Determining the effective characteristics of inhomogeneous viscoelastic bodies (Q2714030)

The author exposes an approach for obtaining the so-called effective modules of viscoelastic bodies which differs from the previously developed methods in that the equality of energy deformations is assumed. The method presented in the article under review is based on the equivalence assumption for energies of the medium with common deformations and different stresses. This approach leads to an extremal problem for finding effective characteristics and time-effective modules of viscoelastic bodies. The method worked out in the article for finding solutions to the extremal problem makes it possible to obtain the well-known modules and also solutions of other types. In addition, the author discusses some aspects of finding a generalized solution to the viscoelastic linear problem by an iterative method and obtaining integral inequalities for the functionals of potential energies of stresses and deformations calculated on the exact and approximate solutions. A test example is presented.