# Numerical Modeling of Plasticity in Metal Matrix Fiber Composites
## 1 Introduction
[30] proposed a design for a spiral fiber-reinforced metal matrix composite, aiming to enhance its mechanical strength with an analytical model to predict torsional behavior and torque-twist requirements during fabrication. Also, in reference [16], an analytical method is proposed to study the elastic-plastic behavior of short-fiber-reinforced metal matrix composites under tensile loading. Using a micromechanical approach with an axisymmetric unit cell, the elastic solution is derived first. The matrix undergoes plastic deformation while the fiber remains elastic under normal loading. Successive elastic solutions determine the plastic strain in the matrix. The elastic-plastic stress transfer behavior is analyzed and compared with finite element analysis results, demonstrating the method's capability to predict plastic strain and stress terms in the matrix. [PERSON] et al. [31] developed a numerical procedure for predicting the parameters of a yield criterion for metal matrix composites based on the known mechanical properties of the matrix and fibers. [PERSON] and [PERSON] [32] proposed a shear-lag and deformation-theory-based model for a metal matrix composite reinforced by continuous unidirectional fibers, accounting for fiber and matrix cracking, matrix plasticity, and fiber-matrix interfacial sliding. [PERSON] et al. [33] conducted a micromechanical analysis of a SiC/Ti6 Al4V composite under complex stress states, highlighting mechanical property degradation under complex conditions. An analytical method is proposed in [5] to study how short-fiber-reinforced metal matrix composites behave elastically and plastically under tension. Using a micromechanical approach with an axisymmetric unit cell, the study derives governing equations and boundary conditions and calculates an elastic solution using shear lag methods. The model considers plastic deformation in the matrix due to normal loading while the fiber remains elastic. The analysis examines how this plastic deformation affects stress transfer within the composite. When carrying out a structural analysis of structural elements, the real properties of composite materials are replaced by the properties of equivalent homogeneous materials. The components of metal matrix composites have significantly different mechanical properties. The elastic properties of fibers can be anisotropic, but matrices are predominantly isotropic. The conditions for the onset of plasticity differ both quantitatively and qualitatively. Beyond elasticity, the stress-strain diagrams of the components obey different hardening laws. All of these differences significantly complicate the construction of plastic deformation models for equivalent homogeneous materials. A promising direction in the field of homogenization of composite materials is to perform a micromechanical numerical analysis of representative volumes of a composite based on the results of experimental studies of the properties of its components. This approach is used in this work to create physical relationships for the elastic-plastic deformation of boron-aluminum fiber composites. The advantage of conducting a numerical prediction of the plastic properties of composites is the possibility of analyzing a large number of variants of structure and properties of components. The approach proposed in this paper requires a minimal amount of experimental data and makes it possible to determine the parameters of the yield criterion and the characteristics of deformation diagrams for different types of loading. The cost-effectiveness of this approach makes it possible to use it for the optimal design of metal matrix composites.