A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and compressive components of elastic waves. The faster component can overtake the slower one resulting in their dissipative annihilation through energy cascades. Efficient absorbing assemblies are presented and analysed numerically. The length of the asymmetric part needed to damp a harmonic signal is determined analytically and validated numerically. Transmission properties for random self-affine wave packets are studied: a universal scaling for the transmission factor variation with the length of the asymmetric part was established.
La propagation unidimensionnelle des ondes à travers des milieux élastiquement asymétriques est étudiée. Une classe de métamatériaux possédant une asymétrie élastique arbitraire est proposée. Cette asymétrie entraîne différentes vitesses des composants de traction et de compression : le composant le plus rapide dépasse le plus lent, entraînant leur annihilation dissipative par des cascades d’énergie. Des assemblages de damping efficace sont présentés et analysés numériquement. La longueur de la partie asymétrique nécessaire pour amortir un signal harmonique est déterminée analytiquement et validée numériquement. Les propriétés de transmission pour les paquets d’ondes auto-affines aléatoires sont étudiées : une mise à l’échelle universelle pour la variation du facteur de transmission avec la longueur de la partie asymétrique a été établie.
Revised:
Accepted:
Published online:
Mots-clés : Asymétrie élastique, Damping des ondes, Propagation des ondes, Annihilation des ondes, Matériaux architecturés, Contacts internes
Vladislav A. Yastrebov 1
CC-BY 4.0
@article{CRMECA_2022__350_G1_1_0,
author = {Vladislav A. Yastrebov},
title = {Wave propagation through an elastically asymmetric architected material},
journal = {Comptes Rendus. M\'ecanique},
pages = {1--26},
publisher = {Acad\'emie des sciences, Paris},
volume = {350},
year = {2022},
doi = {10.5802/crmeca.100},
language = {en},
}
Vladislav A. Yastrebov. Wave propagation through an elastically asymmetric architected material. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 1-26. doi : 10.5802/crmeca.100. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.100/
[1] Stress–strain relations for materials with different moduli in tension and compression, AIAA J., Volume 15 (1977) no. 1, pp. 16-23 | DOI
[2] Effective elastic properties of an anisotropic material with arbitrarily oriented interacting cracks, J. Mech. Phys. Solids, Volume 42 (1994) no. 4, pp. 561-584 | DOI | Zbl
[3] Mechanics of a fiber network within a non-fibrillar matrix: model and comparison with collagen–agarose co-gels, Ann. Biomed. Eng., Volume 40 (2012) no. 10, pp. 2111-2121 | DOI
[4] Remodeling of fibrous extracellular matrices by contractile cells: predictions from discrete fiber network simulations, Biophys. J., Volume 107 (2014) no. 8, pp. 1829-1840 | DOI
[5] Towards gigantic RVE sizes for 3D stochastic fibrous networks, Int. J. Solids Struct., Volume 51 (2014) no. 2, pp. 359-376 | DOI
[6] Mechanical behavior in living cells consistent with the tensegrity model, Proc. Natl. Acad. Sci. USA, Volume 98 (2001) no. 14, pp. 7765-7770 | DOI
[7] Negative normal stress in semiflexible biopolymer gels, Nat. Mater., Volume 6 (2007) no. 1, pp. 48-51 | DOI
[8] Microbuckling of fibrin provides a mechanism for cell mechanosensing, J. R. Soc. Interface, Volume 12 (2015) no. 108, 20150320 | DOI
[9] Fiber networks amplify active stress, Proc. Natl. Acad. Sci. USA, Volume 113 (2016) no. 11, pp. 2827-2832 | DOI
[10] A new computational framework for materials with different mechanical responses in tension and compression and its applications, Int. J. Solids Struct., Volume 100 (2016), pp. 54-73 | DOI
