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مساله‌ی متقارن کروی در نظریه‌ی گرادیان دوم کرنش | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 3، دوره 53، شماره 2، اردیبهشت 1400، صفحه 709-728 اصل مقاله (2.38 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2019.16554.6388 | ||
| نویسنده | ||
| فرزانه اجاق نژاد* | ||
| گروه عمران، دانشکده فنی و مهندسی، دانشگاه الزهرا، تهران، ایران | ||
| چکیده | ||
| هدف، حل مساله‌ی متقارن کروی یک/دو فازی با استفاده از الاستیسیته‌ی گرادیان دوم کرنش و مقایسه با الاستیسیته‌ی کلاسیک است. نظر به قابلیت گرادیان دوم کرنش در پیش‌بینی اثرات سطح، اندازه و ماهیت گسسته‌ی مواد، مساله‌ی متقارن کروی مدلسازی و تحت اثرات مذکور مطالعه می‌شود. با تبیین گرادیان دوم کرنش در دستگاه مختصات کروی، معادلات تعادل، میدان تنش و کرنش، روابط آنها و نیروهای سطحی استخراج می‌شود. بعد از آسایش سطحی، بارگذاری خارجی متقارن روی سازه اعمال و پاسخ مکانیکی بررسی می‌شود. خواص مکانیکی پوسته تک‌فازی از بلور الماس و پوسته‌ی دوفازی از سیلیکون بلوری با پوشش کربنی مطالعه می‌شود. مقادیر ثابت‌های مواد توسط محاسبات کوانتومی، نظریه‌ی دینامیک شبکه و مدلسازی محیط پیوسته محاسبه می‌شود. محاسبات نشان می‌دهد که پیش‌بینی نظریه‌ی تقویت‌یافته از خواص نانوسازه تفاوت چشمگیری با پیش‌بینی کلاسیک دارد. مثلا، در پوسته‌ی کربنی با شعاع داخلی و خارجی به ترتیب 2 و 10 برابر پارامتر شبکه، تحت بارگذاری فشاری خارجی یکه شده‌ی 0001/0، تنش شعاعی کلاسیک یکه، ثابت و حدود 0001/0- است، درحالیکه در گرادیان کرنش، تنش شعاعی یکه از مقادیر 001/0- و 0002/0- در مرزهای داخلی و خارجی، به ترتیب، به 0003/0 در میانه متغیر است. با افزایش شعاع داخلی، اختلاف دو نظریه در میانه‌ی محیط کاهش می‌یابد اما در نزدیکی سطوح اختلاف قابل ملاحظه است. | ||
| کلیدواژه‌ها | ||
| نظریه‌ی گرادیان دوم کرنش؛ اثر اندازه؛ اثر سطح؛ لمه‌گونه‌ی کروی؛ تقارن کروی | ||
| عنوان مقاله [English] | ||
| Spherical Lame-Type Problem in Second Strain Gradient Theory | ||
| نویسندگان [English] | ||
| Farzaneh Ojaghnezhad | ||
| Engineering Department, Alzahra University, Tehran, Iran | ||
| چکیده [English] | ||
| Second strain gradient theory is employed to examine the spherical single/double-phase Lame-type problem. Due to the capability of strain gradient theory to capture the effects of the surface, size, and discrete nature of materials, the pertinent relaxed configuration is sought. The theory is written in the spherical coordinate system and the equilibrium equations, stress/strain components, constitutive relations, and tractions are derived. The relaxed configuration is obtained for both the diamond carbon and carbon-coated crystalline silicon shell. Afterwards, the external symmetric loading is applied to the relaxed configuration to analyze the mechanical response. The elastic material parameters are calculated via the quantum computations, lattice dynamics, and material continuum description. The analysis shows that the mechanical response in the augmented theory is significantly different from that in the classical elasticity. For example, in the single-phase problem with an inner and outer radius equal to two and ten lattice parameter, respectively, under a normalized external pressure of about 0.0001, the classic elasticity predicts an approximately constant normalized radial stress of about -0.0001 in the nanoshell. However, in the framework of strain gradient theory, the normalized radial stress is varying from about -0.001 and -0.0002 in the vicinity of the inner and outer boundaries, respectively, to about 0.0003 in the middle of the hollow nanoshell. With increasing the inner radius, the difference between the two results in the middle points decreases. | ||
