Advani SG, Tucker CL III (1987) The use of tensors to describe and predict fiber orientation in short fiber composites. J Rheol 31(8):751–784
Advani SG, Tucker CL III (1990) Closure approximations for three-dimensional structure tensors. J Rheol 34(3):367–386
Agboola BO, Jack DA, Montgomery-Smith S (2012) Effectiveness of recent fiber-interaction diffusion models for orientation and the part stiffness predictions in injection molded short-fiber reinforced composites. Compos Part A: Appl Sci Manuf 43(11):1959–1970
Altan MC, Subbiah S, Güçeri SI, Pipes RB (1990) Numerical prediction of three-dimensional fiber orientation in Hele–Shaw flows. Polym Eng Sci 30(14):848–859
Bay RS, Tucker CL (1992) Fiber orientation in simple injection moldings. Part I: theory and numerical methods. Polym Compos 13(4):317–331
Bay RS, Tucker CL (1992) Stereological measurement and error estimates for three-dimensional fiber orientation. Polym Eng Sci 32(4):240–253
Boulekbache B, Hamrat M, Chemrouk M, Amziane S (2010) Flowability of fibre-reinforced concrete and its effect on the mechanical properties of the material. Constr Build Mater 24(9):1664–1671
Bounoua S, Lemaire E, Férec J, Ausias G, Zubarev A, Kuzhir P (2016) Apparent yield stress in rigid fibre suspensions: the role of attractive colloidal interactions. J Fluid Mech 802:611–633
Brannon RM (2003) Functional and structured tensor analysis for engineers. New Mexico
Breitenbücher R, Meschke G, Song F, Zhan Y (2014) Experimental, analytical and numerical analysis of the pullout behaviour of steel fibres considering different fibre types, inclinations and concrete strengths. Struct Concr 15(2):126–135
Carmona S, Molins C, Aguado A, Mora F (2016) Distribution of fibers in SFRC segments for tunnel linings. Tunn Undergr Space Technol 51:238–249
Chung DH, Kwon TH (2001) Improved model of orthotropic closure approximation for flow induced fiber orientation. Polym Compos 22(5):636–649
Cintra J, Joaquim S, Tucker CL III (1995) Orthotropic closure approximations for flow-induced fiber orientation. J Rheol 39(6):1095–1122
Crespo A (2008) Development of the smoothed particle hydrodynamics model sphysics. Ph.D. thesis, Departamento de Física Aplicada. Universidad de Vigo
Crespo AJ, Domínguez JM, Rogers BD, Gómez-Gesteira M, Longshaw S, Canelas R, Vacondio R, Barreiro A, García-Feal O (2015) DualSPHysics: open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH). Comput Phys Commun 187:204–216
Deeb R, Kulasegaram S, Karihaloo BL (2014) 3D modelling of the flow of self-compacting concrete with or without steel fibres. Part I: slump flow test. Comput Part Mech 1(4):373–389
Deeb R, Kulasegaram S, Karihaloo BL (2014) 3D modelling of the flow of self-compacting concrete with or without steel fibres. Part II: L-box test and the assessment of fibre reorientation during the flow. Comput Part Mech 1(4):391–408
Domínguez JM, Crespo AJ, Gómez-Gesteira M, Marongiu JC (2011) Neighbour lists in smoothed particle hydrodynamics. Int J Numer Methods Fluids 67(12):2026–2042
Fan X, Phan-Thien N, Zheng R (1998) A direct simulation of fibre suspensions. J Non-Newton Fluid Mech 74(1):113–135
Ferrara L, Cremonesi M, Faifer M, Toscani S, Sorelli L, Baril MA, Rthor J, Baby F, Toutlemonde F, Bernardi S (2017) Structural elements made with highly flowable UHPFRC: correlating computational fluid dynamics (CFD) predictions and non-destructive survey of fiber dispersion with failure modes. Eng Struct 133:141–296
Ferrara L, Ozyurt N, Di Prisco M (2011) High mechanical performance of fibre reinforced cementitious composites: the role of casting-flow induced fibre orientation. Mater Struct 44(1):109–128
Ferrara L, Shyshko S, Mechtcherine V (2012) Predicting the flow-induced dispersion and orientation of steel fibers in self-consolidating concrete by distinct element method. In: Fibre Reinforced Concrete: challenges and opportunities, Proceedings BEFIB 2012, 8th International RILEM Symposium, pp 1–12
Folgar F, Tucker CL III (1984) Orientation behavior of fibers in concentrated suspensions. J Reinf Plast Compos 3(2):98–119
Ghanbari A, Karihaloo BL (2009) Prediction of the plastic viscosity of self-compacting steel fibre reinforced concrete. Cem Concr Res 39(12):1209–1216
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-sphericalstars. Mon Not R Astron Soc 181(3):375–389
Gomez-Gesteira M, Rogers BD, Crespo AJ, Dalrymple RA, Narayanaswamy M, Domínguez JM (2012) SPHysics-development of a free-surface fluid solver—part 1: theory and formulations. Comput Geosci 48:289–299
Grünewald S (2004) Performance-based design of self-compacting fibre reinforced concrete. Ph.D. thesis, Delft University of Technology, Department of Structural and Building Engineering
Harris J, Pittman J (1975) Equivalent ellipsoidal axis ratios of slender rod-like particles. J Colloid Interface Sci 50(2):280–282
