Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials—Part I: Crack Perpendicular to the Material Gradation | Zendy

Gláucio H. Paulino | Zendy; Albert Fannjiang | Zendy; Youn-Sha Chan | Zendy

Open Access

Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials—Part I: Crack Perpendicular to the Material Gradation

Author(s) -

Gláucio H. Paulino,

Albert Fannjiang,

Youn-Sha Chan

Publication year - 2003

Publication title -

journal of applied mechanics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 97

eISSN - 1528-9036

pISSN - 0021-8936

DOI - 10.1115/1.1532321

Subject(s) - mathematical analysis , stress intensity factor , chebyshev polynomials , elasticity (physics) , fracture mechanics , materials science , mathematics , boundary value problem , length scale , geometry , mechanics , physics , composite material

ing partial differential equations PDEs are derived, and the Fourier transform method is introduced and applied to convert the governing PDE into an ordinary differential equation ODE .A fterward, the crack boundary value problem is described, and a specific complete set of boundary conditions is given. The governing hypersingular integrodifferential equation is derived and discretized using the collocation method. Next, various relevant aspects of the numerical discretization are described in detail. Subsequently, numerical results are given, conclusions are inferred, and potential extensions of this work are discussed. One appendix, providing the hierarchy of the PDEs and the corresponding integral equations, supplements the paper.

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