METHOD OF ASYMPTOTIC HOMOGENIZATION OF THERMOVISCOELASTICITY EQUATIONS IN PARAMETRIC SPACE: PART II (PRACTICAL)

The paper develops an analytical-numerical algorithm for estimating the relaxation kernels of a dispersed viscoelastic composite based on the data of experimental measuring the properties of the initial material and the method of asymptotic homogenization applied to the equations of thermoviscoelasticity. Here, a viscoelastic analogy is used that makes it possible to obtain a description of the thermoviscoelastic characteristics of a filled composite material by the equations of the theory of elasticity with rapidly oscillating coefficients of complex value that depend on spatial coordinates and temperature. For the problem on a cell with the conditions of a periodic jump, a special analytical-numerical method has been developed for its solution, based on approximations by a system of functions that exactly satisfy the equations and contact conditions on the interfaces. The conditions of a periodic jump are then solved using the generalized Trefftz method for the equations of the theory of elasticity with complex coefficients. The paper presents examples of using the developed method to determine the time modulus and loss tangent of styrene-butadiene rubber depending on the volume fraction of the filler.