Hérault A, Bilotta G, Vicari A, Rustico E, Del Negro C (2011) Numerical simulation of lava flow using a GPU SPH model. Annals of Geophysics 54(5):600–620
Jeffery GB (1922) The motion of ellipsoidal particles immersed in a viscous fluid. Proc R Soc Lond A: Math Phys Eng Sci 102(715):161–179
Joung C, Phan-Thien N, Fan X (2001) Direct simulation of flexible fibers. J Non-Newton Fluid Mech 99(1):1–36
Junk M, Illner R (2007) A new derivation of Jefferys equation. J Math Fluid Mech 9(4):455–488
Kang ST, Kim JK (2012) Numerical simulation of the variation of fiber orientation distribution during flow molding of ultra high performance cementitious composites (uhpcc). Cem Concr Compos 34(2):208–217
Kindlmann G (2004) Superquadric tensor glyphs. In: Proceedings of the sixth joint Eurographics—IEEE TCVG conference on visualization. Eurographics Association, pp 147–154
Kolařík F, Patzák B, Thrane L (2015) Modeling of fiber orientation in viscous fluid flow with application to self-compacting concrete. Comput Struct 154:91–100
Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82:1013–1024
Monaghan J (2012) Smoothed particle hydrodynamics and its diverse applications. Ann Rev Fluid Mech 44:323–346
Monaghan JJ (1992) Smoothed particle hydrodynamics. Ann Rev Astron Astrophys 30(1):543–574
Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Progr Phys 68(8):1703
Montgomery-Smith S, Jack D, Smith DE (2011) The fast exact closure for Jefferys equation with diffusion. J Non-Newton Fluid Mech 166(7):343–353
Montgomery-Smith S, Jack DA, Smith DE (2010) A systematic approach to obtaining numerical solutions of Jefferys type equations using spherical harmonics. Compos Part A: Appl Sci Manuf 41(7):827–835
Morris JP, Fox PJ, Zhu Y (1997) Modeling low Reynolds number incompressible flows using SPH. J Comput Phys 136(1):214–226
Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31(5):385–404
Petrie CJ (1999) The rheology of fibre suspensions. J Non-Newton Fluid Mech 87(2):369–402
Phan-Thien N, Fan XJ, Tanner R, Zheng R (2002) Folgar–Tucker constant for a fibre suspension in a Newtonian fluid. J Non-Newton Fluid Mech 103(2):251–260
Phelps JH, Tucker CL (2009) An anisotropic rotary diffusion model for fiber orientation in short-andlong-fiber thermoplastics. J Non-Newton Fluid Mech 156(3):165–176
Price DJ (2011) Smoothed particle hydrodynamics: things I wish my mother taught me. arXiv preprint arXiv:1111.1259
Sepehr M, Ausias G, Carreau PJ (2004) Rheological properties of short fiber filled polypropylene in transient shear flow. J Non-Newton Fluid Mech 123(1):19–32
Sepehr M, Carreau PJ, Moan M, Ausias G (2004) Rheological properties of short fiber model suspensions. J Rheol 48(5):1023–1048
Shao S, Lo EY (2003) Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv Water Resour 26(7):787–800
Skoptsov KA, Sheshenin SV, Galatenko VV, Malakho AP, Shornikova ON, Avdeev VV, Sadovnichy VA (2016) Particle simulation for predicting effective properties of short fiber reinforced composites. Int J Appl Mech 8(02):1650016
Stähli P, Custer R, van Mier JG (2008) On flow properties, fibre distribution, fibre orientation and flexural behaviour of FRC. Mater Struc 41(1):189–196
Vandewalle L, Heirman G, Van Rickstal F (2008) Fibre orientation in self-compacting fibre reinforced concrete. In: Proceedings of the 7th international RILEM symposium on fibre reinforced concrete: design and applications (BEFIB2008), pp 719–728
Verleye V, Couniot A, Dupret F (1993) Prediction of fiber orientation in complex injection molded parts. In: ICCM/9, vol. 3, pp. 642–650
Violeau D, Leroy A (2014) On the maximum time step in weakly compressible SPH. J Comput Phys 256:388–415
Violeau D, Rogers BD (2016) Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future. J Hydraul Res 54(1):1–26
Švec O, Skocek J, Olesen JF, Stang H (2012) Fibre reinforced self-compacting concrete flow simulations in comparison with L-box experiments using carbopol. In: 8th Rilem international symposium on fibre reinforced concrete
Švec O, Skoček J, Stang H, Geiker MR, Roussel N (2012) Free surface flow of a suspension of rigid particles in a non-newtonian fluid: a lattice boltzmann approach. J Non-Newton Fluid Mech 179:32–42
Wang J, OGara JF, Tucker CL III (2008) An objective model for slow orientation kinetics in concentratedfiber suspensions: theory and rheological evidence. J Rheol 52(5):1179–1200
Yamane Y, Kaneda Y, Dio M (1994) Numerical simulation of semi-dilute suspensions of rodlike particlesin shear flow. J Non-Newton Fluid Mech 54:405–421
Zak G, Park C, Benhabib B (2001) Estimation of three-dimensional fibre-orientation distribution in short-fibre composites by a two-section method. J Compos Mater 35(4):316–339
Zhan Y, Meschke G (2016) Multilevel computational model for failure analysis of steel-fiber-reinforced concrete structures. J Eng Mech 142(11):04016090