| کلیدواژه‌ها [English] | ||
| Second strain gradient theory, Size effect, Surface effect, Spherical Lame-type problem, Spherical symmetry | ||
| اصل مقاله | ||
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| مراجع | ||
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[1] H. Hatami, M. Hosseini, Elastic-plastic analysis of bending moment-axial force interaction in metallic beam of T-section, J. Applied Comp. Mech., 5 (2019) 162-173. [2] H. Hatami, M. Hosseini, A.K. Yasuri, Perforation of thin Aluminum targets under hypervelocity impact of aluminum spherical projectiles, Materials Evaluation, 77 (2019) 411-422. [3] M. Shariati, H. Hatami, H.R. Eipakchi, H. Yarahmadi, H. Torabi, Experimental and numerical investigations on softening behavior of POM under cyclic strain-controlled loading, Polymar-Plastics Technology and Engineering, 50 (2011) 1576-1582. [4] M. Lazar, Dislocations and Cracks in Generalized Continua. Encyclopedia of Continuum Mechanics, Springer-Verleg GmbH, Germany, 2018. [5] M. Lazar, E. Agiasofitu, Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor, dislocation key-formulas and dislocation loops, Philosophical Magazine, 94(35) (2014) 4080-4101. [6] G. Po, N.C. Admal, M. Lazar, The Green tensor of Mindlin’s anisotropic first strain gradient elasticity, Materials Theory, 3(1) (2019) 3. [7] M.R. Delfani, S. Shojaeimanesh, V. Bagherpour, Effective shear modulus of functionally graded fibrous composites in second strain gradient elasticity, Journal of Elasticity, 137(1) (2018) 43-62. [8] R.A. Toupin, Theories of elasticity with couple-stress, Archive for Rational Mechanics and Analysis, 17(2) (1964) 85-112. [9] R.A. Toupin, D.C. Gazis, Surface effects and initial stress in continuum and lattice models of elastic crystals, in: Wallis (Ed.) International Conference on Lattice Dynamics, Pergamon press, Copenhagen, 1963, pp. 597-602. [10] R.D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, 1 (1965) 417-438. [11] F. Ojaghnezhad, H.M. Shodja, A combined first principles and analytical determination of the modulus of cohesion, surface energy, and the additional constants in the second strain gradient elasticity, International Journal of Solids and Structures, 50(24) (2013) 3967-3974. [12] F. Ojaghnezhad, H.M. Shodja, Surface elasticity revisited in the context of second strain gradient theory, Mechanics of Materials, 93 (2016) 220-237. [13] M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis, 57 (1975) 291-323. [14] A.C. Eringen, Mechanics of continua, Robert E. Krieger publishing compan, New York, 1980. [15] X. Ji, A.Q. Li, S.J. Zhou, The strain gradient elasticity theory in orthogonal curvilinear coordinates and its applications, Journal of Mechanics, 34(3) (2016) 311-323. [16] S. Zhou, A. Li, B. Wang, A reformulation of constitutive relations in the strain gradient elasticity theory for isotropic materials, International Journal of Solids and Structures, 80 (2016) 28-37. [17] F. Ojaghnezhad, H.M. Shodja, Second strain gradient theory in orthogonal curvilinear coordinates: Prediction of the relaxation of a solid nanosphere and embedded spherical nanocavity, Applied Mathematical Modelling, 76 (2019) 