Effect of surface tension on the antiplane deformation of bimaterial with a thin interface microinclusion
| dc.citation.epage | 77 | |
| dc.citation.issue | 1 | |
| dc.citation.spage | 69 | |
| dc.contributor.affiliation | Українська академія друкарства | |
| dc.contributor.affiliation | Інститут прикладних проблем механіки і математики | |
| dc.contributor.affiliation | Ukrainian Academy of Printing | |
| dc.contributor.affiliation | Pidstryhach Institute for Applied Problems of Mechanics and Mathematics | |
| dc.contributor.author | Піскозуб, Йосиф Збігнєвич | |
| dc.contributor.author | Piskozub, Y. Z. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2023-10-03T09:31:49Z | |
| dc.date.available | 2023-10-03T09:31:49Z | |
| dc.date.created | 2021-03-01 | |
| dc.date.issued | 2021-03-01 | |
| dc.description.abstract | У межах концепції мікромеханіки запропоновано методику врахування впливу поверхневих напружень для тонкого міжфазного мікровключення у біматеріалі за умов поздовжнього зсуву. При цьому передбачено можливість неідеального контакту між включенням та матрицею, зокрема контакту з натягом. Це значно розширює сферу застосовності результатів. Побудовано узагальнену модель тонкого включення з довільними пружними механічними властивостями. На основі застосування теорії функції комплексної змінної та методу функцій стрибка проведено розрахунок поля напружень в околі включення при його взаємодії з гвинтовою дислокацією. Виявлено ряд ефектів, які можуть бути використані для оптимізації енергетичних параметрів задачі. | |
| dc.description.abstract | Within the framework of the concept of micromechanics, a method for taking into account the effect of surface energy for a thin interface micro-inclusion in the bimaterial under conditions of longitudinal shear has been proposed. The possibility of non-ideal contact between inclusion and matrix is provided, in particular, tension contact. This significantly extends the scope of applicability of the results. A generalized model of a thin inclusion with arbitrary elastic mechanical properties was built. Based on the application of the theory of functions of a complex variable and the jump function method, the stress field in the vicinity of the inclusion during its interaction with the screw dislocation was calculated. Several effects have been identified that can be used to optimize the energy parameters of the problem. | |
| dc.format.extent | 69-77 | |
| dc.format.pages | 9 | |
| dc.identifier.citation | Piskozub Y. Z. Effect of surface tension on the antiplane deformation of bimaterial with a thin interface microinclusion / Y. Z. Piskozub // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 1. — P. 69–77. | |
| dc.identifier.citationen | Piskozub Y. Z. Effect of surface tension on the antiplane deformation of bimaterial with a thin interface microinclusion / Y. Z. Piskozub // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 1. — P. 69–77. | |
| dc.identifier.doi | doi.org/10.23939/mmc2021.01.069 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/60331 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 1 (8), 2021 | |
| dc.relation.references | [1] Kizler P., Uhlmann D., Schmauder S. Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress-strain curves owing to dislocation theory. Nuclear Engineering and Design. 196 (2), 175–183 (2000). | |
| dc.relation.references | [2] Kizler P., Uhlmann D., Schmauder S. Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress-strain curves owing to dislocation theory. Naukova dumka, Kyiv (1978), (in Ukrainian). | |
| dc.relation.references | [3] Mura T. Micromechanics of Defects in Solids. Springer, Dordrecht (1987). | |
| dc.relation.references | [4] Nemat-Nasser S., Hori M. Micromechanics: overall properties of heterogeneous materials. Elsevier, Amsterdam (1999). | |
| dc.relation.references | [5] Sharma P., Ganti S., Bhate N. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82 (4), 535–537 (2003). | |
| dc.relation.references | [6] Duan H. L., Wang J., Huang Z. P., Karihaloo B. L. Eshelby formalism for nano-inhomogeneities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 461 (2062), 3335–3353 (2005). | |
| dc.relation.references | [7] Wang J., Karihaloo B. L., Duan H. L. Nano-mechanics or how to extend continuum mechanics to nano-scale. J. Bulletin of the Polish academy of sciences. Technical sciences. 55 (2), 133–140 (2007). | |
| dc.relation.references | [8] Gurtin M. E., Murdoch A. I. Surface Stress in Solids. International Journal of Solids and Structures. 14 (6), 431–440 (1978). | |
