Failure of Functionally Graded Materials

Paulino, Gláucio H.; Jin, Z.-H.; Dodds, Robert H.

doi:10.1016/b0-08-043749-4/02101-7

Cited by 75 publications

(40 citation statements)

References 122 publications

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“…In the present analysis, all material parameters in the constitutive equations (31) are considered to be dependent on the (r, z)-coordinates.…”

Section: Local Boundary Integral Equations For 3-d Axisymmetric Problemsmentioning

confidence: 99%

“…Originally these materials have been introduced to benefit from the ideal performance of its constituents, e.g., high heat and corrosion resistance of ceramics on one side, and large mechanical strength and toughness of metals on the other side. A review on various aspects of FGMs can be found in the monograph of Suresh and Mortensen [39] and the review chapter by Paulino et al [31]. Later, the demand for piezoelectric materials with high strength, high toughness, low thermal expansion coefficient and low dielectric constant encourages the study of functionally graded piezoelectric materials [19,42,50].…”

Section: Introductionmentioning

confidence: 99%

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Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG

Sládek

Solek

et al. 2008

Comput Mech

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A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric magneto-electric-elastic solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-D boundary value problem into a 2-D problem in axial cross section. Stationary and transient dynamic problems are considered in this paper. The local weak formulation is employed on circular subdomains where surrounding nodes randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. The accuracy of the present method for computing the stress intensity factors (SIF), electrical displacement intensity factors (EDIF) and magnetic induction intensity factors (MIIF) are discussed by comparison with numerical solutions for homogeneous materials.

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“…In the present analysis, all material parameters in the constitutive equations (31) are considered to be dependent on the (r, z)-coordinates.…”

Section: Local Boundary Integral Equations For 3-d Axisymmetric Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG

Sládek

Solek

et al. 2008

Comput Mech

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“…As a further demonstration of the accuracy of the method, we consider the BVP governed by Equation (29) in a square [1,2] × [1,2] with the material coefficient graded in two directions as…”

Section: Examplementioning

confidence: 99%

“…Owing to the continuous change in the material composition and gradation, the material performance can be tailored and optimized to fulfill particular service requirements. Subjects related to the processing, characterization and potential applications of FGMs can be found in the review articles by Hirai [1] and Paulino et al [2] as well as in the monographs by Suresh and Martensen [3] and Miyamoto et al [4].…”

Section: Introductionmentioning

confidence: 99%

“…(1 − ξ 2 )[18ξ 1 − 9(3ξ 2 1 + ξ2 2 ) + 10]/32, N 7 ,1 = 9(1 − ξ 2 2 )(1 − 3ξ 2 )/32,N 2 ,1 = (1 − ξ 2 )[18ξ 1 + 9(3ξ 2 1 + ξ 2 2 ) − 10]/32, N 8 ,1 = 9(1 − ξ 2 2 )(1 + 3ξ 2 )/32, N 3 ,1 = (1 + ξ 2 )[18ξ 1 + 9(3ξ 2 1 + ξ 2 2 ) − 10]/32, N 9 ,1 = 9(1 + ξ 2 )(−9ξ 2 1 − 2ξ 1 + 3)/32, N 4 ,1 = (1 + ξ 2 )[18ξ 1 − 9(3ξ 2 1 + ξ 2 2 ) + 10]/32, N 10 ,1 = 9(1 + ξ 2 )(9ξ 2 1 − 2ξ 1 − 3)/32, N 5 ,1 = 9(1 − ξ 2 )(9ξ 2 1 − 2ξ 1 − 3)/32, N 11 ,1 = 9(ξ 2 2 − 1)(1 + 3ξ 2 )/32, N 6 ,1 = 9(1 − ξ 2 )(−9ξ 2 1 − 2ξ 1 + 3)/32, N 12 ,1 = 9(ξ 2 2 − 1)(1 − 3ξ 2 )/32. N 1 ,2 = (1 − ξ 1 )[18ξ 2 − 9(ξ 2 1 + 3ξ 2 2 ) + 10]/32, N 7 ,2 = 9(1 + ξ 1 )(9ξ 2 2 − 2ξ 2 − 3)/32, N 2 ,2 = (1 + ξ 1 )[18ξ 2 − 9(ξ 2 1 + 3ξ 2 2 ) + 10]/32, N 8 ,2 = 9(1 + ξ 1 )(−9ξ 2 2 − 2ξ 2 + 3)/32, N 3,2 = (1 + ξ 1 )[18ξ 2 + 9(ξ 2 1 + 3ξ 2 2 ) − 10]/32, N 9 ,2 = 9(1 − ξ 2 1 )(1 + 3ξ 1 )/32, N 4…”

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Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients

Sládek

Zhang

2005

J Eng Math

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A new approach (Domain-Element Local Integro-Differential-Equation Method -DELIDEM) is developed and implemented for the solution of 2-D potential problems in materials with arbitrary continuous variation of the material parameters. The domain is discretized into conforming elements for the polynomial approximation and the local integro-differential equations (LIDE) are considered on subdomains determined by domain elements and collocated at interior nodes. At the boundary nodes, either the prescribed boundary conditions or the LIDE are collocated. The applicability and reliability of the method is tested for several numerical examples.

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Fracture Mechanics

Kolednik

2012

Wiley Encyclopedia of Composites

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Fracture mechanics is a continuum mechanics tool for the description of the behavior of cracks in materials and components. The text concentrates on the fundamental understanding of the various parameters that are applied to characterize the crack driving force and the fracture resistance and outlines their physical meanings and their limitations. Then a few important topics are presented, such as the influence of geometry and size on the crack growth resistance, the conditions for unstable crack growth, and the prediction of the crack path. The final focus is the behavior of cracks in inhomogeneous materials, such as composites. Especially interesting here is the understanding, how spatial material property variations influence the crack driving force, since this opens the door for materials and components design, that is, to optimize materials by intentional variations of the material properties so that the fracture resistance increases.

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Failure of Functionally Graded Materials

Cited by 75 publications

References 122 publications

Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG

Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG

Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients

Fracture Mechanics

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