In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eigenstrain do not coincide with those for a spherical inclusion (Eshelby’s solution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.
In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.
This study considers the scattering of compressional and shear waves in SiC-particle-reinforced Al composite with interfacial layers. We assume same-size inclusions and same-thickness layers with nonhomogeneous elastic properties. The effective complex wave numbers follow from the coherent wave equations which depend only upon the scattering amplitude of the single scattering problem. Numerical values of scattering cross-sections, and phase velocities and attenuations of coherent plane waves are obtained for a moderately wide range of frequencies, and the results are graphed to display the effects of concentration of scatterers and interface properties.
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