UDC 620.22-419, 621-039-419 © B. Dandurand, I. Viktorova, S. Alexeeva, S. Goodson NONLINEAR MODELING AND OPTIMIZATION OF PARAMETERS FOR VISCOELASTIC COMPOSITES AND NANOCOMPOSITES The Volterra theory of heredity finds its applications in various branches of mathematical physics. <...> The presented approach is based on the nonlinear hereditary type relationship between stresses, strains and time in viscoelastic solids – materials with memory. <...> It can be modeled by the second type of Volterra's equation (known as Rabotnov's model) (1) It has been shown that such an equation can describe rather successfully the wide range of materials tested including polymers, composites, and metals. <...> The higher the rate of loading, the closer the stress-strain diagram to the model . <...> This model is an upper bound for the whole region of possible deformation of the material under consideration. <...> The choice of kernel for the integral operator in equation (1) is the subject of several objective considerations. <...> Physical and mathematical adequacy are the dominant ones. <...> The exponential of arbitrary order Rabotnov's function presents the most general type to satisfy the above listed constraining considerations. <...> This paper presents two approaches for obtaining the optimal parameter estimates in equation (1) with kernel taken as the exponential of arbitrary order function. <...> Lastly, the models resulting from the optimal parameter estimates are validated against experimental data from creep tests on polymer based composites and nanocomposites. <...> Keywords: viscoelastic solids, hereditary type relationships, materials with memory, integral operator, nonlinear optimization, Laplace-Carson transform. <...> The hereditary mechanics accounting for the time dependent stress-strain relationship (also known as delay or memory effect) had started from Boltzmann’s work in the middle of 19th century and later was developed in fundamental research on integral equations by Volter ra [1]. <...> The appl ication of this mathematical theory to the modeling of deformation proces ses in the vi scoela s t ic sol ids that are characterized by the memory of the history of loading had shown the tremendous potential for var ious engineering applications [2] involving ranging loading conditions l ike short/longterm creep, quasistatic loading, cyclic deformation for wide range of polymer based composites and as the recent studies show for the polymer based nanocomposites [3 <...>