Abstract
In this study, the dynamic response of a growing inclusion in an elastic wave metamaterial with local resonators is investigated. It is assumed that the inclusion at a constant speed is composed of particles with larger or smaller mass than the surrounding lattice is. Based on the integral transform, wave equations of the growing inclusion are derived as the Wiener–Hopf form. In order to show the effect of local resonators, stop band properties and the ratio of the tip to end displacements of the inclusion are considered. Numerical results show that the local resonators can make the displacement ratio tend to the case without inclusion. It indicates that the outstanding ability of elastic wave metamaterials inhibits structural deformation and defect growth.
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Gao, C., Halim, D., Yi, X.: Elastic metamaterial with multiple resonant modes and asymmetric structure design for low-frequency vibration absorption. Acta Mech. 233(5321), 5333 (2022)
Huang, Y., Liu, S.T., Zhao, J.: A gradient-based optimization method for the design of layered phononic band-gap materials. Acta Mech Solida Sin. 29(429), 443 (2016)
Emerson, T.A., Manimala, J.M.: Passive-adaptive mechanical wave manipulation using nonlinear metamaterial plates. Acta Mech. 231, 4665–4681 (2020)
Giorgio, I., Hild, F., Gerami, E., dell’Isola, F., Misra, A.: Experimental verification of 2D Cosserat chirality with stretch-micro-rotation coupling in orthotropic metamaterials with granular motif. Mech. Res. Commun. 126, 104020 (2022)
Abali, B.E., Vazic, B., Newell, P.: Influence of microstructure on size effect for metamaterials applied in composite structures. Mech Res. Commun. 122, 103877 (2022)
Zhang, G., Zheng, C., Qiu, X., Mi, C.: Microstructure-dependent band gaps for elastic wave propagation in a periodic microbeam structure. Acta Mech. Solida Sin. 34(527), 538 (2021)
Ghavanloo, E., El-Borgi, S., Fazelzadeh, S.A.: Formation of quasi-static stop band in a new one-dimensional metamaterial. Arch. Appl. Mech. 93(287), 299 (2022)
Li, Y., Challamel, N., Elishakoff, I.: Effective mass and effective stiffness of finite and infinite metamaterial lattices. Arch. Appl. Mech. 93(301), 321 (2022)
Huang, H.H., Sun, C.T., Huang, G.L.: On the negative effective mass density in acoustic metamaterials. Int. J. Eng. Sci. 47(610), 617 (2009)
Dong, L., Lakes, R.: Advanced damper with high stiffness and high hysteresis damping based on negative structural stiffness. Int. J. Solids Struct. 50(2416), 2423 (2013)
Zareei, A., Alam, M.R.: Broadband cloaking of flexural waves. Phys. Rev. E 95, 063002 (2017)
Huang, G.L., Sun, C.T.: Band gaps in a multiresonator acoustic metamaterial. ASME J. Vib. Acoust. 132, 031003 (2010)
Attarzadeh, M.A., Al Babaa, H., Nouh, M.: On the wave dispersion and non-reciprocal power flow in space-time traveling acoustic metamaterials. Appl. Acoust. 133, 210–214 (2018)
Nassar, H., Chen, H., Norris, A.N., Haberman, M.R., Huang, G.L.: Non-reciprocal wave propagation in modulated elastic metamaterials. Proc. Roy. Soc. A 473, 20170188 (2018)
Zhou, Y., Wei, P., Tang, Q.: Continuum model of a one-dimensional lattice of metamaterials. Acta Mech. 227, 2361–2376 (2016)
Huang, H.H., Sun, C.T.: Locally resonant acoustic metamaterials with 2D anisotropic effective mass density. Philos Mag. 91(981), 996 (2011)
