# Numerical Modeling of Plasticity in Metal Matrix Fiber Composites
## 1 Introduction  
Composites with a light alloy metal matrix have remarkable strength, low density, and good corrosion resistance [1; 2]. Due to the unique combinations of these properties, metal matrix composites (MMCs) are increasingly being used for various applications in the automotive and defense industries. Due to their high specific strength and stiffness, boron-aluminum composites are used in the most critical structural elements of aerospace equipment. In many applications, the operating conditions allow the appearance of plastic deformations. In addition, studies of the plasticity of composites are necessary for calculations of limit states of structural elements. This is the reason for the considerable interest in the development of theories of plastic deformation of composite materials. A large number of publications devoted to the problems of the application of MMCs with an aluminum matrix in the aviation industry are reviewed [3]. Metal matrix particulate composites are typically characterized by a metal matrix embedded with a distribution of particles, such as graphite, ceramic whiskers, intermetallics, or second-phase particles. These particles generally range in size from 10 \(\upmu\)m to 200 \(\upmu\)m and are spaced at similar intervals [4]. Understanding the deformation plasticity behavior of MMCs is essential for optimizing their design and manufacturing processes to meet specific application requirements. The transfer of stress from the matrix to the fiber is recognized as the primary mechanism that influences the deformation and fracture behavior of these MMCs [5]. The fracture strengths of various MMCs, prepared through different manufacturing techniques such as liquid metallurgy, powder metallurgy, and precipitation, have been extensively analyzed [4]. These studies have revealed distinct trends in the strength versusvolume fraction relationship, shedding light on the underlying fracture mechanisms and microstructural influences. Furthermore, investigations into the initial yield and collapse behavior of fiber-reinforced MMCs have provided valuable insights into the complex interplay between matrix plasticity, the fiber-matrix interface, and residual stresses [6]. The findings from this study indicate that the loads required to induce failure in MMCs are significantly higher than those needed to initiate initial yielding, especially when accounting for residual stresses generated during manufacturing. [PERSON] et al. [7] presented a framework for creating 3D statistically similar representative volume elements (SSRVEs) to assess the mechanical properties of AA7075 alloy composites reinforced with carbon fibers at various volume fractions. A numerical analysis showed that the elastic modulus increased with the fiber content, consistent with the rule of mixtures. However, significant differences were found between the simulated yield stresses and those predicted using the shear-lag model. Another study [8] used the Discrete Element Model (DEM) to simulate fracture toughness tests on a dual material with a structured metal matrix composite (MMC) inside martensitic steel. Various MMC micro-lattices (gyroid, octet-truss, and FBCCZ) were analyzed for their energy absorption and crack resistance. Experimental tests validated the DEM, showing less than 10% error in stress intensity factors. The FBCCZ structure was found to absorb the most energy during crack propagation. Thermal cycling effects on the mechanical properties of MMCs have also been studied, highlighting the role of material ratcheting in determining the inelastic deformation under cyclic loading conditions [9]. Additionally, numerical simulations and experimental observations have elucidated the effects of reinforcement orientation on the tensile response of particle and whisker-reinforced MMCs, emphasizing the importance of microstructural alignment and bonding characteristics [10].