Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Abstract

A better understanding of the mechanical behavior of the multi-layered structure under external loading is the most important item for the structural design and the risk assessment. The objective of this study are to propose and develop an analytical solution for the mechanical behaviors of multi-layered structure generated by axisymmetric loading, and to investigate the impact of anisotropic layers and interlayer conditions on the multi-layered structure. To reach these objectives, first, according to the governing equations, the analytical solution for a single layer was formulated by adopting the spatial Hankel transform. Then the global matrix technique is applied to achieve the analytical solution of multi-layered structure in Hankel domain. The sliding and bonded interlayer conditions were considered in this process. Finally, the numerical inversion of integral transform was used to solve the components of displacement and stress in real domain. Gauss-Legendre quadrature is a key scheme in the numerical inversion process. Moreover, following by the verification of the proposed analytical solution, one typical three-layered flexible pavement was applied as the computing carrier of numerical analysis for the multi-layered structure. The results have shown that the anisotropic layers and the interlayer conditions significantly affect the mechanical behaviors of the proposed structure.

Keywords

multi-layered structure / Hankel transformation / anisotropic / transversely isotropic / interlayer condition / Gauss-Legendre quadrature

References

[1] Tafreshi S M, Khalaj O, Dawson A. Repeated loading of soil containing granulated rubber and multiple geocell layers. Geotextiles and Geomembranes, 2014, 42(1): 25–38

[2] You L, Yan K, Hu Y, Zollinger D G. Spectral element solution for transversely isotropic elastic multi-layered structures subjected to axisymmetric loading. Computers and Geotechnics, 2016, 72: 67–73

[3] Cai Y, Pan E. Surface loading over a transversely isotropic and multilayered system with imperfect interfaces: Revisit enhanced by the dual-boundary strategy. International Journal of Geomechanics, 2018, 18(6): 04018032

[4] Xu Q, Prozzi J A. A time-domain finite element method for dynamic viscoelastic solution of layered-half-space responses under loading pulses. Computers & Structures, 2015, 160: 20–39

[5] Pandolfi A, Gizzi A, Vasta M. Visco-electro-elastic models of fiber-distributed active tissues. Meccanica, 2017, 52(14): 3399–3415

[6] Ai Z Y, Cheng Y C, Zeng W Z. Analytical layer-element solution to axisymmetric consolidation of multilayered soils. Computers and Geotechnics, 2011, 38(2): 227–232

[7] Zhang Y, Luo R, Lytton R L. Microstructure-based inherent anisotropy of asphalt mixtures. Journal of Materials in Civil Engineering, 2011, 23(10): 1473–1482

[8] Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227

[9] Chen G. Steady-state solutions of multilayered and cross-anisotropic poroelastic half-space due to a point sink. International Journal of Geomechanics, 2005, 5(1): 45–57

[10] Kim I, Tutumluer E. Field validation of airport pavement granular layer rutting predictions, Transportation Research Record. Transportation Research Record: Journal of the Transportation Research Board, 2006, 1952(1): 48–57

[11] Lv S, Wang S, Liu C, Zheng J, Li Y, Peng X. Synchronous testing method for tension and compression moduli of asphalt mixture under dynamic and static loading states. Journal of Materials in Civil Engineering, 2018, 30(10): 04018268

[12] Al-Qadi I L, Wang H, Yoo P J, Dessouky S H. Dynamic analysis and in situ validation of perpetual pavement response to vehicular loading. Transportation Research Record: Journal of the Transportation Research Board, 2008, 2087(1): 29–39

[13] Talebi H, Silani M, Bordas S P, Kerfriden P, Rabczuk T. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071

[14] Msekh M A, Cuong N, Zi G, Areias P, Zhuang X, Rabczuk T. Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model. Engineering Fracture Mechanics, 2018, 188: 287–299

[15] Kim D W, Choi H S, Lee C, Blumstein A, Kang Y. Investigation on methanol permeability of Nafion modified by self-assembled clay-nanocomposite multilayers. Electrochimica Acta, 2004, 50(2–3): 659–662

[16] Malwitz M M, Lin-Gibson S, Hobbie E K, Butler P D, Schmidt G. Orientation of platelets in multilayered nanocomposite polymer films. Journal of Polymer Science. Part B, Polymer Physics, 2003, 41(24): 3237–3248

[17] Ai Z Y, Cao Z. Vibration isolation of row of piles embedded in transverse isotropic multi-layered soils. Computers and Geotechnics, 2018, 99: 115–129

[18] Ai Z Y, Ye Z, Zhao Z, Wu Q L, Wang L J. Time-dependent behavior of axisymmetric thermal consolidation for multilayered transversely isotropic poroelastic material. Applied Mathematical Modelling, 2018, 61: 216–236

