Wave propagation in 3D viscoelastic auxetic and textile materials by homogenized continuum micropolar models

Composite Structures

Volumn 141, Issue , 2016, Pages 328-345

  Reda, H ^a,b   Rahali, Y ^c   Ganghoffer, J F ^a   Lakiss, H ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b LEBANESE UNIVERSITY   (Lebanon)

^c UNIVERSITY OF TUNIS   (Tunisia)

Author keywords

Auxetic lattices; Effective micropolar continua; Textiles; Viscoelastic periodic network; Wave absorption; Wave propagation

Indexed keywords

DAMPING; DISPERSION (WAVES); ENERGY GAP; EQUATIONS OF MOTION; FREQUENCY BANDS; PERIODIC STRUCTURES; TEXTILES; WAVE PROPAGATION; WEAVING;

MICROPOLAR CONTINUUM; NEGATIVE POISSON'S RATIOS; PERIODIC NETWORKS; PLAIN WEAVE TEXTILES; RE-ENTRANT CONFIGURATION; VISCOELASTIC RESPONSE; WAVE ABSORPTION; WAVE PROPAGATION CHARACTERISTICS;

VISCOELASTICITY;

EID: 84958841667     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2016.01.071     Document Type: Article

References (55)

1. Gibson L.J., Ashby F. Cellular solids: structure and properties 1999, Cambridge University Press, p. 532. second ed.
2. Dingreville R., Robbins J., Voth T.E. Multiresolution modeling of the dynamic loading of metal matrix composites. JOM 2013, 65(2):203-214.
3. Germain P. The method of virtual power in continuum mechanics. Part 2: microstructure. SIAM J Appl Math 1973, 25(3):556-575.
4. Eringen A.C. Microcontinuum field theories 1999, Springer, p. 325.
5. Forest S., Sievert R. Nonlinear microstrain theories. Int J Solids Struct 2006, 43(24):7224-7245.
6. Mindlin R.D. Microstructures in linear elasticity. Arch Rat Mech Anal 1964, 10:51-78.
7. Mindlin R.D. Second gradient of strain and surface tension in linear elasticity. Int J Solids Struct 1965, 1(4):417-438.
8. Mindlin R.D., Eshel N.N. On first strain-gradient theories in linear elasticity. Int J Solids Struct 1968, 4(1):109-124.
9. Aifantis E.C. On the role of gradients in the localization of deformation and fracture. Int J Eng Sci 1992, 30(10):1279-1299.
10. Altan S., Aifantis E.C. On the structure of the mode III crack-tip in gradient elasticity. Scr Metall Mater 1992, 26(2):319-324.
11. Ru C.Q., Aifantis E.C. A simple approach to solve boundary value problems in gradient elasticity. Acta Mech 1993, 101(1):59-68.
12. Aifantis E.C. Update on a class of gradient theories. Mech Mater 2003, 35(3-6):259-280.
13. Metrikine A.V., Askes H. One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure: Part 1: generic formulation. Eur J Mech A/Solids 2002, 21(4):555-572.
14. Metrikine A.V. On causality of the gradient elasticity models. J Sound Vib 2006, 297(3-5):727-742.
15. Pasternak E., Mühlhaus H.B. Generalised homogenisation procedures for granular materials. J Eng Math 2005, 52(1):199-229.
16. Pasternak E., Mühlhaus H.B., Dyskin A.V. Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern. Philos Mag 2006, 86(21-22):3339-3371.
17. Ostoja-Starzewki M. Lattice models in micromechanics. Appl Mech Rev 2002, 55(1):35-60.
18. Papargyri-Beskou S., Polyzos D., Beskos D.E. Wave dispersion in gradient elastic solids and structures: a unified treatment. Int J Solids Struct 2009, 46(21):3751-3759.
19. Andrianov I., Awrejcewicz J., Weichert D. Improved continuous models for discrete media. Math Prob Eng 2010, 2010. ID 986242.
20. Askes H., Aifantis E.C. Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results. Int J Solids Struct 2011, 48(13):1962-1990.
21. Charalambopoulous L., Gergidis N. On the gradient elastic wave propagation in cylindrical waveguides with microstructure. Compos B 2012, 43(6):2613-2627.
22. Lomabardo M., Askes H. Higher-order gradient continuum modelling of periodic lattice materials. Comput Mater Sci 2012, 52(1):204-208.
23. Eringen A.C., Suhubi E.S. Nonlinear theory of simple micro-elastic solids. Int J Eng Sci 1964, 2(2):189-203.
24. Eringen AC. Theory of micro-polar elasticity. In Liebowitz H, editor. Fracture, an advanced treatise, vol. II. 1968. p. 621-93 [Chapter 7].
25. Cosserat E., Cosserat F. Théorie des corps déformables Paris: A 1909, Hermann et Cie, p. 235.
26. Mindlin R.D., Tiersten H.F. Effects of couple-stresses in linear elasticity. Arch Rat Mech Anal 1962, 11(1):415-448.
27. Koiter W.T. Couple-stresses in the theory of elasticity. Proc Ned Akad Wet 1964, 67:17-44.
