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TR N DUY THIÊN PHÂN TÍCH V T N T CONG NG I TUY N TÍNH BA CHI U NG C A N NH NG SU T B M T 8580201 01 2022 -HCM , HCM, ngày 21 tháng 01 2 TS TS Liêu Xuân Quí h i C GIA TP.HCM - ê - MSHV:1870106 15/08/1994 An Giang Chuyên ngành: I Mã s : 8580201 TÀI: ANALYSIS OF NON-PLANAR CRACKS IN THREE-DIMENSIONAL LINEAR ELASTIC MEDIA WITH CONSIDERATION OF SURFACE STRESS EFFECTS : Phát tri n m t mơ hình tốn h c phù h p v m t v t lý d a lý thuy c môi ng liên t c có kh tn t t l c nano, Xây d ng m t quy trình tính tốn b hi u qu xác ng v m c thông tin c n thi t ( n v m v t n t, chuy n v t v t n t, ng su t pháp, ng su t ti p vùng lân c n c a crack av tn t t l c nano Kh o sát tính ch t ph thu cc a v tn t t l c nano II : 22/02/2021 III 12/12/2021 III CÁN B N: Tp HCM, ngày 29 tháng 12 CÁN B NG D N MÔN 21 ii L IC c h t xin g i l i c nv TS Nguy i khuy lúc cu i c i ng d n c a tôi, ng d n h tr t lúc b n ng hoàn thành lu tri n s hi u bi t v ch ng d n h tr liên t c nghiên c u Lu tr c a th y Th u ki n m i khơng th c s hồn thành n u khơng có s h tr tơi su t lu i s kiên nh n ki n th c c a th y Tơi mu n bày t lịng bi c pm c t i H c Bách Khoa ng giáo d c t v h c t p nghiên c u Tơi mu n bày t lịng bi i th p ki n th c m t cách cu n hút r ch ng ki n th Tôi mu n g i l ng gi ng d y tơi có th t tin vào ã có n t t c b n bè c a tôi, nh tr c ti p gián ti p vi c chu n b lu i cùng, mu n c m anh trai c a tơi, tình u nh ng n l c không ng ng ngh c a h n khích tơi th c hi n m c tiêu c a iii TĨM T T LU T KHĨA: BEM, FEM-SGBEM COUPLING, GURTIN - MURDOCH MODEL, NANO-CRACKS, SIZE DEPENDENCY, SURFACE STRESSES, WEAKLY SINGULAR TÀI: PHÂN TÍCH V T N I TUY N TÍNH BA CHI N NG C A NG SU T B M T NG D N: TS NGUY N THÁI BÌNH Lu hi u qu ng ba chi u vơ h i n tính, k ng su t b m t Khái ni m ng su t b m c u hi ng quy mô c tốn h c có kh mơ hình hóa v t n t phát tri n m t mô hình ng v t n c nano Trên b m t v t n t, i di n b ng m t b m c liên k t hoàn h o v i kh i v t th v i ng x dày b ng không c ki m soát b i lý thuy h i b m t Gurtinm o d ng y u cho ph n b c xây d ng b i tc cs d thành l id trình ch mb ck d l c b m t b m t v t n s d ng c a c s d ng r ng rãi nghiên cs d m t l p v t li u c c m n o c a kh i v t th i v i n chuy n v FEM-SGBEM k t h p gi i h kh p m x p x g i chu phân g cs d a s tích d k d y u t n t xu t d a gi i pháp chu n hi xu v t n t kí hi n kh cs li u b m t v t n t, v i c bi xác th pháp s c o Do ch ch a b c k d y u i suy liên t c b c C0 d ng nv cs d u tra hi u ng quy mô c c nano Nhi u kh o sát s nh m c iv i c th c hi th xu t K t qu phân tích tham s tồn di n ch r ng s hi n di n c a ng su t b m t không ch iv c ng c a l p v t li u g n b m t mà t o ng x ph thu c a k t qu s làm gi m ng su t vùng lân c n c a crack front c v ABSTRACT KEYS: BEM, FEM-SGBEM COUPLING, GURTIN - MURDOCH MODEL, NANO-CRACKS, SIZE DEPENDENCY, SURFACE STRESSES, WEAKLY SINGULAR TOPIC: ANALYSIS OF NON-PLANAR CRACKS IN THREE-DIMENSIONAL LINEAR ELASTIC MEDIA WITH CONSIDERATION OF SURFACE STRESS EFFECTS INSTRUCTIONS: DR NGUYEN THAI BINH This thesis presents an effective numerical approach for modeling non-planar cracks in a 3D, linear elastic, infinite media while taking into account the effects of surface stresses The notion of surface stresses, which has been extensively used in the study of nanoscale phenomena, is used to develop a mathematical model