| dc.relation.references | [9] Hrytsyna O. Determination of solids surface energy. Physico-mathematical modelling and information technologies. 17, 43–54 (2013), (in Ukrainian). | |
| dc.relation.references | [10] Kim C. I., Schiavone P., Ru C. Q. The Effects of Surface Elasticity on Mode-III Interface Crack. Archives of Mechanics. 63 (3), 267–286 (2011). | |
| dc.relation.references | [11] Kushch V. I., Shmegera S. V., Buryachenko V. A. Interacting elliptic inclusions by the method of complex potentials. Interacting elliptic inclusions by the method of complex potentials. 42 (20), 5491–5512 (2005). | |
| dc.relation.references | [12] Povstenko Yu. Z. Theoretical investigation of phenomena caused by heterogeneous surface-tension in solids. Journal of the Mechanics and Physics of Solids. 41 (9), 1499–1514 (1993). | |
| dc.relation.references | [13] Steigmann D. J., Ogden R.W. Elastic surface — substrate interactions. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. 455 (1982), 437–474 (1999). | |
| dc.relation.references | [14] Gurtin M. E., Murdoch A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis. 57, 291–323 (1975). | |
| dc.relation.references | [15] Sharma P., Ganti S. Size-Dependent Eshelby’s Tensor for embedded nano-inclusions incorporating surface/interface energies. J. Appl. Mech. 71 (5), 663–671 (2004). | |
| dc.relation.references | [16] Eshelby J. D. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 241 (1226), 376–396 (1957). | |
| dc.relation.references | [17] Wang J., Duan H. L., Huang Z. P., Karihaloo B. L. A scaling law for properties of nano-structured materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 462 (2069), 1355–1363 (2006). | |
| dc.relation.references | [18] Wang Xu, Schiavone P. A mode III interface crack with surface strain gradient elasticity. Journal of integral equations and applications. 28, 123–148 (2016). | |
| dc.relation.references | [19] Sulim G. T., Piskozub J. Z. Thermoelastic equilibrium of piecewise homogeneous solids with thin inclusions. Journal of Engineering Mathematics. Special Issue Thermomechanics. 61, 315–337 (2008). | |
| dc.relation.references | [20] Sulym H., Piskozub L., Piskozub Y., Pasternak I. Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction. 2. Repeating and Cyclic loadingv. Acta Mechanica et Automatica. 9 (3), 178–184 (2015). | |
| dc.relation.references | [21] Sulym H., Piskozub L., Piskozub Y., Pasternak I. Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction. I. Single loading. Acta Mechanica et Automatica. 9 (2), 115–121 (2015). | |
| dc.relation.references | [22] Sulym H. et al. Longitudinal shear of a bimaterial with frictional sliding contact in the interfacial crack Journal of Theoretical and Applied Mechanics. 54 529 (2015). | |
| dc.relation.references | [23] Sulym H. T., Piskozub I. Z. Nonlinear deformation of a thin interface inclusion. Materials Science. 53, 600–608 (2018). | |
| dc.relation.references | [24] Sulym H. T. Bases of the mathematical theory of thermoelastic equilibrium of deformable solids with thin inclusions. Research and Publishing center of NTSh, L’viv (2007), (in Ukrainian). | |
| dc.relation.references | [25] Benveniste Y., Miloh T. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials. 33 (6), 309–323 (2001). | |
| dc.relation.references | [26] Piskozub I. Z., Sulym H. T. Asymptotic of stresses in the vicinity of a thin elastic interphase inclusion. Materials Science. 32, 421–432 (196). | |
| dc.relation.referencesen | [1] Kizler P., Uhlmann D., Schmauder S. Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress-strain curves owing to dislocation theory. Nuclear Engineering and Design. 196 (2), 175–183 (2000). | |
| dc.relation.referencesen | [2] Kizler P., Uhlmann D., Schmauder S. Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress-strain curves owing to dislocation theory. Naukova dumka, Kyiv (1978), (in Ukrainian). | |
| dc.relation.referencesen | [3] Mura T. Micromechanics of Defects in Solids. Springer, Dordrecht (1987). | |
| dc.relation.referencesen | [4] Nemat-Nasser S., Hori M. Micromechanics: overall properties of heterogeneous materials. Elsevier, Amsterdam (1999). | |
| dc.relation.referencesen | [5] Sharma P., Ganti S., Bhate N. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82 (4), 535–537 (2003). | |
| dc.relation.referencesen | [6] Duan H. L., Wang J., Huang Z. P., Karihaloo B. L. Eshelby formalism for nano-inhomogeneities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 461 (2062), 3335–3353 (2005). | |