Liu, C., Reina, C.: Broadband locally resonant metamaterials with graded hierarchical architecture. J. Appl. Phys. 123, 095108 (2018)
Slepyan, L.I., Movchan, A.B., Mishuris, G.S.: Crack in a lattice waveguide. Int J. Fract. 162(91), 106 (2010)
Pechenik, L., Levine, H., Kessler, D.A.: Steady-state mode I cracks in a viscoelastic triangular lattice. J. Mech. Phys. Solids 50(583), 613 (2002)
Slepyan, L.I.: Feeding and dissipative waves in fracture and phase transition II. Phase-transition waves. J. Mech. Phys. Solids 49(513), 550 (2001)
Slepyan, L.I.: Feeding and dissipative waves in fracture and phase transition. III. Triangular-cell lattice. J. Mech. Phys. Solids 49, 2839–2875 (2001)
Sharma, B.L.: Diffraction of waves on square lattice by semi-infinite crack SIAM. J. Appl. Math. 75(1171), 1192 (2015)
Özturk, T., Poole, W.J., Embury, J.D.: The deformation of Cu–W laminates. Mater. Sci. Eng. A 148, 175–178 (1991)
Yue, Q., Chen, H., Yao, C., Lu, D., Zhang, J., Huang, F.: Review of collision and growth on non-metallic inclusion in steel. J. Iron Steel Res. 24, 1–5 (2012)
Dal Corso, F., Bigoni, D., Gei, M.: The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part I. Full-field solution and asymptotics. J. Mech. Phys. Solids 56, 815–838 (2008)
Bigoni, D., Dal Corso, F., Gei, M.: The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part II. Implications on shear band nucleation, growth and energy release rate. J. Mech. Phys. Solids 56, 839–857 (2008)
Nugent, E.E., Calhoun, R.B., Mortensen, A.: Experimental investigation of stress and strain fields in a ductile matrix surrounding an elastic inclusion. Acta Mater. 48, 1451–1467 (2000)
Sharma, B.L.: Diffraction of waves on square lattice by semi-infinite rigid constraint. Wave Motion 59(52), 68 (2015)
Sharma, B.L., Maurya, G.: Discrete scattering by a pair of parallel defects. Philos. Trans. R. Soc. A 378, 20190102 (2020)
Colquitt, D.J., Nieves, M.J., Jones, I.S., Movchan, A.B., Movchan, N.V.: Localization for a line defect in an infinite square lattice. Proc. R. Soc. A 469, 20120579 (2013)
Osharovich, G.G., Ayzenberg-Stepanenko, M.V.: Wave localization in stratified square-cell lattices: the antiplane problem. J. Sound Vib. 331(1378), 1397 (2012)
Nieves, M.J., Jones, I.S., Movchan, A.B.: Dynamic response of a growing inclusion in a discrete system. Int. J. Solids Struct. 51(2990), 3001 (2014)
Mishuris, G.S., Movchan, A.B., Slepyan, L.I.: Waves and fracture in an inhomogeneous lattice structure. Waves Random Complex Media 17, 409–428 (2007)
Mishuris, G.S., Movchan, A.B., Slepyan, L.I.: Dynamics of a bridged crack in a discrete lattice Q. J. Mech. Appl. Mech. 61(151), 160 (2008)
Huang, K.X., Shui, G.S., Wang, Y.Z., Wang, Y.S.: Meta-arrest of a fast propagating crack in elastic wave metamaterials with local resonators. Mech Mater. 148, 103497 (2020)
Slepyan, L.I.: Models and Phenomena in Fracture Mechanics. Springer, Berlin (2002)
Gorbushin, N., Mishuris, G.: Dynamic fracture of a discrete media under moving load. Int J. Solids Struct. 130–131(280), 295 (2018)
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Huang, KX., Shui, GS. Growth of a semi-infinite inclusion in an elastic wave metamaterial with local resonators. Acta Mech 234, 3161–3171 (2023). https://doi.org/10.1007/s00707-023-03549-8
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DOI: https://doi.org/10.1007/s00707-023-03549-8