Heat distribution in a plane with a crack with a variable coefficient of thermal conductivity

Glushko, A. V.; Ryabenko, A. S.; Petrova, Vera; Loginova, E. A.

doi:10.3233/asy-161369

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…Two different criteria for cracking (face conductivity change from finite value to zero) are tested -the emergence of spatially random cracks, and the emergence of cracks at faces with maximal heat flux density. It should be noted, that the problem of thermal conduction in cracked solids has been a subject of analytical studies with associated constraints on domain and crack geometries and spatial distributions: an infinitely large plate with a single crack [21,22], a plate with isotropic distribution of identical cracks [23], cracks with specific geometries [24,25,26], and cracks in domains with specific geometry [27,28,29]. The proposed formulation avoids all constraints and allows for analysis of heterogeneous, anisotropic materials with an arbitrary criterion for the evolution of properties.…”

Section: Introductionmentioning

confidence: 99%

TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

2015

ACM Trans. Math. Softw.

1,299

777

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TetGen is a C++ program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available.This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other softwares are presented. ACM Reference Format:Hang Si. 2015. TetGen, a Delaunay-based quality tetrahedral mesh generator.

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Section: Introductionmentioning

confidence: 99%

TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

2015

ACM Trans. Math. Softw.

1,299

777

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Section: Resultsmentioning

confidence: 91%

“…Different models (or different values of the gradation parameter λ in the rule of mixtures model) provided different profiles of material change, which meant different KIc values near the crack tip. As can be seen from Equation (10), pcr/p0 depended on KIc. Different values of the critical load for different material models (as seen in Figure 3) but the same crack showed a difference in the fracture toughness values determined by these models, which in turn showed different concentrations of ceramic (metal) near the crack tip.…”

Section: Resultsmentioning

confidence: 91%

“…The influence of material constants and the conductivity ratio was investigated to shed light on the material selection with respect to the temperature distribution. It should be noted that in [10], the use of the Robin boundary condition in the stationary problem of heat conduction helped to derive explicit representations of the singular terms of the asymptotic expansion of the heat flow in the vicinity of the crack tips in an FGM plate with a crack.…”

Section: Introductionmentioning

confidence: 99%

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Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures

2023

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This paper is devoted to the problem of the thermal fracture of a functionally graded coating (FGC) on a homogeneous substrate (H), i.e., FGC/H structures. The FGC/H structure was subjected to thermo-mechanical loadings. Systems of interacting cracks were located in the FGC. Typical cracks in such structures include edge cracks, internal cracks, and edge/internal cracks. The material properties and fracture toughness of the FGC were modeled by formulas based on the rule of mixtures. The FGC comprised two constituents, a ceramic on the top and a metal as a homogeneous substrate, with their volume fractions determined by a power law function with the power coefficient λ as the gradation parameter for the FGC. For this study, the method of singular integral equations was used, and the integral equations were solved numerically by the mechanical quadrature method based on the Chebyshev polynomials. Attention was mainly paid to the determination of critical loads and energy release rates for the systems of interacting cracks in the FGCs in order to find ways to increase the fracture resistance of FGC/H structures. As an illustrative example, a system of three edge cracks in the FGC was considered. The crack shielding effect was demonstrated for this system of cracks. Additionally, it was shown that the gradation parameter λ had a great effect on the fracture characteristics. Thus, the proposed model provided a sound basis for the optimization of FGCs in order to improve the fracture resistance of FGC/H structures.

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“…Two different criteria for cracking (face conductivity change from finite value to zero) are tested -the emergence of spatially random cracks, and the emergence of cracks at faces with maximal heat flux density. It should be noted, that the problem of thermal conduction in cracked solids has been a subject of analytical studies with associated constraints on domain and crack geometries and spatial distributions: an infinitely large plate with a single crack [22,23], a plate with isotropic distribution of identical cracks [24], cracks with specific geometries [25][26][27], and cracks in domains with specific geometry [28][29][30]. The proposed formula-tion avoids all constraints and allows for analysis of heterogeneous, anisotropic materials with an arbitrary criterion for the evolution of properties.…”

Section: Introductionmentioning

confidence: 99%