| dc.relation.referencesen | [7] Wang J., Karihaloo B. L., Duan H. L. Nano-mechanics or how to extend continuum mechanics to nano-scale. J. Bulletin of the Polish academy of sciences. Technical sciences. 55 (2), 133–140 (2007). | |
| dc.relation.referencesen | [8] Gurtin M. E., Murdoch A. I. Surface Stress in Solids. International Journal of Solids and Structures. 14 (6), 431–440 (1978). | |
| dc.relation.referencesen | [9] Hrytsyna O. Determination of solids surface energy. Physico-mathematical modelling and information technologies. 17, 43–54 (2013), (in Ukrainian). | |
| dc.relation.referencesen | [10] Kim C. I., Schiavone P., Ru C. Q. The Effects of Surface Elasticity on Mode-III Interface Crack. Archives of Mechanics. 63 (3), 267–286 (2011). | |
| dc.relation.referencesen | [11] Kushch V. I., Shmegera S. V., Buryachenko V. A. Interacting elliptic inclusions by the method of complex potentials. Interacting elliptic inclusions by the method of complex potentials. 42 (20), 5491–5512 (2005). | |
| dc.relation.referencesen | [12] Povstenko Yu. Z. Theoretical investigation of phenomena caused by heterogeneous surface-tension in solids. Journal of the Mechanics and Physics of Solids. 41 (9), 1499–1514 (1993). | |
| dc.relation.referencesen | [13] Steigmann D. J., Ogden R.W. Elastic surface - substrate interactions. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. 455 (1982), 437–474 (1999). | |
| dc.relation.referencesen | [14] Gurtin M. E., Murdoch A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis. 57, 291–323 (1975). | |
| dc.relation.referencesen | [15] Sharma P., Ganti S. Size-Dependent Eshelby’s Tensor for embedded nano-inclusions incorporating surface/interface energies. J. Appl. Mech. 71 (5), 663–671 (2004). | |
| dc.relation.referencesen | [16] Eshelby J. D. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 241 (1226), 376–396 (1957). | |
| dc.relation.referencesen | [17] Wang J., Duan H. L., Huang Z. P., Karihaloo B. L. A scaling law for properties of nano-structured materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 462 (2069), 1355–1363 (2006). | |
| dc.relation.referencesen | [18] Wang Xu, Schiavone P. A mode III interface crack with surface strain gradient elasticity. Journal of integral equations and applications. 28, 123–148 (2016). | |
| dc.relation.referencesen | [19] Sulim G. T., Piskozub J. Z. Thermoelastic equilibrium of piecewise homogeneous solids with thin inclusions. Journal of Engineering Mathematics. Special Issue Thermomechanics. 61, 315–337 (2008). | |
| dc.relation.referencesen | [20] Sulym H., Piskozub L., Piskozub Y., Pasternak I. Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction. 2. Repeating and Cyclic loadingv. Acta Mechanica et Automatica. 9 (3), 178–184 (2015). | |
| dc.relation.referencesen | [21] Sulym H., Piskozub L., Piskozub Y., Pasternak I. Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction. I. Single loading. Acta Mechanica et Automatica. 9 (2), 115–121 (2015). | |
| dc.relation.referencesen | [22] Sulym H. et al. Longitudinal shear of a bimaterial with frictional sliding contact in the interfacial crack Journal of Theoretical and Applied Mechanics. 54 529 (2015). | |
| dc.relation.referencesen | [23] Sulym H. T., Piskozub I. Z. Nonlinear deformation of a thin interface inclusion. Materials Science. 53, 600–608 (2018). | |
| dc.relation.referencesen | [24] Sulym H. T. Bases of the mathematical theory of thermoelastic equilibrium of deformable solids with thin inclusions. Research and Publishing center of NTSh, L’viv (2007), (in Ukrainian). | |
| dc.relation.referencesen | [25] Benveniste Y., Miloh T. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials. 33 (6), 309–323 (2001). | |
| dc.relation.referencesen | [26] Piskozub I. Z., Sulym H. T. Asymptotic of stresses in the vicinity of a thin elastic interphase inclusion. Materials Science. 32, 421–432 (196). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2021 | |
| dc.subject | мікронеоднорідності | |
| dc.subject | біматеріал | |
| dc.subject | поверхневі напруження | |
| dc.subject | неідеальний контакт | |
| dc.subject | функції стрибка | |
| dc.subject | дислокації | |
| dc.subject | micro-inhomogeneities | |
| dc.subject | bimaterial | |
| dc.subject | surface tension | |
| dc.subject | nonperfect contact | |
| dc.subject | jump functions | |
| dc.subject | dislocation | |
| dc.title | Effect of surface tension on the antiplane deformation of bimaterial with a thin interface microinclusion | |
| dc.title.alternative | Вплив поверхневих напружень на антиплоске деформування біматеріалу з тонким міжфазним мікровключенням | |
| dc.type | Article |
Files
License bundle
1 - 1 of 1