[19] You L, Yan K, Liu N, Shi T, Lv S. Assessing the mechanical responses for anisotropic multi-layered medium under harmonic moving load by Spectral Element Method (SEM). Applied Mathematical Modelling, 2019, 67: 22–37

[20] Liu K, Li Y, Wang F, Xie H, Pang H, Bai H. Analytical and model studies on behavior of rigid polyurethane composite aggregate under compression. Journal of Materials in Civil Engineering, 2019, 31(3): 04019007

[21] Lefeuve-Mesgouez G, Le Houédec D, Peplow A. Ground vibration in the vicinity of a high-speed moving harmonic strip load. Journal of Sound and Vibration, 2000, 231(5): 1289–1309

[22] Hung H H, Yang Y B. Elastic waves in visco-elastic half-space generated by various vehicle loads. Soil Dynamics and Earthquake Engineering, 2001, 21(1): 1–17

[23] Zhai W, Song E. Three dimensional FEM of moving coordinates for the analysis of transient vibrations due to moving loads. Computers and Geotechnics, 2010, 37(1–2): 164–174

[24] Dehghan Manshadi S, Khojasteh A, Nategh S, Rahimian M. Interaction between annular crack and rigid disc inclusion in a transversely isotropic solid. Meccanica, 2018, 53(11–12): 2973–2997

[25] Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics, 1955, 26(2): 182–185

[26] Biot M A. Theory of deformation of a porous viscoelastic anisotropic solid. Journal of Applied Physics, 1956, 27(5): 459–467

[27] Hematiyan M, Khosravifard A, Shiah Y. A new stable inverse method for identification of the elastic constants of a three-dimensional generally anisotropic solid. International Journal of Solids and Structures, 2017, 106–107: 240–250

[28] Eskandari M, Samea P, Ahmadi S F. Axisymmetric time-harmonic response of a surface-stiffened transversely isotropic half-space. Meccanica, 2017, 52(1-2): 183–196

[29] Lv S, Liu C, Yao H, Zheng J. Comparisons of synchronous measurement methods on various moduli of asphalt mixtures. Construction & Building Materials, 2018, 158: 1035–1045

[30] Wang L, Hoyos L R, Mohammad L, Abadie C. Characterization of asphalt concrete by multi-stage true triaxial testing. Journal of ASTM International, 2005, 2(10): 12276

[31] Pan T, Tutumluer E, Anochie-Boateng J. Aggregate morphology affecting resilient behavior of unbound granular materials, Transportation Research Record. Transportation Research Record: Journal of the Transportation Research Board, 2006, 1952(1): 12–20

[32] Tutumluer E, Seyhan U. Laboratory determination of anisotropic aggregate resilient moduli using an innovative test device, Transportation Research Record. Transportation Research Record: Journal of the Transportation Research Board, 1999, 1687(1): 13–21

[33] Oda M. Initial fabrics and their relations to mechanical properties of granular material. Soils and foundations, 1972, 12(1): 17–36

[34] Alkhalifah T, Tsvankin I. Velocity analysis for transversely isotropic media. Geophysics, 1995, 60(5): 1550–1566

[35] You L, Yan K, Hu Y, Ma W. Impact of interlayer on the anisotropic multi-layered medium overlaying viscoelastic layer under axisymmetric loading. Applied Mathematical Modelling, 2018, 61: 726–743

[36] Kim S H, Little D N, Masad E, Lytton R L. Estimation of level of anisotropy in unbound granular layers considering aggregate physical properties. International Journal of Pavement Engineering, 2005, 6(4): 217–227

[37] Tutumluer E, Little D, Kim S H. Validated model for predicting field performance of aggregate base courses. Transportation Research Record: Journal of the Transportation Research Board, 2003, 1837(1): 41–49

[38] Masad S, Little D, Masad E. Analysis of flexible pavement response and performance using isotropic and anisotropic material properties. Journal of Transportation Engineering, 2006, 132(4): 342–349

[39] Wang L, Hoyos L R, Wang J, Voyiadjis G, Abadie C. Anisotropic properties of asphalt concrete: Characterization and implications for pavement design and analysis. Journal of Materials in Civil Engineering, 2005, 17(5): 535–543

[40] Mukhopadhyay A. Stresses produced by a normal load moving over a transversely isotropic layer of ice lying on a rigid foundation. Pure and Applied Geophysics, 1965, 60(1): 29–41

[41] Yan K, Xu H, You L. Analytical layer-element approach for wave propagation of transversely isotropic pavement. International Journal of Pavement Engineering, 2016, 17(3): 275–282

