Determination and analysis of the effective relaxation properties of a composite with viscoelastic components. (English. Ukrainian original) Zbl 1272.74537
Int. Appl. Mech. 46, No. 1, 18-27 (2010); translation from Prik. Mekh., Kiev 46, No. 1, 22-33 (2010).
Summary: The relaxation properties of a two-component material are determined depending on time, volume fraction, and type of reinforcement, and the relationship among them. The type of reinforcement is determined by the aspect ratio of the ellipsoid of revolution that models the inclusion. The effective moduli of the composite are determined from the relaxation properties of the components. It is assumed that the composite components are made of isotropic viscoelastic materials with volume expansion and shear characteristics described by two Rabotnov’s fractional-exponential functions with different orders of fractionality. To obtain the solution in the time domain, its fractional rational representation in the frequency domain is used. Optimizing the parameters of this representation and transforming the parameters of the solution to the time domain make it possible to obtain solutions in compact form in terms of relaxation kernels.
MSC:
| 74Q15 | Effective constitutive equations in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74D05 | Linear constitutive equations for materials with memory |
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