capable of simulating nanoscale cracks On the crack surface, an infinitesimally thin layer of material is represented by a zero-thickness surface that is perfectly bonded to the bulk material and whose behavior is controlled by the Gurtin - Murdoch constitutive relation The governing equations containing the surface stress effect are produced in a weak-form version using the typical Galerkin approach for the zero-thickness surfaces The approach utilizes the classical theory of isotropic linear elasticity to derive the governing equations for the bulk material in terms of singularity-reduced boundary integral equations for displacement and traction on the crack surface The numerical approach of FEM-SGBEM coupling is then used to solve the fully coupled system of equations Due to the weakly singular character of the boundary integral equations involved, typical continuous interpolation functions may be used everywhere to approximate crack-face data, with the exception of specific quadrature for assessing nearly and weakly singular integrals After validating the proposed numerical approach with existing benchmark solutions, it is used to explore the nanoscale effect on nano-sized cracks Numerous examples are provided to show the method's capability and robustness The results of a comprehensive parametric analysis indicate that the presence of surface stresses not only enhances vi near-surface material stiffness but also introduces the size-dependent behavior of solutions and stress reduction in the zone ahead of the crack front vii L li u k t qu nghiên c u lu cs d lu rõ ngu n g c b o v m t h c v M i s cc cho vi c th c hi n n lu c ch TPHCM, ngày 29 tháng 12 2021 c phép công b i th c hi n TR N DUY THIÊN viii M CL C trang i L IC ii TÓM T T LU C iii ABSTRACT .v L vii DANH M C CÁC KÍ HI U VI T T T xi DANH M C CÁC HÌNH xiii I THI U .1 1.1 T NG QUAN V NGHIÊN C U 1.2 M C TIÊU NGHIÊN C U 1.3 PH M VI NGHIÊN C U U U .6 1.6 N I DUNG C A LU NG QUAN I B M T 2.2 CÁC BÀI TOÁN V V T N T T L C NANO 11 C V BEM VÀ FEM-BEM K T H P CHO BÀI TOÁN N T18 O .20 3.1 MƠ T BÀI TỐN .20 3.2 PHÂN TÁCH MI N KH O SÁT 21 O C A PH N KH I V T TH .22 O C A PH N B M T V T N T 24 95 TÀI LI U THAM KH O [1] Nature, vol 354, no 6348, pp 56 58, 1991 [2] S Iijima, shell carbon nanotubes of nm Nature, vol 363, no 6430, pp 603 605, 1993 [3] B Peng, M Locascio, P Zapol, S Li, S L Mielke, G C Schatz, and H D ultimate strength for multiwalled carbon nanotubes and irradiation Nat Nano., vol 3, no 10, pp 626 631, 2008 [4] A Karimi, Y Wang, T Cselle, anisms in Thin Solid Films, vol 420 421, pp 275 280, 2002 [5] T Sumomogi, M Nakamura, T Endo, T Goto, surface and subsurface cracks in 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SURFACE STRESSES, WEAKLY SINGULAR TÀI: PHÂN TÍCH V T N I TUY N TÍNH BA CHI N NG C A NG SU T B M T NG D N: TS NGUY N THÁI BÌNH Lu hi u qu ng ba chi u vô h i n tính, k ng su t b m t Khái ni m ng su... c c a v t n t ph ng ng ba i n tính ch u ng s [36] ng c a thành p t c phát tri n nghiên c u 17 c a mình, phân tích v t n t ph ng có hình d vơ h ng nh i n tính s d Murdoch bao g m c thành ph n s... u biên, t c tri n khai s có th s d ng ph n t b c C0 tiêu chu tính g tích phân s thơng d ng hi n s b tính tốn v m t s h c t t c tích phân liên quan [41, 42, 115, 116, 120] singular SGBEM có th
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