TY - JOUR
T1 - Compression of a sphere with radially varying elastic moduli
AU - Lutz, Melanie P.
AU - Ferrari, Mauro
N1 - Funding Information:
Acknowledgement-This work was supported by the National Science Foundation Graduate Engineering Education for Women and Minorities Fellowship No. EID-9018414.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1993
Y1 - 1993
N2 - We present the exact solution to the problem of hydrostatic compression of a spherical body whose elastic moduli vary linearly with radius. The solution is developed as a power series in the radius r, and in ε{lunate}, a parameter that quantifies the degree of elastic inhomogeneity of the sphere. In contrast to a homogeneous sphere, the stresses and strains are found to vary with the radius. We also find the effective bulk modulus of the inhomogeneous sphere, and compare it to the predictions of the Voigt, Reuss and Hashin-Shtrikman bounds. This solution should be of use in the analysis of functionally gradient materials.
AB - We present the exact solution to the problem of hydrostatic compression of a spherical body whose elastic moduli vary linearly with radius. The solution is developed as a power series in the radius r, and in ε{lunate}, a parameter that quantifies the degree of elastic inhomogeneity of the sphere. In contrast to a homogeneous sphere, the stresses and strains are found to vary with the radius. We also find the effective bulk modulus of the inhomogeneous sphere, and compare it to the predictions of the Voigt, Reuss and Hashin-Shtrikman bounds. This solution should be of use in the analysis of functionally gradient materials.
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U2 - 10.1016/0961-9526(93)90045-L
DO - 10.1016/0961-9526(93)90045-L
M3 - Article
AN - SCOPUS:0040349423
VL - 3
SP - 873
EP - 884
JO - Composites Engineering
JF - Composites Engineering
SN - 0961-9526
IS - 9
ER -