Elastic study on singularities interacting with interfaces using alternating technique

Choi, Seung Tae; Earmme, Youn-Young

doi:10.1016/s0020-7683(01)00230-x

Cited by 51 publications

(43 citation statements)

References 15 publications

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“…It is known that there are infinite images for this problem. One possible way to solve this problem has been proposed by Aderogba (2003), which resembles the Schwarz-Neumann's alternating in complex variable theory with analytical continuity across interfaces (see Choi and Earmme 2002).…”

Section: C2 Image Methodsmentioning

confidence: 99%

Numerical studies on crack problems in three-layered elastic media using an image method

Zhang

Jeffrey

2006

Int J Fract

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Two-dimensional crack problems in a three-layered material are analyzed numerically under the conditions of plane strain. An image method is adopted to obtain fundamental solutions for dislocation dipoles in trilayered media. The governing equations for equilibrium cracks can be constructed by distributed dislocation technique and their solutions are sought in terms of the displacement discontinuity method (DDM). Comparisons are made with available analytical or reference solutions for several examples at various contrasts of material constants, and good agreements are found. A crack within a brittle adhesive layer joining two semi-infinite blocks can propagate in a variety of ways. In particular, crack paths in the form of sigmoidal waves within the adhesive layer are revisited to reveal the sensitivities of cracking paths to initial crack locations and directions and residual stresses. In addition, Z-shape and H-shape cracks alternating from interface to interface are re-examined to highlight the transition of failure modes and the role of the interlayer thickness.

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Section: C2 Image Methodsmentioning

confidence: 99%

Numerical studies on crack problems in three-layered elastic media using an image method

Zhang

Jeffrey

2006

Int J Fract

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“…For a bimaterial half-space, see Fig. 1, the solution can be worked out due to recent findings by Choi and Earmme (2002), who studied singularities in anisotropic trimaterials. For the case of unbridged crack, the solution based upon the findings of Choi and Earmme (2002) has been worked out in the accompanying paper by Profant et al (2007).…”

Section: Introductionmentioning

confidence: 99%

“…1, the solution can be worked out due to recent findings by Choi and Earmme (2002), who studied singularities in anisotropic trimaterials. For the case of unbridged crack, the solution based upon the findings of Choi and Earmme (2002) has been worked out in the accompanying paper by Profant et al (2007). First, Profant et al (2007) have tested in details the validity of the semi-analytical solution of Choi and Earmme (2002) using FEM.…”

Section: Introductionmentioning

confidence: 99%

“…For the case of unbridged crack, the solution based upon the findings of Choi and Earmme (2002) has been worked out in the accompanying paper by Profant et al (2007). First, Profant et al (2007) have tested in details the validity of the semi-analytical solution of Choi and Earmme (2002) using FEM. Afterwards, this solution has been applied in modelling of unbridged crack and both the generalized stress intensity factor (GSIF) and the T -stress have been evaluated.…”

Section: Introductionmentioning

confidence: 99%

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Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space

et al. 2007

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The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of "large" slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem ( -integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.

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“…Based on the Fourier-transform technique in association with the stiffness-matrix approach, Choi and Thangjitham [4,5] obtained solutions for multilayered anisotropic elastic media. Choi and Earmme [6,7] employed the alternating technique to obtain solutions for singularity problems in an isotropic and anisotropic trimaterial. Chao and Chen [8] used analytic continuation combined with the alternating technique to solve the thermoelastic problem of an isotropic trimaterial.…”

Section: Introductionmentioning

confidence: 99%

Thermal stresses in a viscoelastic trimaterial with a combination of a point heat source and a point heat sink

et al. 2007

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A general solution for a thermoviscoelastic trimaterial combined with a point heat source and a point heat sink is presented in this work. Based on the method of analytic continuation associated with the alternation technique, the solutions to the heat-conduction and thermoelastic problems for three dissimilar, sandwiched media are derived. A rapidly convergent series solution for both the temperature and stress field, expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin-Maxwell model is applied to simulate the thermoviscoelastic properties, while a thermorheologically simple material is considered. Based on the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real-time solution can then be solved numerically by taking the inverse Laplace transform. A typical example concerning the interfacial stresses generated from a combined arrangement of a heat source and sink are discussed in detail. The corresponding thin-film problem is also discussed.

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Elastic study on singularities interacting with interfaces using alternating technique

Cited by 51 publications

References 15 publications

Numerical studies on crack problems in three-layered elastic media using an image method

Numerical studies on crack problems in three-layered elastic media using an image method

Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space

Thermal stresses in a viscoelastic trimaterial with a combination of a point heat source and a point heat sink

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