Journal ArticleDOI
Fracture in Functionally Gradient Materials Subjected to the Time‐Dependent Anti‐Plane Shear Load
R. Babaei,S.A. Lukasiewicz +1 more
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In this paper, a finite crack subjected to a general time-dependent antiplane shear load in functionally gradient materials is studied and the elastic properties of the interfacial layer are assumed to vary continuously between those of two dissimilar homogeneous bonding layers.Abstract:
In this article, a finite crack subjected to a general time-dependent anti-plane shear load in functionally gradient materials is studied. The elastic properties of the interfacial layer are assumed to vary continuously between those of two dissimilar homogeneous bonding layers. Laplace and Fourier transforms are applied to reduce this mixed boundary value problem to a system of dual integral equations which in turn will be reduced to a standard Fredholm integral equation of the second kind. The dynamic crack tip stress fields are determined analytically while the dynamic stress intensity factors are evaluated numerically from the standard Fredholm integral equation. The Laplace inversion is performed numerically by using Gauss-quadrature and Jacobi polynomials. In general, the dynamic stress intensity factor is found to be a function of the crack length, location of the crack in interfacial layer, and material properties of the surrounding layers as well as interfacial layer.read more
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On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Anti-Plane Deformation
TL;DR: In this paper, a multi-layered model is developed for a functionally graded interfacial zone between two dissimilar elastic solids based on the fact that an arbitrary curve can be approached by a continuous but piecewise linear curve.
Journal ArticleDOI
Symmetry classification and optimal systems of a non-linear wave equation
TL;DR: In this paper, the complete Lie group classification of a non-linear wave equation is obtained in the case of a hyperelastic homogeneous bar with variable cross-section, and the reduced equations are obtained for the same case.
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Impact behavior of an inclined edge crack in a layered medium with a graded nonhomogeneous interfacial zone: antiplane deformation
TL;DR: In this article, the impact response of an inclined edge crack in a layered medium with a functionally graded interfacial zone is investigated under the state of antiplane deformation, and the peak values of the dynamic stress intensity factors are further obtained versus the crack orientation angle.
Journal ArticleDOI
Effects of graded properties on the impact response of an interface crack in a coating/substrate system subjected to antiplane deformation
Ho‐Joon Lee,Hyung Jip Choi +1 more
TL;DR: In this article, an elastodynamic analysis of an interface crack in coated media with functionally graded properties is performed under the condition of antiplane shear impact, where the nonhomogeneity is represented in terms of power-law variations of shear modulus and mass density.
Journal ArticleDOI
Dynamic interaction of plates in an inhomogeneous transversely isotropic space weakened by a crack
TL;DR: In this paper, the problem of axisymmetric vibration of a flat thin rigid circular plate located inside a vertically exponentially graded, transversely isotropic material of infinite extent is addressed by means of a displacement potential method.