Modification of the Time-Effective Moduli of Viscoelastic Bodies

The problem on constructing new time-effective characteristics of a linear viscoelastic body is considered. The initial medium is modeled as a viscoelastic composite. One its part has properties determined by time-effective moduli of the Lagrangian type, but the other part has properties determined by moduli of the Castigliano type. This model makes it possible to employ the methods of mechanics of composite materials, for example, to formulate the effective Voigt and Reuss moduli and to construct iterative transformations narrowing the Voigt and Reuss fork. These transformations are constructed in such a way that, at each iteration, the inequalities following from the minimum total potential energy principle and the theorem of complementary work are satisfied for the effective moduli. It is shown that, at each moment of time t, the sequences of iteratively transformed Voigt and Reuss moduli converge to the same limit, equal to the geometric mean of their initial values. By the example of the problem on bending of a viscoelastic plate, the approximate solutions obtained on the basis of the new time-effective characteristics found, are compared with an analytical solution. Their good agreement points to a high accuracy of the approximate solutions.