1. Партон В. З., Морозов Е. М. Механика упруго-пластического разрушения. М.: Наука, 1974.
2. Черепанов Г. П. Механика хрупкого разрушения. М.: Наука, 1974.
3. Itou H., Khludnev A. M., Rudoy E. M., Tani A. Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity // Z. Angew. Math. Mech. 2012. V. 92, N 9. P. 716-730.
4. Liang F., Wang Z.-X., Zhang B., Luo X.-M., Zhang G.-P. Heterogeneous interface-enhanced strength of Ni/Ni-W laminated nanocomposites for high-temperature MEMS devices // Composites Part B: Eng. 2022. V. 15. Art. ID 110170.
5. Serrano F. R., Steinhardt E., Wood R. J. Considerations for the design and rapid manufacturing of pop-up MEMS devices // Adv. Mater. Technol. 2024. V. 9. Art. ID 2301940.
6. Xue Z., Saif M.T.A., Huang Y. The strain gradient effect in microelectromechanical systems (MEMS) // J. Microelectromech. Syst. 2002. V. 11. P. 27-35.
7. Mindlin R. D. Micro-structure in linear elasticity // Arch. Ration. Mech. Anal. 1964. V. 16. P. 51-78.
8. Mindlin R. D., Eshel N. N. On first strain-gradient theories in linear elasticity // Int. J. Solids Struct. 1968. V. 4, N 1. P. 109-124.
9. Niiranen J., Khakalo S., Balobanov V., Niemi A. H. Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/ stress problems // Comput. Methods Appl. Mech. Eng. 2016. V. 308. P. 182-211.
10. Desai S., Sidhardh S. Beyond classical elasticity: A review of strain gradient theories, emphasizing computer modeling, physical interpretations, and multifunctional applications // CMES: Comput. Model. Eng. Sci. 2025. V. 144, N 2. P. 1271-1334.
11. Ru C. Q., Aifantis E. C. A simple approach to solve boundary-value problems in gradient elasticity // Acta Mech. 1993. V. 101. P. 59-68.
12. Altan S. B., Aifantis E. C. On some aspects in the special theory of gradient elasticity // J. Mech. Behav. Mater. 1997. V. 8, N 3. P. 231-282.
13. Aifantis E. C. Strain gradient interpretation of size effects // Int. J. Fract. 1999. V. 95. P. 299-314.
14. Садовский В. М., Садовская О. В. Задача о бегущей краевой дислокации // Прикл. механика и техн. физика. 2025. № 1. С. 163-173.
15. Chen Y.-H., Lu T. J. Recent developments and applications of invariant integrals // Appl. Mech. Rev. 2003. V. 56, N 5. P. 515-551.
16. Andrieux S., Ben Abda A., Bui Y. Reciprocity principle and crack identification // Inverse Probl. 1999. V. 15. P. 59-69.
17. Goldstein R., Shifrin E., Shushpannikov P. Application of invariant integrals to the problems of defect identification // Int. J. Fract. 2007. V. 147. P. 45-54.
18. Zhang L., Huang Y., Chen J. Y., Hwang K. C. The mode III full-field solution in elastic materials with strain gradient effects // Int. J. Fract. 1998. V. 92. P. 325-348.
19. Georgiadis H. G., Grentzelou C. G. Energy theorems and the J-integral in dipolar gradient elasticity // Int. J. Solids Struct. 2006. V. 43. P. 5690-5712.
20. Lubarda V. A., Markensco X. Conservation integrals in couple stress elasticity // J. Mech. Phys. Solids. 2000. V. 48. P. 553-564.
21. Khludnev A. M., Sokolowski J. The Griffith formula and the Rice-Cherepanov integral for crack problems with unilateral conditions in nonsmooth domains // Eur. J. Appl. Math. 1999. V. 10. P. 379-394.
22. Kovtunenko V. A. Primal-dual methods of shape sensitivity analysis for curvilinear cracks with nonpenetration // IMA J. Appl. Math. 2006. V. 71. P. 635-657.
23. Rudoy E. M., Khludnev A. M. Unilateral contact of a plate with a thin elastic obstacle // J. Appl. Ind. Math. 2009. V. 4, N 3. С. 389-398.
24. Furtsev A., Itou H., Rudoy E. Modeling of bonded elastic structures by a variational method: Theoretical analysis and numerical simulation // Int. J. Solids Struct. 2020. V. 182-183. P. 100-111.
25. Kovtunenko V. A., Lazarev N. The energy release rate for non-penetrating crack in poroelastic body by fluid-driven fracture // Math. Mech. Solids. 2023. V. 28, N 2. P. 592-610.
26. Khludnev A. M., Shcherbakov V. V. Singular path-independent energy integrals for elastic bodies with Euler-Bernoulli inclusions // Math. Mech. Solids. 2017. V. 22, N 11. P. 2180-2195.
27. Lomakin E. V., Lurie S. A., Rabinskiy L. N., Solyaev Y. O. Stress concentration near stiff cylindrical inclusions under anti-plane shear loading // Dokl. Phys. 2020. V. 65, N 11. P. 390- 395.
28. Unger D. J., Aifantis E. C. Strain gradient elasticity theory for antiplane shear cracks. I: oscillatory displacements // Theor. Appl. Fract. Mech. 2000. V. 34. P. 243-252.
29. Unger D. J., Aifantis E. C. Strain gradient elasticity theory for antiplane shear cracks. II: monotonic displacements // Theor. Appl. Fract. Mech. 2000. V. 34. P. 253-265.
30. Vardoulakis I., Exadaktylos G., Aifantis E. Gradient elasticity with surface energy: mode-III crack problem // Int. J. Solids Struct. 1996. V. 33, N 30. P. 4531-4559.
31. Rudoy E., Sazhenkov S. Imperfect interface models for elastic structures bonded by a strain gradient layer: the case of antiplane shear // Z. Angew. Math. Phys. 2025. V. 76, N 1. Art. ID 42.
32. Хлуднев А. М. Задачи теории упругости в негладких областях. М.: Физматлит, 2010.
33. Khludnev A. M. Nonlinear boundary problem in strain gradient elasticity for a body with a crack // Comput. Math. Model. 2026. (to appear).
34. Nečas J. Direct methods in the theory of elliptic equations. Berlin: Springer, 2012.
35. Rudoy E. M. Invariant integrals for the equilibrium problem for a plate with a crack // Sib. Math. J. 2004. V. 45, N 2. P. 388-397.
36. Rudoy E. M. Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut // Sib. Math. J. 2009. V. 50, N 2. P. 341-354.
37. Browder F. E. On the regularity properties of solutions of elliptic differential equations // Commun. Pure Appl. Math. 1956. V. 9, N 3. P. 351-361.
38. Кошелев А. И. Об ограниченности в Lp производных решений эллиптических уравнений и систем // Успехи мат. наук. 1958. Т. 13, № 4. С. 29-88.
39. Рудой Е. М. Формула Гриффитса для пластины с трещиной // Сиб. журн. индустр. математики. 2002. Т. 5, № 3. С. 155-161.