A numerical-analytical model of elasto-plastic deformation of matrix composites

Based on the first-order Mori–Tanaka secant model, a numerical-analytical model of elasto-plastic deformation of matrix composites is developed. The calculation results of the analytical model are "fitted" to the results of numerical simulation. The fitting parameter of the model is the ratio of the constrained equivalent strain of the matrix in the numerical model to the constrained equivalent strain of the matrix in the Mori–Tanaka model. Identification of the fitting parameter is performed using a reference stress–strain curve calculated numerically for a basic composite composition. For an arbitrary composition composite, a linear dependence of the fitting parameter on the inclusion volume fraction is used. A good agreement was obtained between the results of the calculation by the numerical-analytical model and the numerical data for isotropic and transversely isotropic composites with different contents, morphology, and contrast properties of the phases.