The problem of multilevel model development for calculating of an elastic property of polymer composite materials with a complex reinforcement structure at high temperatures is considered. It is assumed that thermal destruction processes take place in the matrix and fibers at high temperatures. In order to take into account the change in the elastic properties of the composite depending on the temperature and heating time, a 3-level structural model of the composite is proposed. At the lower level mono-fibers and a matrix consisting of 4 phases, the ratio between which changes when heated are considered. At this level, the analytical relations proposed earlier in the works of Yu.I. Dimitrienko. At the next level of the model, a unidirectional composite is considered, consisting of bundles of monofilaments and a matrix. To calculate elastic properties at this level, the method of asymptotic averaging is used, and a finite element algorithm for solving local problems of the theory of thermoelasticity arising in this method. At the 3rd structural level of the model, composites with complex reinforcement structures, in particular, fabric composites, are considered. The method of asymptotic averaging is also used to calculate the elastic properties of the composite at this level. For the numerical calculation of the elastic characteristics of polymer composites at high temperatures, specialized software has been developed that operates under the control of the SMCM software package created at the Scientific and Educational Center for Supercomputer Engineering Modeling and Development of Software Systems of the Bauman Moscow State Technical University. The article provides examples of the application of the developed multilevel model and software for textile composites based on an epoxy matrix and glass fibers. The values of all components of the tensor of the elastic moduli of the composite are calculated, which vary depending on the heating program of the composite. The microstress fields in the composite are obtained. A comparison is made of the fields of microstresses and effective elastic constants at normal temperatures, with similar values obtained using the ANSYS software package, which has been modified to enable the calculation of effective elastic constants in accordance with the proposed model. A very good agreement was obtained between the calculation results, both of the effective constants and of the microstresses fields, which allows us to speak of the high accuracy of the developed software.
Димитриенко Ю.И., Юрин Ю.В., Сборщиков С.В., Богданов И.О., Яхновский А.Д., Баймурзин Р.Р. Конечно-элементное моделирование упругих свойств тканевых полимерных композитов при высоких температурах. Математическое моделирование и численные методы. 2020. № 1. с. 3–27