TY - JOUR

T1 - Successive iteration method applied to composites containing sliding inclusions

T2 - effective modulus and anelasticity

AU - Shibata, Shoichi

AU - Jasiuk, Iwona M

AU - Mori, T.

AU - Mura, T.

PY - 1990/11/19

Y1 - 1990/11/19

N2 - The effective shear modulus and Poisson's ratio of a body containing spherical sliding inclusions are calculated. First, the amount of sliding on the surface of a single spherical sliding inclusion is determined so that the tangential traction of the stresses due to the sliding, the Somigliana dislocations, cancels that of the external stresses on the surface of the inclusion. Next, the influence of other inclusions is accounted for by using a successive iteration method based on the average field theory. The successive iteration converges into closed forms, leading to analytical forms of the effective elastic constants. It is shown that the sliding occurs in a first order kinetics, the relaxation time of which is proportional to the radius of the inclusions with a constant depending on the volume fraction of the inclusions. The two-dimensional problem of a body containing aligned cylindrical fibers is also solved.

AB - The effective shear modulus and Poisson's ratio of a body containing spherical sliding inclusions are calculated. First, the amount of sliding on the surface of a single spherical sliding inclusion is determined so that the tangential traction of the stresses due to the sliding, the Somigliana dislocations, cancels that of the external stresses on the surface of the inclusion. Next, the influence of other inclusions is accounted for by using a successive iteration method based on the average field theory. The successive iteration converges into closed forms, leading to analytical forms of the effective elastic constants. It is shown that the sliding occurs in a first order kinetics, the relaxation time of which is proportional to the radius of the inclusions with a constant depending on the volume fraction of the inclusions. The two-dimensional problem of a body containing aligned cylindrical fibers is also solved.

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U2 - 10.1016/0167-6636(90)90005-Z

DO - 10.1016/0167-6636(90)90005-Z

M3 - Article

AN - SCOPUS:0025517174

VL - 9

SP - 229

EP - 243

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

IS - 3

ER -