The Eshelby-Mori-Tanaka method is extended into the Laplace domain to examine the linearly viscoelastic behavior in two types of composite materials: a transversely isotropic one with aligned spheroidal inclusions and an isotropic one with randomly oriented inclusions. Though approximate in nature, the method offers both simplicity and versatility, with explicit results for the sphere, disk, and fiber reinforcements in the transformed domain. The results coincide with some exact solutions for the composite sphere and cylinder assemblage models and, with spherical voids or rigid inclusions, the effective shear property also lies between Christensen’s bounds. Consistent with the known elastic behavior, the inverted creep compliances in the time domain indicate that, along the axial direction, aligned needles or fibers provide the most effective improvement for the creep resistance of the aligned composite, but that in the transverse plane the disk reinforcement is far superior. For the isotropic composite disks are always the most effective shape, whereas spheres are the poorest. Comparison with the experimental data for the axial creep strains of a glass/ED-6 resin composite containing 54 percent of aligned fibers indicates that the theory is remarkably accurate in this case.

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