28. Toupin R.A. Theories of elasticity with couple-stresses. Arch Rat Mech Anal 1964, 17(2):85-112.
29. Tsepoura K.G., Papargyri-Beskou S., Polyzos D., Beskos D.E. Static and dynamic analysis of a gradient elastic bar in tension. Arch Appl Mech 2002, 72(6):483-497.
30. Georgiadis H.G., Vardoulakis I., Lykotrafitis G. Torsional surface waves in a gradient-elastic half-space. Wave Motion 2000, 31(4):333-348.
31. Qian L.F., Batra R.C., Chen L.M. Elastostatic deformations of a thick plate by using a higher-order shear and normal deformable plate theory and two meshless local Petrov-Galerkin (MLPG) methods. Comput Model Eng Sci 2003, 4:161-176.
32. Engelbrecht J., Berezovski A., Pastrone F., Braun M. Waves in microstructured materials and dispersion. Philos Mag 2005, 85(33-35).
33. Engelbrecht J., Pastrone F., Braun M., Berezovski A. Hierarchies of waves in nonclassical materials. Universality of nonclassical nonlinearity: applications to non-destructive evaluations and ultrasonics 2006, 29-47. Springer, New York.
34. Papargyri-Beskou S., Polyzos D., Beskos D.E. Wave dispersion in gradient elastic solids and structures: a unified treatment. Int J Solids Struct 2009, 46(21):3751-3759.
35. Fafalis D.A., Filopoulos S.P., Tsamasphyros G.J. On the capability of generalized continuum theories to capture dispersion characteristics at the atomic scale. Eur J Mech A Solids 2012, 36:25-37.
36. Berezovski A., Engelbrecht J., Salupere A., Tamm K., Peets T., Berezovski M. Dispersive waves in microstructured solids. Int J Solids Struct 2013, 50(3):1981-1990.
37. Mead D.J. A general theory of harmonic wave propagation in linear periodic systems with multiple coupling. J Sound Vib 1973, 27(2):235-260.
38. Hussein M.I. Theory of damped Bloch waves in elastic media. Phys Rev B 2009, 80:212301.
39. Merheb B., Deymier P.A., Muralidharan K., Bucay J., Jain M., Aloshyna-Lesuffleur M., et al. Viscoelastic effect on acoustic band gaps in polymer-fluid composites. Model Simul Mater Sci Eng 2009, 17(7):075013.
40. Liu Y.Z., Yu D.L., Zhao H.G., Wen J.H., Wen X.S. Theoretical study of two-dimensional phononic crystals with viscoelasticity based on fractional derivative models. J Phys D Appl Phys 2008, 41:065503.
41. Mukherjee S., Lee E.H. Dispersion relations and mode shapes for waves in laminated viscoelastic composites by finite difference methods. Comput Struct 1975, 5(5-6):279-285.
42. Bacigalupo A., Bellis M. Auxetic anti-tetrachiral materials: equivalent elastic properties and frequency band-gaps. Compos Struct 2015, 131:530-544.
43. Bacigalupo A., Gambarotta L. Homogenization of periodic hexa- and tetrachiral cellular solids. Compos Struct 2014, 116:461-476.
44. Wang Y.F., Wang Y.S., Laude V. Elastic wave propagation in two-dimensional viscoelastic metamaterials. Phys Rev B 2015, 92:104110.
45. Goda I., Assidi M., Ganghoffer J.F. A 3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure. Biomech Model Mechanobiol 2014, 13(1):53-83.
46. Dos Reis F., Ganghoffer J.F. Equivalent mechanical properties of auxetic lattices from discrete homogenization. Comput Mater Sci 2012, 51(1):314-321.
47. Caillerie D., Mourad A., Raoult A. Discrete homogenization in graphene sheet modeling. J Elast 2006, 84(1):33-68.
48. Goda I., Assidi M., Ganghoffer J.F. Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization. J Mech Phys Solids 2013, 61(12):2537-2565.
49. Dos Reis F., Ganghoffer J.F. Construction of micropolar models from lattice homogenization. Comput Struct 2012, 112-113:354-363.
50. Hussein M.I., Frazier M.J. Metadamping: an emergent phenomenon in dissipative metamaterials. J Sound Vib 2013, 332(20):4767-4774.
51. Liu X.N., Huang G.L., Hu G.K. Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices. J Mech Phys Solids 2012, 60(11):1907-1921.
52. Rahali Y., Goda I., Ganghoffer J.F. Numerical identification of classical and nonclassical moduli of 3D woven textiles and analysis of scale effects. Compos Struct 2016, 135:122-139.
53. Phani A.S., Woodhouse J., Fleck N.A. Wave propagation in two-dimensional periodic lattices. J Acoust Soc Am 2006, 119(4):1995-2005.
54. Lane C. The development of a 2D ultarsonic array inspection for single crystal turbine blades. Springer 2014.
55. Phani A.S., Hussein M.I. Analysis of damped Bloch waves by the Rayleigh perturbation method. J Vib Acoust 2013, 135(4):041014.