[11] Discrete breathers in one-dimensional diatomic granular crystals, Phys. Rev. Lett., Volume 104 (2010) no. 24, 244302 | DOI
[12] Nonlinear normal modes and band zones in granular chains with no pre-compression, Nonlinear Dyn., Volume 63 (2011) no. 3, pp. 359-385 | DOI | MR
[13] Traveling waves in 2D hexagonal granular crystal lattices, Granul. Matter, Volume 16 (2014) no. 4, pp. 531-542 | DOI
[14] Cyclic behavior of extruded magnesium: experimental, microstructural and numerical approach, Int. J. Plast., Volume 27 (2011) no. 12, pp. 2068-2084 | DOI | Zbl
[15] Deformation by grain boundary hinge-like behavior, Mater. Lett., Volume 62 (2008) no. 1, pp. 57-60 | DOI
[16] Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review, Philos. Trans. R. Soc. Lond. A, Volume 368 (2010) no. 1929, pp. 4775-4806 | DOI
[17] Kirigami skins make a simple soft actuator crawl, Sci. Robot., Volume 3 (2018) no. 15, eaar7555 | DOI
[18] Buckling-induced kirigami, Phys. Rev. Lett., Volume 118 (2017) no. 8, 084301 | DOI
[19] Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials, Eng. Fract. Mech., Volume 74 (2007) no. 10, pp. 1539-1560 | DOI
[20] Modeling microdefects closure effect with isotropic/anisotropic damage, Int. J. Damage Mech., Volume 17 (2008) no. 1, pp. 65-96 | DOI
[21] Basic equations in the theory of elasticity for materials with different stiffness in tension and compression, Mech. Solids, Volume 1 (1966) no. 2, pp. 29-34
[22] Two-dimensional bi-linear orthotropic elastic materials, J. Compos. Mater., Volume 3 (1969) no. 4, pp. 725-727 | DOI
[23] Constitutive equations for bimodulus elastic materials, AIAA J., Volume 10 (1972) no. 4, pp. 516-518 | DOI
[24] Equations of the plane problem heteroresisting or heteromodular theory of elasticity, Izv. Akad. Nauk Armyanskoy SSR, Mekh., Volume 19 (1966) no. 2, pp. 3-19
[25] Theory of Heteromodular Elasticity, Nauka, Moscow, Russia, 1982
[26] The Boussinesq problem for a material with different moduli in tension and compression, Q. J. Mech. Appl. Math., Volume 30 (1977) no. 4, pp. 449-466 | DOI | MR | Zbl
[27] A theory of elasticity for an isotropic body with different moduli in tension and compression, Mech. Solids, Volume 13 (1978) no. 6, pp. 25-30 in Russian, Mekhanika Tverdogo Tela 6 (1978), p. 29-34
[28] Propagation of longitudinal and transverse waves in a multimodulus elastic medium, J. Appl. Mech. Tech. Phys., Volume 50 (2009) no. 4, pp. 691-697 | DOI | Zbl
[29] Propagation of converging spherical deformation waves in a heteromodular elastic medium, J. Appl. Mech. Tech. Phys., Volume 57 (2016) no. 4, pp. 701-708 | DOI | MR | Zbl
[30] Elastic solids with different moduli in tension and compression, J. Elast., Volume 7 (1977) no. 4, pp. 369-386 | DOI | Zbl
[31] Conewise linear elastic materials, J. Elast., Volume 37 (1994) no. 1, pp. 1-38 | DOI | MR
[32] A review on the research of mechanical problems with different moduli in tension and compression, J. Mech. Sci. Technol., Volume 24 (2010) no. 9, pp. 1845-1854 | DOI
[33] Micromechanics: Overall Properties of Heterogeneous Materials, 37, Elsevier, Amsterdam, The Netherlands, 2013
[34] General theory of the solutions of the equations of motion of an elastic medium of different moduli, J. Appl. Math. Mech., Volume 49 (1985) no. 3, pp. 322-336 | DOI | MR | Zbl
[35] Asymmetric wave propagation in nonlinear systems, Phys. Rev. Lett., Volume 106 (2011), 164101 | DOI
[36] Wave propagation in a semi-infinite heteromodular elastic bar subjected to a harmonic loading, J. Sound Vib., Volume 331 (2012) no. 20, pp. 4464-4480 | DOI
[37] Propagation of nonlinear acoustic waves in bimodular media with linear dissipation, Wave Motion, Volume 50 (2013) no. 2, pp. 191-196 | DOI | MR | Zbl
[38] Stationary waves in a bimodular rod of finite radius, Wave Motion, Volume 75 (2017), pp. 72-76 | DOI | MR | Zbl