[42] You L, Yan K, Hu Y, Liu J, Ge D. Spectral element method for dynamic response of transversely isotropic asphalt pavement under impact load. Road Materials and Pavement Design, 2018, 19(1): 223–238

[43] Yan K, Shi T, You L, J Man. Spectral element method for dynamic response of multilayered half medium subjected to harmonic moving load. International Journal of Geomechanics, 2018, 18(12): 04018161

[44] You L, You Z, Dai Q, Xie X, Washko S, Gao J. Investigation of adhesion and interface bond strength for pavements underlying chip-seal: Effect of asphalt-aggregate combinations and freeze-thaw cycles on chip-seal. Construction & Building Materials, 2019, 203: 322–330

[45] Canestrari F, Ferrotti G, Lu X, Millien A, Partl M N, Petit C, Phelipot-Mardelé A, Piber H, Raab C. Mechanical testing of interlayer bonding in asphalt pavements. Advances in Interlaboratory Testing and Evaluation of Bituminous Materials, 2013, 9: 303–360

[46] Borawski B, Singh J, Todd J A, Wolfe D E. Multi-layer coating design architecture for optimum particulate erosion resistance. Wear, 2011, 271(11–12): 2782–2792

[47] Sui Y, Appenzeller J. Screening and interlayer coupling in multilayer graphene field-effect transistors. Nano Letters, 2009, 9(8): 2973–2977

[48] Chun S, Kim K, Greene J, Choubane B. Evaluation of interlayer bonding condition on structural response characteristics of asphalt pavement using finite element analysis and full-scale field tests. Construction & Building Materials, 2015, 96: 307–318

[49] Stenzler J S, Goulbourne N. Effect of Polyacrylate Interlayer microstructure on the impact response of multi-layered polymers. Time Dependent Constitutive Behavior and Fracture/Failure Processes, 2011, 3: 241–258

[50] Chupin O, Chabot A, Piau J M, Duhamel D. Influence of sliding interfaces on the response of a layered viscoelastic medium under a moving load. International Journal of Solids and Structures, 2010, 47(25–26): 3435–3446

[51] Liu N, Yan K, Shi C, You L. Influence of interface conditions on the response of transversely isotropic multi-layered medium by impact load. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 77: 485–493

[52] You L, Yan K, Shi T, Man J, Liu N. Analytical solution for the effect of anisotropic layers/interlayers on an elastic multi-layered medium subjected to moving load. International Journal of Solids and Structures, 2019, 172: 10–20

[53] Jiang Y, Lee F C. Single-stage single-phase parallel power factor correction scheme. In: Power Electronics Specialists Conference, PESC’94 Record. IEEE, 1994, 1145–1151

[54] You L, You Z, Yan K. Effect of anisotropic characteristics on the mechanical behavior of asphalt concrete overlay. Frontiers of Structural and Civil Engineering, 2019, 13(1): 110–122

[55] Schmidt H, Tango G. Efficient global matrix approach to the computation of synthetic seismograms. Geophysical Journal International, 1986, 84(2): 331–359

[56] Zhang P, Liu J, Lin G, Wang W. Axisymmetric dynamic response of the multi-layered transversely isotropic medium. Soil Dynamics and Earthquake Engineering, 2015, 78: 1–18

[57] Cornille P. Computation of Hankel transforms. SIAM Review, 1972, 14(2): 278–285

[58] Kim J. General viscoelastic solutions for multilayered systems subjected to static and moving loads. Journal of Materials in Civil Engineering, 2011, 23(7): 1007–1016

[59] Ai Z, Cang N, Cheng C. Analytical layer-element method for axisymmetric problem of transversely isotropic multi-layered soils. Chinese Journal of Geotechnical Engineering, 2012, 34: 863–867

[60] Masad E, Tashman L, Somedavan N, Little D. Micromechanics-based analysis of stiffness anisotropy in asphalt mixtures. Journal of Materials in Civil Engineering, 2002, 14(5): 374–383

[61] Tutumluer E, Thompson M. Anisotropic modeling of granular bases in flexible pavements. Transportation Research Record: Journal of the Transportation Research Board, 1997, 1577(1): 18–26

[62] Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84

[63] Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95

[64] Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

[65] Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464

[66] Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535

Acknowledgements

This study was funded by the National Natural Science Foundation of China (Grant Nos: 51278188, 50808077, and 51778224) and Project of Young Core Instructor Growth from Hunan Province of China. The first author also acknowledges the financial support from the China Scholarship Council (CSC) under No.201606130003. The authors are sincerely grateful for their financial support. The views and findings of this study represent those of the authors and may not reflect those of NSFC, Hunan University, and CSC.

RIGHTS & PERMISSIONS

2020 Higher Education Press