Dynamic fracture of a dissimilar chain

Gorbushin, Nikolai; Mishuris, Gennady

doi:10.1098/rsta.2019.0103

Cited by 12 publications

(4 citation statements)

References 38 publications

(75 reference statements)

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“…The solutions to the Wiener-Hopf problems encountered in [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][18][19][20][21][22] allow one to determine the profile of the medium for any considered speed. However, as already well established in the literature, this does not necessarily mean that such a profile can physically exist [29] or is observable in simulations.…”

Section: Introductionmentioning

confidence: 99%

“…Owing to recent trends in advanced materials, the approach has subsequently initiated a range of works investigating how different physics and mechanical elements influence steady failure regimes for the purpose of designing new elastic media. We mention the investigation of anisotropic [6,7] or dissimilar elastic properties in promoting steady failure processes [8][9][10], lattices with embedded high-contrast interfaces undergoing separation due to the action of highly localized waves [11] and the failure of materials with non-local elastic interactions [12].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic fracture regimes for initially prestressed elastic chains

Movchan

Livasov

Mishuris

2022

Phil. Trans. R. Soc. A.

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We study the propagation of a bridge crack in an anisotropic multi-scale system involving two discrete elastic chains that are interconnected by links and possess periodically distributed inertia. The bridge crack is represented by the destruction of every other link between the two elastic chains, and this occurs with a uniform speed. This process is assumed to be sustained by energy provided to the system through its initial configuration, corresponding to the alternating application of compression and tension to neighbouring links. The solution, based on the Wiener–Hopf technique and presented in Ayzenberg-Stepanenko et a l . (Ayzenberg-Stepanenko et al. 2014 Proc. R. Soc. A 470 , 20140121 ( doi:10.1098/rspa.2014.0121 )) is used to compute the profile of the medium undergoing failure. We investigate when this solution, representing the steady failure process, is physically acceptable. It is shown that the analytical solution is not always physically applicable and can be used to determine the onset of non-steady failure regimes. These arise from the presence of critical deformations in the wake of the crack front at the sites of the intact links. Additionally, we demonstrate that the structural integrity of the discrete elastic chains can significantly alter the range of speeds for which the bridge crack can propagate steadily. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic fracture regimes for initially prestressed elastic chains

Movchan

Livasov

Mishuris

2022

Phil. Trans. R. Soc. A.

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“…For a homogeneous square lattice, a remote force is applied to provide sufficient energy for crack propagation and a mass–spring chain with two parallel cracks is considered [38]. Under an externally moving load, the crack propagations in a double chain of two identical [39] and different [40] materials are investigated.…”

Section: Introductionsmentioning

confidence: 99%

Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

et al. 2021

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Previous investigations on wave scattering and crack propagation in the discrete periodic structure are concentrated on the conditional mass–spring model, in which the internal mass is not included. In this work, elastic wave metamaterials with local resonators are studied to show the scattering of elastic waves by a semi-infinite crack and the arrest behaviour. The influences of internal mass–spring structure are analysed and the discrete Wiener–Hopf method is used to obtain the displacement solution. Numerical calculations are performed to show that the dynamic negative effective mass and band gaps can be observed owing to the local resonance of the internal mass. Therefore, the scattering of an elastic wave with a specific frequency by a semi-infinite crack can be avoided by tuning the structural parameters. Moreover, the energy release ratio which characterizes the splitting resistance is presented and the meta-arrest performance is found. It is expected that this study will increase understanding of how to control the scattering characteristics of elastic waves by a semi-infinite crack in locally resonant metamaterials and also help to improve their fracture resistance.

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“…Two-dimensional models have been also used to address effects encountered in dynamic crack propagation problems. For example, in work [3] the crack velocity oscillations are explained using a lattice model, while in [4] a bi-material model is studied in order to investigate various regimes of the interface crack propagation. The chain models have been also used to address martensitic phase transformations as seen from work [5].…”

Section: Introductionmentioning

confidence: 99%

Dynamic fracture effects observed in a one-dimensional discrete mechanical system

et al. 2020

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Dynamic fracture of a one-dimensional chain of identical linear oscillators (masses connected by springs) is considered in the work. The system is supposed to consist of arbitrary but finite number of links and the first mass is supposed to be fixed. Two loading conditions are discussed: free oscillations of an initially statically prestressed chain and loading the chain with a short deformation pulse. Both problems are solved analytically for an arbitrary number of links. The obtained solutions are investigated and a dynamic fracture effect related to an explicitly discrete structure of the system is revealed: a deformation wave travelling through the chain is distorted and some links may be subjected to critical deformation. The obtained solutions for the chain are compared to the solutions of analogous problems stated for an elastic rod – a continuum counterpart of the considered discrete system. It is shown that the discussed fracture effect cannot be found in a continuous system.

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Dynamic fracture of a dissimilar chain

Cited by 12 publications

References 38 publications

Dynamic fracture regimes for initially prestressed elastic chains

Dynamic fracture regimes for initially prestressed elastic chains

Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

Dynamic fracture effects observed in a one-dimensional discrete mechanical system

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