[39] About distribution of flat one-dimensional waves and their interaction with barrier in the media differently reacting to a stretching and compression, Dal’nevostochnyi Matematicheskii Zh., Volume 6 (2005) no. 1, pp. 94-105 (in Russian)
[40] Analysis of wave propagation in a discrete chain of bilinear oscillators, Nonlinear Process. Geophys., Volume 24 (2017) no. 3, pp. 455-460 | DOI
[41] Non-reciprocal wave transmission in a bilinear spring-mass system, J. Vibr. Acoust., Volume 142 (2020) no. 2, 021006
[42] Broadband non-reciprocity with robust signal integrity in a triangle-shaped nonlinear 1D metamaterial, Nonlinear Dyn., Volume 100 (2020), pp. 1-13 | DOI
[43] Acoustic diode: rectification of acoustic energy flux in one-dimensional systems, Phys. Rev. Lett., Volume 103 (2009) no. 10, 104301 | DOI
[44] Unilateral and nonreciprocal transmission through bilinear spring systems, Extreme Mech. Lett., Volume 42 (2021), 101087 | DOI
[45] One-dimensional wave propagation in materials with different moduli in tension and compression, Int. J. Eng. Sci., Volume 18 (1980) no. 6, pp. 815-827 | DOI | Zbl
[46] Free longitudinal vibrations of bimodular beams: a comparative study, Int. J. Struct. Stab. Dyn., Volume 11 (2011) no. 01, pp. 23-56 | DOI | MR | Zbl
[47] Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, PA, USA, 1973 | DOI
[48] On fronts of strong and weak discontinuities in solutions of the equations of different-modulus elasticity theory, J. Appl. Math. Mech., Volume 53 (1989) no. 2, pp. 230-235 | DOI | Zbl
[49] Longitudinal waves in an elastic medium with a piecewise-linear dependence of the stress on the strain, J. Appl. Math. Mech., Volume 54 (1990) no. 5, pp. 663-668 | DOI
[50] Wave propagation in linear, bilinear and trilinear elastic bars, Wave Motion, Volume 15 (1992) no. 1, pp. 77-92 | DOI | MR
[51] Longitudinal oscillations of bimodular rods, Int. J. Struct. Stab. Dyn., Volume 5 (2005) no. 01, pp. 37-54 | DOI | MR | Zbl
[52] Non-linear real and complex modes of conewise linear systems, J. Sound Vib., Volume 174 (1994) no. 3, pp. 289-313 | DOI | MR | Zbl
[53] Chaos after period-doubling bifurcations in the resonance of an impact oscillator, Phys. Lett. A, Volume 91 (1982) no. 1, pp. 5-8 | DOI | MR
[54] Dynamics of multiple-degree-of-freedom oscillators with colliding components, J. Sound Vib., Volume 165 (1993) no. 3, pp. 439-453 | DOI | MR | Zbl
[55] Study of forced vibrations of the Kelvin–Voigt model with an asymmetric spring, Mech. Solids, Volume 50 (2015) no. 3, pp. 294-304 | DOI
[56] Bifurcation and Chaos in Nonsmooth Mechanical Systems, 45, World Scientific, Singapore, 2003 | DOI
[57] Dynamic stability analysis of an elastic composite material having a negative-stiffness phase, J. Mech. Phys. Solids, Volume 57 (2009) no. 7, pp. 1122-1138 | DOI | Zbl
[58] Harnessing buckling to design tunable locally resonant acoustic metamaterials, Phys. Rev. Lett., Volume 113 (2014) no. 1, 014301 | DOI
[59] Programmable mechanical metamaterials, Phys. Rev. Lett., Volume 113 (2014) no. 17, 175503 | DOI
[60] Buckling and collapse of embedded carbon nanotubes, Phys. Rev. Lett., Volume 81 (1998) no. 8, pp. 1638-1641 | DOI
[61] Macroscopic properties of carbon nanotubes from molecular-mechanics simulations, Phys. Rev. B, Volume 69 (2004) no. 23, 235406 | DOI
[62] Strong, lightweight, and recoverable three-dimensional ceramic nanolattices, Science, Volume 345 (2014) no. 6202, pp. 1322-1326 | DOI
[63] Nonlinear effects for coda-type elastic waves in stressed granular media, Phys. Rev. E, Volume 80 (2009) no. 1, 011306 | DOI
[64] Mechanics of Continua, Robert E. Krieger Publishing Co., Huntington, NY, USA, 1980
[65] Code, data and scripts to study wave dynamics in asymmetric material, 2021 (Zenodo, https://doi.org/10.5281/zenodo.4461652)
Cited by Sources:
Comments - Policy