Abstract
A fast multipole boundary element method (FMBEM) is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces. The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice, the Kelvin type model is introduced. The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration. Since all the integrals are evaluated analytically, high accuracy and fast convergence of the numerical scheme are obtained. Several numerical examples, including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented. The numerical results are compared with the developed analytical solutions, which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces. The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.
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References
Rizzo F J, Shippy D J. An application of the correspondence principle of linear viscoelasticity theory. J Appl Math, 1971, 21: 321–330
Kusama T, Mitsui Y. Boundary element method applied to linear viscoelastic analysis. Appl Math Modelling 1982; 6: 285–294
Sun B N, Hsiao C C. Viscoelastic boundary method for analysing polymer quasi fracture. Comput Struct, 1988, 30: 963–966
Liu Y, Antes H. Application of visco-elastic boundary element method to creep problems in chemical engineering structures. Int J Pres Ves & Piping, 1997, 70: 27–31
Tschoegl N W. The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction. New York: Springer, 1989
Mesquita A D, Coda H B, Venturini W S. An alternative time marching process for viscoelastic analysis by BEM and FEM. Int J Numer Meth Eng, 2001, 51: 1157–1173
Mesquita A D, Coda H B. An alternative time integration procedure for Boltzmann viscoelasticity: a BEM approach. Comput Struct, 2001, 79/16: 1487–1496
Mesquita A D, Coda H B. Boundary integral equation method for general viscoelastic analysis. Int J Solids Struct, 2002, 39: 2643–2664
Mesquita A D, Coda H B. A simple Kelvin and Boltzmann viscoelastic analysis of three-dimensional solids by the boundary element method. Engng Anal Bound Elem, 2003, 27: 885–895
Huang Y, Steven L C, Sofia G M. A time domain direct boundary integral method for a viscoelastic plane with circular holes and elastic inclusions. Engng Anal Bound Elem, 2005, 29: 725–737
Sensale B, Greus G J. Boundary element analysis of viscoelastic fracture. In: Brebbia C A, Rencis J J, eds. Bounday Element XV, vol. 2. Stress Analysis. Boston: Computational Mechanics Publication, 1993
Sensale B. On the solution of viscoelastic problems using boundary elements techniques. Doctoral Dissertation, CEMACOM, UFRGS, Porto Alegre, Portuguese, 1997
Sensale B, Partridge P W, Creus G J. General boundary elements solution for aging viscoelastic structures. Int J Numer Meth Eng, 2001, 50: 1455–1468
Birgisson B, Sangpetngam B, Roque R. Prediction of the viscoelastic response and crack growth in asphalt mixtures using the boundary element method. Transp Res Rec, 2002, 1789: 129–135
Birgisson B, Soranakom C, Napier J A L, et al. Microstructure and fracture in asphalt mixtures using a boundary element approach. J Mater Civ Eng, 2004, 16: 116–121
Wang J L, Birgisson B. A time domain boundary element method for modeling the quasi-static viscoelastic behavior of asphalt pavements. Engng Anal Bound Elem, 2007, 31: 226–40
Lane F, Leguillon D. Homogenized constitutive law for a partially cohesive composite material. Intl J Solids Struct, 1982, 18: 443–458
Greengard L F, Kropinski M C, Mayo A. Integral equation methods for Stokes flow and isotropic elasticity in the plane. J Comput Phys, 1996, 125: 403–414
Greengard L F, Helsing J. On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites. J Mech Phys Solids, 1998, 46: 1441–1462
Peirce A P, Napier J A L. A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics. Int J Numer Meth Eng, 1995, 38: 4009–4034
Yao Z, Kong F, Wang H, et al. 2D simulation of composite materials using BEM. Engng Anal Bound Elem, 2004, 28: 927–935
Wang H, Yao Z, Wang P. On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics. Engng Anal Bound Elem, 2005, 29: 673–688
Liu Y J, Nishimura N, Otani Y. Large-scale modeling of carbon-nanotube composites by the boundary element method based on a rigid-inclusion model. Comput Mater Sci, 2005, 34: 173–187
Liu Y J. A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems. Int J Numer Meth Eng, 2005, 65: 863–881
Liu Y J, Nishimura N, Otani Y, et al. A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model. J Appl Mech, 2005, 72: 115–128
Liu Y J. A fast multipole boundary element method for 2-D multi-domain elastostatic problems based on a dual BIE formulation. Comput Mech, 2008, 42: 761–773
Liu Y J. Fast Multipole Boundary Element Method-Theory and Applications in Engineering. Cambridge: Cambridge University Press, 2009
Chen W Q, Zhu X Y, Huang Z Y. Modeling of multi-inclusion composites with interfacial imperfections: Micromechanical and numerical simulations. Sci China Ser E-Tech Sci, 2010, 53(3): 720–730
Lee S S, Westmann RA. Application of boundary element method to visco-elastic problems. In: Brebbia C A, Rencis J J. eds. Boundary Element XV, vol 2, Stress Analysis. Boston: Computational Mechanics Publications, 1993
Lee S S. Boundary element analysis of linear viscoelastic problems using realistic relaxation functions. Comput Struct, 1995, 55(6): 1027–1036
Achenbach J D, Zhu H. Effect of interfacial zone on mechanical behavior and failure of fiber-reinforced composites. J Mech Phys Solids, 1989, 37(3): 381–393
Hu N, Wang B, Tan GW, Yet al. Effective elastic properties of 2D solids with circular holes: numerical simulations. Compos Sci Tech, 2000, 60: 1184–1123
Ranja B, Animesh D, Sumit B. Numerical simulation of mechanical behavior of asphalt mix. Constr Build Mater, 2008, 22: 1051–1058
Dai Q L, You Z P. Prediction of creep stiffness of asphalt mixture with micromechanical finite-element and discrete-element models. J Eng Mech-ASCE, 2007, 2: 163–173
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Zhu, X., Chen, W., Huang, Z. et al. Fast multipole boundary element analysis of 2D viscoelastic composites with imperfect interfaces. Sci. China Technol. Sci. 53, 2160–2171 (2010). https://doi.org/10.1007/s11431-010-4023-3
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DOI: https://doi.org/10.1007/s11431-010-4023-3