Phương pháp phần tử hữu hạn tổng quát cho các vết nứt ba chiều trong vật liệu composit gia cố bằng sợi

Meccanica - Tập 56 - Trang 1441-1473 - 2020
Phillipe D. Alves1, Angelo Simone2,3, C. Armando Duarte1
1Newmark Laboratory, Department of Civil and Environmental Eng., University of Illinois at Urbana-Champaign, Urbana, USA
2Department of Industrial Engineering, University of Padova, Padua, Italy
3Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands

Tóm tắt

Bài báo này trình bày một phương pháp phân tích các vết nứt tĩnh ba chiều trong các vật liệu gia cố bằng sợi. Các sợi được mô hình hóa rời rạc sử dụng một biến thể của phương pháp gia cố nhúng với trượt liên kết (mERS) cho phép kết hợp với phương pháp phần tử hữu hạn tổng quát (GFEM) cho các vết nứt ba chiều. Do lưới GFEM không cần phải phù hợp với bề mặt vết nứt hoặc sợi, GFEM-mERS có thể xử lý các sợi nối qua các mặt vết nứt ở các góc tùy ý. Phương pháp này được xác minh với các nghiệm pháp FEM ba chiều sử dụng phân rã phù hợp cho bề mặt vết nứt và biên giới sợi. So sánh giữa phương pháp và dữ liệu thực nghiệm cũng như các nghiên cứu hội tụ của phiên bản h- và p-phương pháp cũng được trình bày.

Từ khóa

#vết nứt ba chiều #phương pháp phần tử hữu hạn #vật liệu gia cố bằng sợi #phương pháp gia cố nhúng với trượt liên kết #phân rã phù hợp

