Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks

Radi, Enrico; Movchan, A. B.; Movchan, N. V.

doi:10.1177/1081286512462299

Cited by 14 publications

(53 citation statements)

References 28 publications

(155 reference statements)

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“…Different instances of bicoupled periodic structures are investigated in [28]. In the case examined M int is the transfer matrix of an intact beam of period l: 11) where β = (ρAω 2 /EJ) 1/4 , ω is the radian frequency, whereas A and J are respectively the area and the second moment of inertia of the beam cross section. Furthermore, the matrix I appearing in equation (3.10) represents the 4 × 4 identity matrix, whereas K is the 'stiffness matrix' given by…”

Section: (B) Dispersion In the Asymptotic Reduced Modelmentioning

confidence: 99%

“…Boundary layers near the vertices of the cracks are analysed in problems involving unbounded domains, and full analytical solutions are derived by solving an equation of the Wiener-Hopf type. An alternative powerful approach used in [11] uses Stroh formalism and analysis of solutions to corresponding Riemann-Hilbert problems. Waves in non-periodic composites have received substantial attention in both mechanics and geophysics applications.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic response and localization in strongly damaged waveguides

2014

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In this paper, we investigate the formation of band-gaps and localization phenomena in an elastic strip nearly disintegrated by an array of transverse cracks. We analyse the eigenfrequencies of finite, strongly damaged, elongated solids with reference to the propagation bands of an infinite strip with a periodic damage. Subsequently, we determine analytically the band-gaps of the infinite strip by using a lower-dimensional model, represented by a periodically damaged beam in which the small ligaments between cracks are modelled as 'elastic junctions'. The effective rotational and translational stiffnesses of the elastic junctions are obtained from an ad hoc asymptotic analysis. We show that, for a finite frequency range, the dispersion curves for the reduced beam model agree with the dispersion data determined numerically for the two-dimensional elastic strip. Exponential localization, boundary layers and standing waves in strongly damaged systems are discussed in detail.

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Section: (B) Dispersion In the Asymptotic Reduced Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic response and localization in strongly damaged waveguides

2014

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“…As the method used in Morini et al [17] was for general matrices H and W, it is immediately clear that these results also hold for piezoelectric materials.…”

Section: Weight Functions For Piezoelectric Bimaterials: Definitionmentioning

confidence: 67%

“…In Section 2.2, the definition of weight functions proposed in Piccolroaz et al [23] and Morini et al [17] is extended to the case of interfacial cracks between dissimilar piezoelectric materials. Finally, in Section 2.3, the expression for the Betti's formula generalized to piezoelectric media by Hadjesfandiari [24] is reported.…”

Section: Problem Formulation and Preliminary Resultsmentioning

confidence: 99%

Interfacial cracks in piezoelectric bimaterials: an approach based on weight functions and boundary integral equations

Pryce¹,

Andreeva²,

Zagnetko³

2017

Meccanica

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The focus of this paper is on the analysis of a semi-infinite crack lying along a perfect interface in a piezoelectric bimaterial with arbitrary loading on the crack faces. Making use of the extended Stroh formalism for piezoelectric materials combined with Riemann-Hilbert formulation, general expressions are obtained for both symmetric and skew-symmetric weight functions associate with plane crack problems at the interface between dissimilar anisotropic piezoelectric media. The effect of the coupled electrical fields is incorporated in the derived original expressions for the weight function matrices. These matrices are used together with Betti's reciprocity identity in order to obtain singular integral equations relating the extended displacement and traction fields to the loading acting on the crack faces. In order to study the variation of the piezoelectric effect, two different poling directions are considered. Examples are shown for both poling directions with a number of mechanical and electrical loadings applied to the crack faces.

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“…22 (ξ , 0 + ), j = 1, 2 are Fourier transform of the traction at the interface (see e.g., Morini et al [37]) and…”

Section: (A) Elastic Potentialsmentioning

confidence: 99%

Boundary integral formulation for interfacial cracks in thermodiffusive bimaterials

Morini,

Piccolroaz

2015

Proc. R. Soc. A.

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An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight function matrices are used together with a generalized Betti's reciprocity theorem in order to derive a system of integral equations that relate the applied loading, the temperature and mass concentration fields, the heat and mass fluxes on the fracture surfaces and the resulting crack opening. The obtained integral identities can have many relevant applications, such as for the modelling of crack and damage processes at the interface between different components in electrochemical energy devices characterized by multi-layered structures (solid oxide fuel cells and lithium ions batteries).

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Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks

Cited by 14 publications

References 28 publications

Dynamic response and localization in strongly damaged waveguides

Dynamic response and localization in strongly damaged waveguides

Interfacial cracks in piezoelectric bimaterials: an approach based on weight functions and boundary integral equations

Boundary integral formulation for interfacial cracks in thermodiffusive bimaterials

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