Laplace-domain, high-order homogenization for transient dynamic response of viscoelastic composites

International Journal for Numerical Methods in Engineering

Volumn 103, Issue 13, 2015, Pages 937-957

  Hui, Tong ^a   Oskay, Caglar ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Bandgap; Homogenization; Laplace transform; Viscoelastic behavior; Wave dispersion

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPOSITE MATERIALS; ENERGY DISSIPATION; ENERGY GAP; HOMOGENIZATION METHOD; LAPLACE TRANSFORMS; MORPHOLOGY; TRANSIENT ANALYSIS; VISCOELASTICITY; WAVE PROPAGATION;

CONSTITUTIVE RELATIONSHIPS; MACROSCOPIC DEFORMATIONS; MICROSTRUCTURE MORPHOLOGIES; TRANSIENT DYNAMIC RESPONSE; VISCO-ELASTIC BEHAVIORS; VISCOELASTIC COMPOSITES; WAVE DISPERSION; WAVE PROPAGATION CHARACTERISTICS;

DISPERSION (WAVES);

EID: 84940756017     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4916     Document Type: Article

References (37)

1. Cosserat E, Cosserat F. Theorie des Corps Deformables. Hermann & Fils: Paris, France, 1909.
2. Eringen C, Suhubi ES. Nonlinear theory of micro-elastic solids II. International Journal of Engineering Science 1964; 2:189-203.
3. Mindlin RD. Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis 1964; 16:51-78.
4. Dontsov EV, Tokmashev RD, Guzina BB. A physical perspective of the length scales in gradient elasticity through the prism of wave dispersion. International Journal of Solids and Structures 2013; 50(22):3674-3684.
5. Hui T, Oskay C. A high order homogenization model for transient dynamics of heterogeneous media including micro-inertia effects. Computer Methods in Applied Mechanics and Engineering 2014; 273:181-203.
6. Santosa F, Symes WW. A dispersive effective medium for wave propagation in periodic composites. SIAM Journal on Applied Mathematics 1991; 51:984-1005.
7. Wang ZP., Sun CT. Modeling micro-inertia in heterogeneous materials under dynamic loading. Wave Motion 2002; 36:473-485.
8. Engelbrecht J, Berezovski A, Pastrone F, Braun M. Waves in microstructured materials and dispersion. Philosophical Magazine 2005; 85:4127-4141.
9. Gonella S, Greene MS, KamLiu W. Characterization of heterogeneous solids via wave methods in computational microelasticity. Journal of the Mechanics and Physics of Solids 2011; 59:959-974.
10. Yablonovitch E, Leung KM. Photonic band structure: non-spherical atoms in the face-centered-cubic case. Physica B 1991; 175(1):81-86.
11. Yablonovitch E, Gmitter TJ, Leung KM. Photonic band structure: the face-centered-cubic case employing nonspherical atoms. Physical Review Letters 1991; 67(17):2295-2299.
12. Kafesaki M, Sigalas MM, Economou EN. Elastic wave band gaps in 3-D periodic polymer matrix composites. Solid State Communications 1995; 96(5):285-289.
13. Sigalas MM, Economou EN. Elastic waves in plates with periodically placed inclusions. Journal of Applied Physics 1994; 75(6):2845-2850.
14. Vasseur JO, Djafari-Rouhani B, Dobrzynski L, Kushwaha MS, Halevi P. Complete acoustic band gaps in periodic fibre reinforced composite materials: the carbon/epoxy composite and some metallic systems. Journal of Physics: Condensed Matter 1994; 6(42):8759-8770.
15. Suzuki T, Yu PKL. Tunneling in photonic band structures. Journal of the Optical Society of America B 1995; 12(5):804-820.
16. Suzuki T, Yu PKL. Complex elastic wave band structures in three-dimensional periodic elastic media. Journal of the Mechanics and Physics of Solids 1998; 46(1):115-138.