Tài liệu tham khảo

Abaqus (2014) Version 6.14 documentation. Dassault Systemes Simulia Corporation, Providence, RI Aragon A, Simone A (2017) The discontinuity-enriched finite element method. Int J Numer Methods Eng 112(11):1589–1613. https://doi.org/10.1002/nme.5570 Babuška I, Melenk J (1997) The partition of unity method. Int J Numer Methods Eng 40:727–758 Balakrishnan S, Murray DW (1986) Finite element prediction of reinforced concrete behavior. Technical Report Structural Engineering Report No. 138, Department of Civil Engineering, The University of Alberta Belytschko T, Lu Y, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37:229–256 Bolander JE, Saito S (1997) Discrete modeling of short-fiber reinforcement in cementitious composites. Adv Cement Based Mater 6(3):76–86 Bolander JE, Choi S, Duddukuri SR (2008) Fracture of fiber-reinforced cement composites: effects of fiber dispersion. Int J Fract 154(1–2):73–86 Bouhala L, Makradi A, Belouettar S, Kiefer-Kamal H, Fréres P (2013) Modelling of failure in long fibres reinforced composites by X-FEM and cohesive zone model. Compos B 55:352–361 Caner FC, Bažant ZP, Wendner R (2013) Microplane model M7f for fiber reinforced concrete. Eng Fract Mech 105:41–57 Carvalho M, Barros J, Zhang Y, Dias-da-Costa D (2020) A computational model for simulation of steel fibre reinforced concrete with explicit fibres and cracks. Comput Methods Appl Mech Eng 363:112879. https://doi.org/10.1016/j.cma.2020.112879 Cusatis G, Pelessone D, Mencarelli A (2011) Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. I: theory. Cement Concrete Compos 33(9):881–890 Dias-da-Costa D, Alfaiate J, Sluys L, Areias P, Júlio E (2013) An embedded formulation with conforming finite elements to capture strong discontinuities. Int J Numer Methods Eng 93(2):224–244. https://doi.org/10.1002/nme.4393 Duarte C, Babuška I, Oden J (2000) Generalized finite element methods for three dimensional structural mechanics problems. Comput Struct 77:215–232. https://doi.org/10.1016/S0045-7949(99)00211-4 Elwi AE, Hrudey TM (1989) Finite element model for curved embedded reinforcement. J Eng Mech 115(4):740–754 Farahani BV, Tavares PJ, Belinha J, Moreira PMGP (2017) A fracture mechanics study of a compact tension specimen: digital image correlation, finite element and meshless method. In: 2nd International conference on structural integrity, ICSI 2017, vol 5, pp 920–927 Garzon J, O’Hara P, Duarte C, Buttlar W (2014) Improvements of explicit crack surface representation and update within the generalized finite element method with application to three-dimensional crack coalescence. Int J Numer Methods Eng 97(4):231–273. https://doi.org/10.1002/nme.4573 Guedes JM, Kikuchi N (1990) Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng 83(2):143–198 Gupta P, Duarte C, Dhankhar A (2017) Accuracy and robustness of stress intensity factor extraction methods for the generalized/eXtended Finite Element Method. Eng Fract Mech 179:120–153. https://doi.org/10.1016/j.engfracmech.2017.03.035 Hartl H (2002) Development of a continuum-mechanics-based tool for 3D finite element analysis of reinforced concrete structures and application to problems of soil-structure interaction. PhD thesis, Graz University of Technology Heath M (1997) Scientific computing: an introductory survey. McGraw-Hill series in computer science. McGraw-Hill, Boston. ISBN 9780070276840 Jones A (2015) Solvent-based self-healing approaches for fiber-reinforced composites. PhD thesis, University of Illinois at Urbana-Champaign Kang J, Kim K, Lim Y, Bolander J (2014) Modeling of fiber-reinforced cement composites: discrete representation of fiber pullout. Int J Solids Struct 51:1970–1979 Karimi M, Bayesteh H, Mohammadi S (2019) An adapting cohesive approach for crack-healing analysis in SMA fiber-reinforced composites. Comput Methods Appl Mech Eng 349:550–575 Kozicki J, Tejchman J (2010) Effect of steel fibres on concrete behavior in 2D and 3D simulations using lattice model. Arch Mech 62:1–28 Kruzic JJ (2009) Predicting fatigue failures. Science 325:156–158 Kruzic JJ, Campbell JP, Ritchie RO (1999) On the fatigue behavior of g-based titanium aluminides: role of small cracks. Acta Mater 47:801–816 Kunieda M, Ogura H, Ueda N, Nakamura H (2011) Tensile fracture process of strain hardening cementitious composites by means of three-dimensional meso-scale analysis. Cement Concrete Compos 33:956–965 Lee SC, Cho JY, Vecchio FJ (2011) Diverse embedment model for steel fiber-reinforced concrete in tension: model verification. ACI Mater J 108:526–535 Lee SC, Cho JY, Vecchio FJ (2013) Simplified diverse embedment model for steel fiber-reinforced concrete elements in tension. ACI Mater J 110:403–412 Lei Y (2008) Finite element crack closure analysis of a compact tension specimen. Int J Fatigue 30:21–31 Liu W, Jun S, Zhang Y (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20:1081–1106 Lusti H, Gusev A (2004) Finite element predictions for the thermoelastic properties of nanotube reinforced polymers. Model Simul Mater Sci Eng 12:107–119 Melenk J, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139:289–314 Miller-Stephenson (2018) Manual properties EPON. https://miller-stephenson.com. Accessed Mar 2018 Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150 Mortazavi B, Baniassadi M, Bardon J, Ahzi S (2013) Modeling of two-phase random composite materials by finite element. Compos Part B Eng 45:1117–1125 Octávio C, Dias-da-Costa D, Alfaiate J, Júlio E (2016) Modelling the behaviour of steel fibre reinforced concrete using a discrete strong discontinuity approach. Eng Fracture Mech 154:12–23 Oden J, Duarte C (1997) Chapter: clouds, cracks and FEMs. In Reddy B (ed) Recent developments in computational and applied mechanics. International Center for Numerical Methods in Engineering, CIMNE, Barcelona, pp 302–321. http://gfem.cee.illinois.edu/papers/jMartin_color.pdf. Accessed July 2020 Oden J, Duarte C, Zienkiewicz O (1998) A new cloud-based hp finite element method. Comput Methods Appl Mech Eng 153:117–126. https://doi.org/10.1016/S0045-7825(97)00039-X Owenscorning (2018) Manual properties glass fiber 158B-AA-675. https://www.owenscorning.com/. Accessed Mar 2018 Park K, Paulino G, Roesler J (2010) Cohesive fracture model for functionally graded fiber reinforced concrete. Cement Concrete Res 40(6):956–965. https://doi.org/10.1016/j.cemconres.2010.02.004 Park SH, Kim DJ, Ryu GS, Koh KT (2012) Tensile behavior of ultra high performance hybrid fiber reinforced concrete. Cement Concrete Compos 34:172–184 Pereira J, Duarte C, Guoy D, Jiao X (2009) Hp-generalized FEM and crack surface representation for non-planar 3-D cracks. Int J Numer Methods Eng 77(5):601–633. https://doi.org/10.1002/nme.2419 Pike MG, Oskay C (2015a) Modeling random short nanofiber- and microfiber-reinforced composites using the extended finite-element method. J Nanomech Micromech 5(1):A4014005. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000092 Pike MG, Oskay C (2015b) XFEM modeling of short microfiber reinforced composites with cohesive interfaces. Finite Elem Anal Des 106:16–31 Pike MG, Oskay C (2016) Three-dimensional modeling of short fiber-reinforced composites with extended finite-element method. J Eng Mech 142:11–16 Radtke F, Simone A, Sluys L (2010) A partition of unity finite element method for obtaining elastic properties of continua with embedded thin fibres. Int J Numer Methods Eng 84(6):708–732. https://doi.org/10.1002/nme.2916 Reddy J, Robbins D Jr (1994) Theories and computational models for composite laminates. Appl Mech Rev 47(6):147–169. https://doi.org/10.1115/1.3111076 Ruiz G (2001) Propagation of a cohesive crack crossing a reinforcement layer. Int J Fracture 111:265–282 Sanchez-Rivadeneira A, Shauer N, Mazurowski B, Duarte C (2020) A stable generalized/extended p-hierarchical FEM for three-dimensional linear elastic fracture mechanics. Comput Methods Appl Mech Eng 364:112970. https://doi.org/10.1016/j.cma.2020.112970 Schauffert EA, Cusatis G (2012) Lattice discrete particle model for fiber-reinforced concrete. II: tensile fracture and multiaxial loading behavior. J Eng Mech 138(7):834–841 Schweitzer M (2012) Generalizations of the finite element method. Central Eur J Math 10:3–24. https://doi.org/10.2478/s11533-011-0112-1 Shen B, Paulino GH (2011) Identification of cohesive zone model and elastic parameters of fiber-reinforced cementitious composites using digital image correlation and a hybrid inverse technique. Cement Concrete Compos 33:572–585 Spring D, Paulino G (2015) Computational homogenization of the debonding of particle reinforced composites: the role of interphases in interfaces. Comput Mater Sci 109:209–224. https://doi.org/10.1016/j.commatsci.2015.07.012 Strouboulis T, Copps K, Babuška I (2001) The generalized finite element method. Comput Methods Appl Mech Eng 190:4081–4193 Tian W, Qi L, Su C, Zhou J, Jing Z (2016) Numerical simulation on elastic properties of short-fiber-reinforced metal matrix composites: effect of fiber orientation. Compos Struct 152:408–417 Visalvanich K, Naaman AE (1983) Fracture model for fiber reinforced concrete. J Am Concrete Inst 80:128–138 Zhang J, Deng S, Wang Y, Ye L, Zhou L, Zhang Z (2013) Effect of nanoparticles on interfacial properties of carbon fibre-epoxy composites. Compos Part A Appl Sci Manuf 55:35–44 Zhao D, Botsis J (1989) Experimental and numerical studies in model composites part I: experimental results. Int J Fracture 82:153–174 Zhao L, Zhi J, Zhang J, Liu Z, Hu N (2016) XFEM simulation of delamination in composite laminates. Compos A 80:61–71 Zienkiewicz O, Owen D, Phillips D, Nayak G (1972) Finite element methods in the analysis of reactor vessels. Nuclear Eng Des 20(2):507–541