A model of constitutive relations for elastic-plastic composites with cubic symmetry of properties is proposed. This class includes a significant number of composite materials: dispersed-reinforced composites, which have an ordered rather than a chaotic reinforcement system, as well as some types of spatially reinforced composites. To build a model of nonlinear constitutive relations, a tensor-symmetry approach was used, based on the spectral expansions of stress and strain tensors, as well as the spectral representation of nonlinear tensor relations between these tensors. The deformation theory of plasticity is considered, for which the tensor-symmetric approach is used, and specific models are proposed for plasticity functions that depend on the spectral invariants of the strain tensor. To determine the model constants, a method is proposed in which these constants are calculated based on the approximation of deformation curves obtained by direct numerical solution of three-dimensional problems on the periodicity cell of elastic-plastic composites. These problems arise in the method of asymptotic averaging of periodic media. To solve problems on a periodicity cell, a finite element method and special software was used that implements solutions to problems on periodicity cells, developed at the Scientific and Educational Center for Supercomputer Engineering Modeling and Development of Software Packages of Bauman Moscow State Technical University. An example of calculating the constants of a composite model using the proposed method for a dispersed-reinforced composite based on a metal matrix is considered. Also, the verification of the proposed model for various ways of multiaxial loading of the composite was carried out with direct numerical simulation. It is shown that the proposed microstructural model and the algorithm for determining its constants provide a sufficiently high accuracy in predicting the elastic-plastic deformation of the composite.
Димитриенко Ю.И., Сборщиков С.В., Димитриенко А.Ю., Юрин Ю.В. Микроструктурная модель деформационной теории пластичности квази-изотропных композиционных материалов. Математическое моделирование и численные методы, 2021, № 4, с. 17–44.