In this work, a model for predicting effective elastic characteristics (components of the tensor of effective elastic moduli) of foam polymer materials is constructed with consideration of the volume content and shape of unidirectionally oriented non-isometric pores. The model is based on a generalized singular approximation of random field theory. To calculate the effective elastic characteristics of the foam polymers, an iterative method of self-consistency was used, and the elastic modulus tensor values obtained at the previous iteration step were taken as parameters of a homogeneous comparison body. The elastic parameters in the Voight approximation were taken as the initial values of the parameters of the comparison body. This approximation does not require the inversion of the singular matrix of the elastic moduli tensor for such a component of foam polymers as pores filled with air. The usage of this approach allowed providing calculations of the effective elastic moduli of porous materials.

Based on the developed model, a numerical simulation of the effective elastic characteristics of the foamed epoxides and elastic anisotropy parameters in the directions of the axes of a rectangular coordinate system was carried out in this work. An epoxy binder ED-20 was considered as a matrix. It was reckoned that the pores have the form of ellipsoids of revolution oriented by their main semiaxis along the vertical axis. Simulation considered a change in the volumetric content of pores and a variation in their aspect ratio. Numerical calculations showed that with an increase in porosity, the values of the effective elastic moduli decrease without becoming negative, i.e. foams maintain their integrity at a high pore concentration. In addition, an increase in both the volumetric content of pores and deviations from unity of the value of their aspect ratio leads to increased anisotropy in the directions of all axes of the rectangular coordinate system (especially along the direction of the vertical axis).

Построена модель прогнозирования эффективных упругих характеристик пенополимерных материалов с учетом объемного содержания и формы однонаправленно ориентированных неизометричных пор. Модель опирается на обобщенное сингулярное приближение теории случайных полей (в варианте метода самосогласования). Для пеноэпоксидов на основе смолы ЭД-20 проведены численные модельные расчеты значений компонент тензора эффективных модулей упругости и параметров упругой анизотропии в направлениях осей прямоугольной системы координат при изменении их пористости и вариации аспектного отношения эллипсоидальных пор.