastic Solids, 2 edn., M. Nijhoff; Distributors for the U.S. and Canada, Kluwer Academic Publishers, Dordrecht, Netherlands ; Boston : Hingham, MA, USA, 1987 [CrossRef] [Google Scholar]
  13. H. Moulinec, P. Suquet, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, Comptes Rendus Acad. Sci. Sér II Méc. Phys. Chim. Astron. 318, 1417-1423 (1994). [Google Scholar]
  14. H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Eng. 157, 69-94 (1998) [CrossRef] [Google Scholar]
  15. F. Sadeghi, B. Jalalahmadi, T.S. Slack, N. Raje, N.K. Arakere, A review of rolling contact fatigue, J. Tribol. 131, 041403 (2009) [CrossRef] [Google Scholar]
  16. Q.J. Wang, L. Sun, X. Zhang, S. Liu, D. Zhu, FFT-based methods for computational contact mechanics, Front. Mech. Eng. 6, 61 (2020). [CrossRef] [Google Scholar]
  17. S. Lucarini, M.V. Upadhyay, J. Segurado, FFT based approaches in micromechanics: fundamentals, methods and applications, Model. Simul. Mater. Sci. Eng. 30, 023002 (2022). [CrossRef] [Google Scholar]
  18. G. Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, T. Wheelhouse, Nottingham, 1828 [Google Scholar]
  19. J. Fourier, Théorie Analytique de La Chaleur, Firmin Didot, Paris, 1822 [Google Scholar]
  20. I. Polonsky, L. Keer, A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques, Wear 231, 206-219 (1999) [CrossRef] [Google Scholar]
  21. P. Sainsot, A.A. Lubrecht, Efficient solution of the dry contact of rough surfaces: a comparison of fast Fourier transform and multigrid methods, Proc. Inst. Mech. Eng. J 225, 441-448 (2011). [CrossRef] [Google Scholar]
  22. S. Liu, Q. Wang, G. Liu, A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses, Wear 243, 101-111 (2000) [CrossRef] [Google Scholar]
  23. L. Frérot, G. Anciaux, V. Rey, S. Pham-Ba, J.-F. Molinari, Tamaas: a library for elastic–plastic contact of periodic rough surfaces, J. Open Source Softw. 5, 2121 (2020) [CrossRef] [Google Scholar]
  24. M.H. Müser, W.B. Dapp, R. Bugnicourt, P. Sainsot, N. Lesaffre, T.A. Lubrecht, B.N.J. Persson, K. Harris, A. Bennett, K. Schulze, S. Rohde, P. Ifju, W.G. Sawyer, T. Angelini, H. Ashtari Esfahani, M. Kadkhodaei, S. Akbarzadeh, J.-J. Wu, G. Vorlaufer, A. Vernes, S. Solhjoo, A.I. Vakis, R.L. Jackson, Y. Xu, J. Streator, A. Rostami, D. Dini, S. Medina, G. Carbone, F. Bottiglione, L. Afferrante, J. Monti, L. Pastewka, M.O. Robbins, J.A. Greenwood, Meeting the contact-mechanics challenge, Tribol. Lett. 65, 118 (2017) [CrossRef] [Google Scholar]
  25. M. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bureau Standards 49, 409 (1952) [CrossRef] [Google Scholar]
  26. K.L. Johnson, Contact Mechanics. Cambridge University Press, Cambridge, 1987 [Google Scholar]
  27. J.J. Kalker, Three-Dimensional Elastic Bodies in Rolling Contact, vol. 2 of Solid Mechanics and Its Applications. Springer Netherlands, Dordrecht, 1990 [Google Scholar]
  28. G. Duvaut, J.L. Lions, Les inéquations en mécanique et en Physique, Dunod, Paris, 1972 [Google Scholar]
  29. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edn., Cambridge University Press, 1927 [Google Scholar]
  30. C. Mayeur, P. Sainsot, L. Flamand, A numerical elasto- plastic model for rough contact, J. Tribol. 117, 422-429 (1995) [CrossRef] [Google Scholar]
  31. P. Sainsot, C. Jacq, D. Nelias, A numerical model for elasto- plastic rough contact, Comput. Model. Eng. Sci. 3, 497-506 (2002) [Google Scholar]
  32. F. Wang, L.M. Keer, Numerical simulation for three dimensional elastic-plastic contact with hardening behavior, J. Tribol. 127, 494-502 (2005) [CrossRef] [Google Scholar]
  33. K. Zhou, W.W. Chen, L.M. Keer, Q.J. Wang, A fast method for solving three-dimensional arbitrarily shaped inclusions in a half space, Comput. Methods Appl. Mech. Eng. 198, 885-892 (2009) [CrossRef] [Google Scholar]
  34. J. Leroux, B. Fulleringer, D. Nelias, Contact analysis in presence of spherical inhomogeneities within a half-space, Int. J. Solids Struct. 47, 3034-3049 (2010) [Google Scholar]
