Localised knife waves in a structured interface

Mishuris, Gennady; Movchan, Alexander; Slepyan, Leonid I.

doi:10.1016/j.jmps.2009.08.004

Cited by 70 publications

(94 citation statements)

References 16 publications

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“…This admissibility criterion is violated when the feeding wave amplitude (at a given frequency) is high enough. In such cases, alternative ordered regimes arise [Mishuris et al (2009a), Slepyan et al (2015)]. Alternative regimes arising in the considered structure are examined separately.…”

Section: Discussionmentioning

confidence: 99%

“…In the first analytical solutions [Slepyan (1981)] and [Slepyan & Troyankina (1984)] obtained for mass-spring lattices, the role of the microstructure in fracture and phase transition was demonstrated. In particular, it was shown that wave radiation always accompanies the steady-state dynamic crack and phase propagation, [Mishuris et al (2009a), Slepyan (2010b), , Slepyan et al (2015)]. The radiation creates the speed-dependent wave resistance, which cannot be detected in a homogeneous material model, [Slepyan (2002), Slepyan (2010a)].…”

Section: Introductionmentioning

confidence: 99%

“…Constant and oscillatory loads can be embedded into such equations and readily solved to reveal very different dynamical fracture regimes. A collection of such solutions for the mass-spring lattice structures, with different geometries (having square or triangular unit cells), can be found in [Slepyan (2002)], [Mishuris et al (2009a)] and [Slepyan et al (2010)] and for homogeneous structures see in [Slepyan et al (2015)]. …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of dynamic damage propagation in discrete beam structures

Movchan

Mishuris

Slepyan

2016

International Journal of Solids and Structures

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In the last decade, significant theoretical advances were obtained for steady-state fracture propagation in spring-mass lattice structures, that also revealed surprising fracture regimes. Very few articles exist, however, on the dynamic fracture processes in lattices composed of beams. In this paper we analyse a failure (feeding) wave propagating in a beam-made lattice strip with periodically placed point masses. The fracture occurs when the strain of the supporting beam reaches the critical value. The problem reduces to a Wiener-Hopf equation, from which the complete solution is obtained. Two cases are considered when the feeding wave transmits into the intact structure as a sinusoidal wave(s) or only as an evanescent wave. For both cases, a complete analysis of the strain inside the structure is presented. We determine the critical level of the feeding wave, below which the steady-state regime does not exist, and its connections to the feeding wave parameters and the failure wave speed. The accompanied dynamic effects are also discussed. Amongst much else, we show that the switch between the two considered regimes introduces a rapid change in the minimum energy required for the failure wave to propagate steadily. The failure wave developing under an incident sinusoidal wave is remarkable due to the fact that there is an upper bound of the domain where the steady-state regime exists. In the present paper, only the latter is examined; the alternative regimes are considered separately.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of dynamic damage propagation in discrete beam structures

Movchan

Mishuris

Slepyan

2016

International Journal of Solids and Structures

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“…Indeed, for N defects the matrix G has N independent elements. The solvability condition of the spectral problem (2.11) yields a transcendental equation in ω, 13) where I N is the N × N identity matrix. Equation (2.13) is the necessary and sufficient condition for the existence of a localized mode.…”

Section: A Finite Inclusion In An Infinite Square Latticementioning

confidence: 99%

“…For a structured interface and a crack propagating with constant speed within a square lattice, localized modes were analysed by Mishuris et al [13]. In particular, it was shown that the crack propagation can be supported by a sinusoidal wave localized along the crack, which the authors refer to as a knife wave.…”

Section: Introductionmentioning

confidence: 99%

Localization for a line defect in an infinite square lattice

et al. 2013

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Localized defect modes generated by a finite line defect composed of several masses, embedded in an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations of the lattice Green's function are presented and discussed. The problem is reduced to an eigenvalue system and the properties of the corresponding matrix are examined in detail to yield information regarding the number of symmetric and skew-symmetric modes. Asymptotic expansions in the far field, associated with long wavelength homogenization, are presented. Asymptotic expressions for Green's function in the vicinity of the band edge are also discussed. Several examples are presented where eigenfrequencies linked to this system and the corresponding eigenmodes are computed for various defects and compared with the asymptotic expansions. The case of an infinite defect is also considered and an explicit dispersion relation is obtained. For the case when the number of masses within the line defect is large, it is shown that the range of the eigenfrequencies can be predicted using the dispersion diagram for the infinite chain.

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Analysis of dynamic failure of the discrete chain structure with non‐local interactions

Gorbushin

Mishuris

2016

Math Methods in App Sciences

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In the present work the steady-state crack propagation in a chain of oscillators with non-local interactions is considered. The interactions are modeled as linear springs while the crack is presented by the absence of extra springs. The problem is reduced to the Wiener-Hopf type and solution is presented in terms of the inverse Fourier transform. It is shown that the non-local interactions may change the structure of the solution well-known from the classical local interactions formulation. In particular, it may change the range of the region of stable crack motion. The conclusions of the analysis are supported by numerical results. Namely, the observed phenomenon is partially clarified by evaluation of the structure profiles on the crack line ahead.

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Localised knife waves in a structured interface

Cited by 70 publications

References 16 publications

Analysis of dynamic damage propagation in discrete beam structures

Analysis of dynamic damage propagation in discrete beam structures

Localization for a line defect in an infinite square lattice

Analysis of dynamic failure of the discrete chain structure with non‐local interactions

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