# Micromechanical Analysis in Applications of Active Mono-Slip and Continuum Dislocations in the MDCM
## 1 Introduction  
Composite materials are used as structural elements in a wide variety of applications, including space shuttles, marine vehicles, automobiles, and construction sectors. These materials are widely applied for their remarkable in-plane stiffness, bending stiffness, ultimate strength, light weight, and good thermal expansion coefficient during deformation [1; 2; 3; 4]. In a matrix-dominated composite structure (MDCS), permanent deformation can be expressed by the limit of dislocation nucleation and the dislocation energy [5]. The nucleation and energy of the dislocation create internal structural irregularities. These internal irregularities in a matrix-dominated composite (MDC) structural arrangement have been analyzed in the context of intermittent crystallographic dislocations. This means that the created nucleation of dislocations can be grouped to reduce the energy dissipation of the crystals. The new initiation of dislocation is principally the result of the dissipation of crystal energy. Therefore, the initiation of dislocation in the MCDS activates the dislocation energy. Hence, the dislocation energy impedes plastic flow through the dissipation of crystal energy. Thus, all microstructural analyses related to permanent deformation should follow the rules of thermodynamics [6]. This can be a practical method to study MCDS related to poly-dimensional dislocation propagation. Furthermore, experimental investigations have indicated that dislocations in a strained crystal do not act in a fully random arrangement. Along with the above limitation, the distorted MDCS does not have a consistent dislocation density from one end to the other in the inner structure of the unit cell [7; 8; 9; 10; 11; 12]. Therefore, in a micromechanical approach, discrete dislocation analysis is not sufficient to describe the individual and/or small number of dislocations in MDCS. This method has difficulty defining strains along the dislocation line inside the dislocation core [13; 14; 15; 16; 17]. Incontrast to the micromechanical method, the typical characteristics of materials at the macro level can be accurately investigated through the continuum principle. With this concept in mind, the continuum mechanics approach, which aims to include the size effect of the dislocation flow through a strain gradient (nonlocal) component by combining classical and local representations, is based on a massive number of continuous dislocations [18; 19; 20; 21; 22]. Accordingly, there is a huge gap between the micro- and macroscales. Bridging the two extremes requires an appropriate meso-model, namely, continuum dislocation formulations. The formulations of continuum dislocation include the length scale of the material, and hence, the size effects can be accounted for in the mesoscale model [23; 24; 25; 26; 27]. The length scale of the material in a deformed body becomes substantial in the mechanics of the material. This raises a significant question, namely, the degree to which the overall macro-level mechanical properties (strength, hardness, etc.) are determined by the collective parametric length scale associated with the distinctive microstructural magnitude of the material [18; 28; 29; 30; 31]. In this study, we performed an analysis of free energy in unit cells (UCs) that were subjected to dislocation in an active mono-slip system. In the proposed approach, energy is incorporated into the structure caused by geometrically necessary dislocations (GNDs) to determine the material parametric length [6; 32; 33; 34]. The composite material is assumed to comprise a bi-periodic array of unit cells. Additionally, the unit cell is directly isotropic, and the matrix domination is higher, contains free inclusions without dislocation, and is exposed to normal shear stress through kinematic boundary conditions. Many theories in micromechanical analysis use a higher-order PDE approach.