  35. K. Zhou, W. Wayne Chen, L.M. Keer, X. Ai, K. Sawamiphakdi, P. Glaws, Q. Jane Wang, Multiple 3D inhomogeneous inclusions in a half space under contact loading, Mech. Mater. 43, 444-457 (2011) [CrossRef] [Google Scholar]
  36. E. Kröner, Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls, Z. Phys. 151, 504-518 (1958) [CrossRef] [Google Scholar]
  37. F. Willot, Fourier-based schemes for computing the mechanical response of composites with accurate local fields, Comptes Rendus Méc. 343, 232-245 (2015) [Google Scholar]
  38. R.A. Lebensohn, R. Brenner, O. Castelnau, A.D. Rollett, Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper, Acta Materialia 56, 3914-3926 (2008) [CrossRef] [Google Scholar]
  39. P. Suquet, H. Moulinec, O. Castelnau, M. Montagnat, N. Lahellec, F. Grennerat, P. Duval, R. Brenner, Multiscale modeling of the mechanical behavior of polycrystalline ice under transient creep, Procedia IUTAM 3, 76-90 (2012) [CrossRef] [Google Scholar]
  40. J.-B. Gasnier, F. Willot, H. Trumel, B. Figliuzzi, D. Jeulin, M. Biessy, A Fourier-based numerical homogenization tool for an explosive material, Matér. Tech. 103, 308 (2015) [Google Scholar]
  41. A. Schmidt, C. Gierden, J. Waimann, B. Svendsen, S. Reese, Two-scale FE-FFT-based thermo-mechanically coupled modeling of elasto-viscoplastic polycrystalline materials at finite strains, PAMM 22, e202200172 (2023) [CrossRef] [Google Scholar]
  42. N.B. Nkoumbou Kaptchouang, L. Gelebart, Extension des solveurs FFT aux conditions aux limites non périodiques et aux méthodes multi-grilles locales, in: 15ème Colloque National En Calcul Des Structures, (83400 Hyères- les-Palmiers, France), Université Polytechnique Hauts-de- France [UPHF], May 2022. [Google Scholar]
  43. C. Cocke, H. Mirmohammad, M. Zecevic, B. Phung, R. Lebensohn, O. Kingstedt, A. Spear, Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials, Int. J. Plast. 162, 103508 (2023) [CrossRef] [Google Scholar]
  44. M. Zecevic, R.A. Lebensohn, L. Capolungo, Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates, J. Mech. Phys. Solids 173, 105187 (2023) [CrossRef] [Google Scholar]
  45. R. Quey, P. Dawson, F. Barbe, Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing, Comput. Methods Appl. Mech. Eng. 200, 1729-1745 (2011) [CrossRef] [Google Scholar]
  46. W. Voigt, Lehrbuch Der Kristallphysik (Mit Ausschluss Der Kristalloptik), Teubner, Leipzig, Berlin, 1910 [Google Scholar]
  47. T.H. Courtney, Mechanical Behavior of Materials, 2nd edn. Waveland Press, Long Grove, Illinois, 2005 [Google Scholar]
  48. E. Bossy, J. Noyel, X. Kleber, F. Ville, C. Sidoroff, S. Thibault, Competition between surface and subsurface rolling contact fatigue failures of nitrided parts: a Dang Van approach, Tribol. Int. 140, 105888 (2019) [CrossRef] [Google Scholar]
  49. G. Vouaillat, J.-P. Noyel, F. Ville, X. Kleber, S. Rathery, From Hertzian contact to spur gears: Analyses of stresses and rolling contact fatigue, Mech. Ind. 20, 626 (2019) [CrossRef] [EDP Sciences] [Google Scholar]
  50. L. Fourel, J.-P. Noyel, E. Bossy, X. Kleber, P. Sainsot, F. Ville, Towards a grain-scale modeling of crack initiation in rolling contact fatigue – Part 1: shear stress considerations, Tribol. Int. 164, 107224 (2021) [CrossRef] [Google Scholar]
  51. L. Fourel, J.-P. Noyel, E. Bossy, X. Kleber, P. Sainsot, F. Ville, Towards a grain-scale modeling of crack initiation in rolling contact fatigue – Part 2: persistent slip band modeling, Tribol. Int. 163, 107173 (2021) [CrossRef] [Google Scholar]
  52. S. Coulon, F. Ville, and A.A. Lubrecht, Effect of a dent on the pressure distribution in dry point contacts, J. Tribol. 124, 220-223 (2002) [CrossRef] [Google Scholar]
  53. L. Fourel, J.-P. Noyel, X. Kleber, P. Sainsot, F. Ville, Numerical analysis of 3D crack initiation under rolling contact fatigue in polycrystals with surface dents and subsurface inclusions, in preparation, 2023 [Google Scholar]

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