Thermoelastic Green’s Functions for Plane Problems in General Anisotropy

Sturla, Francisco; Barber, J. R.

doi:10.1115/1.3173643

Cited by 10 publications

(5 citation statements)

References 2 publications

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“…This concept of heat vortex first appeared in literature several decades ago and has been studied by many authors, such as Sturla and Barber (1988). But most of the functions of displacement and stress fields due to the heat vortex cannot be directly extended to the dissimilar anisotropic media.…”

Section: Greenõs Functions For Thermo-elastic Dislocations In Anisotrmentioning

confidence: 98%

A solution to the thermo-elastic interface crack branching in dissimilar anisotropic bi-material media

Kardomateas

2006

International Journal of Solids and Structures

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An interface crack or delamination may often branch out of the interface in a laminated composite due to thermal stresses developing around the delamination/crack tip when the media is exposed to heat flow induced by environmental events such as a sudden short-duration fire. In this paper, the thermo-elastic problem of interface crack branching in dissimilar anisotropic bi-media is studied by using the theory of StrohÕs dislocation formalism, extended to thermo-elasticity in matrix notation. Based on the complex variable method and the analytical continuation principle, the thermo-elastic interface crack/delamination problem is examined and a general solution in compact form is derived for dissimilar anisotropic bi-media. A set of GreenÕs functions is proposed for the dislocations (conventional dislocation and thermal dislocation/heat vortex) in anisotropic bi-media. These functions may be more suitable than those which have appeared in the literature on addressing thermo-elastic interface crack branching in dissimilar anisotropic bi-materials. Using the contour integral method, a closed form solution to the interaction between the dislocations and the interface crack is obtained. Within the scope of linear fracture mechanics, the thermo-elastic problem of interface crack branching is then solved by modelling the branched portion as a continuous distribution of dislocations. The influence of thermal loading and thermal properties on the branching behavior is examined, and criteria for predicting interface crack branching are suggested, based on the extensive numerical results from the study of various cases.

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Section: Greenõs Functions For Thermo-elastic Dislocations In Anisotrmentioning

confidence: 98%

A solution to the thermo-elastic interface crack branching in dissimilar anisotropic bi-material media

Kardomateas

2006

International Journal of Solids and Structures

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“…Multiplying both sides by where A and B are the following matrices, identical to those introduced in Piccolroaz & Mishuris [20] and Morini et al [21] for the elastic problem without thermodiffusion: 16) where the matrix M is given by…”

Section: (B) Explicit Integral Identitiesmentioning

confidence: 99%

“…In all these approaches, the displacements and stress fields are defined by integral relations involving the Green's functions, which need to be derived analytically in explicit form [14] or computed numerically [15]. Although Green's functions have been derived for several crack problems in linear thermoelastic and thermodiffusive elastic materials [16][17][18][19], their utilization for calculating physical displacements and stress fields on the crack faces requires challenging numerical estimation of integrals whose convergence should be assessed carefully. Moreover, the approach based on the Green's function method works when the tractions and the thermal and diffusive stresses acting on the discontinuity surface are symmetric, but not in the case where asymmetric mechanical and thermodiffusive loading distributions are applied on the crack faces.…”

Section: Introductionmentioning

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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“…The problem will be formulated in terms of the thermoelastic Green's function derived in a previous paper (Sturla and Barber, 1988), corresponding to a temperature discontinuity of magnitude T 0 on the half-line x 2 = 0, x x > 0. The appropriate heat flux and tractions on the surface x 2 = 0 are…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…K t j is the thermal conductivity tensor and G, is a function of the thermoelastic constants for the material, defined by equation (42) of Sturla and Barber (1988).…”

mentioning

confidence: 99%