17. Andrianov IV, Bolshakov VI, Danishevs'kyy VV, Weichert D. Higher order asymptotic homogenization and wave propagation in periodic composite materials. Proceedings of the Royal Society of London. Series A 2008; 464(2093):1181-1201.
18. Pham K, Kouznetsova VG, Geers MGD. Transient computational homogenization for heterogeneous materials under dynamic excitation. Journal of the Mechanics and Physics of Solids 2013; 61(11):2125-2146.
19. Sanahuja J. Effective behaviour of ageing linear viscoelastic composites: homogenization approach. International Journal of Solids and Structures 2013; 50(19):2846-2856.
20. Tran AB, Yvonnet J, He QC, Toulemonde C, Sanahuja J. A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials. Computer Methods in Applied Mechanics and Engineering 2011; 200(45):2956-2970.
21. Abu-Alshaikh I, Turhan D, Mengi Y. Propagation of transient out-of-plane shear waves in viscoelastic layered media. International Journal of Mechanical Sciences 2001; 43:2911-2928.
22. Naciri T, Navi P, Ehrlacher A. Harmonic wave propagation in viscoelastic heterogeneous materials part I: dispersion and damping relations. Mechanics of Materials 1994; 18:313-333.
23. Nayfeh AH. Discrete Lattice simulation of transient motions in elastic and viscoelastic composites. International Journal of Solids and Structures 1974; 10:231-242.
24. Ting TCT. The effects of dispersion and dissipation on wave propagation in viscoelastic layered composities. International Journal of Solids and Structures 1980; 16:903-911.
25. Tsai L, Prakash V. Structure of weak shock waves in 2-D layered material systems. International Journal of Solids and Structures 2005; 42:727-750.
26. Zhao YP, Wei PJ. The band gap of 1D viscoelastic phononic crystal. Computational Materials Science 2009; 46(3):603-606.
27. Moiseyenko RP, Laude V. Material loss influence on the complex band structure and group velocity in phononic crystals. Physical Review B. Condensed Matter 2011; 83(6):1-6.
28. Psarobas IE. Viscoelastic response of sonic band-gap materials. Physical Review. B, Condensed Matter 2001; 64(1):1-4.
29. Merheb B, Deymier PA, Jain M, Aloshyna-Lesuffleur M, Mohanty S, Berker A, Greger RW. Elastic and viscoelastic effects in rubber/air acoustic band gap structures: a theoretical and experimental study. Journal of Applied Physics 2008; 104(6):1-9.
30. Oh JH., Kim YJ, Kim YY. Wave attenuation and dissipation mechanisms in viscoelastic phononic crystals. Journal of Applied Physics 2013; 113(10):1-3.
31. Hui T, Oskay C. A nonlocal homogenization model for wave dispersion in dissipative composite materials. International Journal of Solids and Structures 2013; 50:38-48.
32. Boutin C. Microstructural effects in elastic composites. International Journal of Solids and Structures 1996; 33:1023-1051.
33. Papanicolopulos SA, Zervos A, Vardoulakis I. A three-dimensional C1 finite element for gradient elasticity. International journal for numerical methods in engineering 2009; 77(10):1396-1415.
34. Cottrell JA, Hughes T, Reali A, Sangalli G. Isogeometric discretizations in structural dynamics and wave propagation. ECOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rethymno, Crete, Greece, 2007; 1-14.
35. Brancik L. Programs for fast numerical inversion of Laplace transforms in MatLab language environment. Sbornik 7. Proc. Matlab 99, Prague, Czech Republic, 1999; 27-39.
36. Macdonald JR. Accelerated convergence, divergence, iteration, extrapolation, and curve fitting. Journal of Applied Physics 1964; 35:3034-3041.
37. Hui T, Oskay C. Computational modeling of polyurea-coated composites subjected to blast loads. Journal of Composite Materials 2012; 46:2167-2178.