Computational optimization of characteristics for composites of viscoelastic components

Abstract

The problem of describing of the viscoelastic properties of composite materials that consist of more than one viscoelastic component is studied. It is supposed that the viscoelastic properties of the components are known. The difficulty in the application of the mixture theory arises in the cases when the properties are described by integral operators with different integral kernels. This difficulty is avoided by the approximations of the viscoelastic operators in the stress-strain relations. A method is proposed to obtain appropriate approximations that reduce all the viscoelastic operators to a general kernel using rational approximations of their Laplace transforms. The proposed method allows for the reduction of the approximation error for related operators. Examples are given for the adjustment of viscoelastic functions in the cases of increase and decrease of functions parameter.

Centennial jubilee of Academician Rabotnov and contemporary handling of his fractional operator

“…In conclusion it should be emphasized that nowadays the ideas of Russian Academician Rabotnov are widely used worldwide for solving intricate static and dynamic problems dealing with behaviour of hereditarily elastic bodies (see as examples the papers [1]- [5], [7,8], [15]- [21], etc. ), since Rabotnov's fractional order operator models allow one to decode rather easily different combinations of viscoelastic operators appearing in problems of mechanics of hereditary elastic bodies.…”