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The axisymmetric crack problem in a nonhomogeneous medium. (English) Zbl 0774.73053
Summary: The axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of \(z\) approximated by \(\mu=\mu_ 0 e^{\alpha z}\). This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formulated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter \(\alpha\) for various loading conditions. Also given are some sample results showing the crack opening displacements.

MSC:
74R99 Fracture and damage
74E05 Inhomogeneity in solid mechanics
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