669-698. [18] H.M. Shodja, F. Ahmadpoor, A. Tehranchi, Calculation of the additional constants for fcc materials in second strain gradient elasticity: behavior of a nano-size Bernoulli-Euler beam with surface effects, ASME Journal of Applied Mechanics, 79 (2012) 021008-021015. [19] H.M. Shodja, H. Moosavian, F. Ojaghnezhad, Toupin–Mindlin first strain gradient theory revisited for cubic crystals of hexoctahedral class: Analytical expression of the material parameters in terms of the atomic force constants and evaluation via ab initio DFT, Mechanics of Materials, 123 (2018) 19-29. [20] H.M. Shodja, F. Ojaghnezhad, A. Etehadieh, M. Tabatabaei, Elastic moduli tensors, ideal strength, and morphology of stanene based on an enhanced continuum model and first principles, Mechanics of Materials, 110 (2017) 1-15. [21] H.M. Shodja, A. Zaheri, A. Tehranchi, Ab initio calculations of characteristic lengths of crystalline materials in first strain gradient elasticity, Mechanics of Materials, 61 (2013) 73-78. [22] Q. He, M. Ashuri, K. Zhang, S. Emani, M.S. Sawicki, J.S. Shamie, L.L. Shaw, Synthesis of carbon-coated hollow silicon nanospheres for Lithium-ion battery application, in: Materials Science & Technology, Pittsburgh, PA, USA, 2014. [23] B. Li, F. Yao, J.J. Bae, J. Chang, M.R. Zamfir, D.T. Le, D.T. Pham, Y. Hongyan, Y.H. Lee, Hollow carbon nanospheres/silicon/alumina core-shell film as an anode for lithium-ion batteries, Scientific Reports, 5 (2015). [24] A. Mukhopadhyay, B.W. Sheldon, Deformation and stress in electrode materials for Li-ion batteries, Progress in Materials Science, 63 (2014) 58-116. [25] X. Su, Q. Wu, J. Li, X. Xiao, A. Lott, W. Lu, B.W. Sheldon, J. Wu, Silicon-based nanomaterials for lithium-ion batteries: A review, Advanced Energy Materials, (2013). [26] L. Xue, G. Xu, Y. Li, S. Li, K. Fu, Q. Shi, X. Zhang, Carbon-coated Si nanoparticles dispersed in carbon nanotube networks as anode material for Lithium-ion batteries, ACS Applied Materials & Interfaces, 5(1) (2013) 21-25. [27] C. Yang, Y. Zhang, J. Zhou, C. Lin, F. Lv, K. Wang, J. Feng, Z. Xu, J. Li, S. Guo, Hollow Si/SiO nanosphere/nitrogen-doped carbon superstructure with a double shell and void for high-rate and long-life lithium-ion storage, Journal of Materials Chemistry A, 6(17) (2018) 8039-8046. [28] Y. Yao, M.T. McDowell, I. Ryu, H. Wu, N. Liu, L. Hu, W.D. Nix, Y. Cui, Interconnected silicon hollow nanospheres for lithium-ion battery anodes with long cycle life, Nano Letters, 11 (2011) 2949-2954. [29] K. Zhao, M. Pharr, S. Cai, J.J. Vlassak, Z. Suo, Large plastic deformation in high-capacity lithium-ion batteries caused by charge and discharge, Journal of American Ceramic Society, 94 (2011) 226-235. [30] K. Zhao, M. Pharr, L. Hartle, J.J. Vlassak, Z. Suo, Fracture and debonding in lithium-ion batteries with electrodes of hollow core-shell nanostructures, Journal of Power Sources, 218 (2012) 6-14. [31] X. Zhou, A. Cao, L. Wan, Y. Guo, Spin-coated silicon nanoparticle/grapheme electrode as a binder-free anode for high-performance lithium-ion batteries, Nano Research, 5 (2012) 845-853. [32] F. Ojaghnezhad, H.M. Shodja, A combined first principles and analytical treatment for determination of the surface elastic constants: application to Si(001) ideal and reconstructed surfaces, Philosophical Magazine Letters, 92(1) (2012) 7-19. | ||
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