## 3 Micromechanical Analysis
### Results and Real World Applications  
Regarding the micromechanics analysis of the present study, the analysis is capable of modeling a unidirectional composite subjected to longitudinal and/or transverse normal loading. Usually, a finite element software is used to help determine the field of stress and strain. The constitutive material parameters, which are a function of time and temperature, are introduced into the model. [PERSON]'s nonlinear constitutive equation for isothermal uniaxial loading conditions is incorporated into the analysis to take into account the nonlinear viscoelastic behavior. From the numerous experimental results, several examples presented in this section demonstrate the potential application of the present method. For the triaxial stress state that is presented in the composite as a result of uniaxial loading, the equivalent stress from the matrix is considered so that all viscoelastic parameters are dependent on a single invariant. [PERSON]'s ratio turned out to be a very weak function of time or almost independent of time, an observation that greatly simplified the constitutive equation. For example, there is a rich body of literature regarding creep behavior in ceramic matrix composites. A three-dimensional analysis of a viscoplastic matrix with progressive deterioration is presented for ceramic matrix composites subjected to creep [105]. The theoretical development followed the theory of [PERSON]'s orthotropic plastic potential, and the temperature dependence was of the Arrhenius type. The results obtained were compared with the existing data in the literature, obtained from measurements. Micromechanical analysis was used for a complex application regarding the creep analysis of minicomposites with ceramic matrix [106]. Local stresses were high enough to cause microcracks in the matrix. In order to perform the analysis, the shear retardation of the fiber was considered. The creep response of the fiber was obtained using a linear Burgers model. One application was for a unidirectional SiCf/SiC minicomposite system for which experimental measurements were also made for validation. The global deformation of a composite material composed of a brittle matrix reinforced with long, continuous fibers is studied in [107]. The aim of the work is to determine the in-service behavior of composites with silicon carbide or oxide matrices. The experimental results confirm the efficiency of the model used in the study. The study of unidirectional fiber-reinforced composites has been an intense field of study for researchers, probably mainly due to the possibility of an easier approach to calculations within the developed models. Thus, different models have been developed for different cases encountered in engineering practice. For example, the creep behavior that occurs in unidirectional fiber-reinforced metal matrix composites due to interface diffusion is studied in [108]. A micromechanical model is proposed for this material that provides results faster and with an accuracy comparable to the results obtained using FEM. A micromechanical model analysis for a composite made of elastic fibers reinforcing resin with viscoelastic but nonlinear behavior is performed in [109]. The viscoelastic behavior is expressed by Schapery's relation. The fibers are made of graphite and reinforce epoxy resin. Creep tests conducted over a period of 8 h validate the model proposed by the authors. The inelastic response of a glass fiber epoxy composite (Vicotex NVE 913/28%/192/EC9756 300 MM produced by HEXCEL Composites Ltd., Amityville, New York USA) is obtained, based on a micromechanical model, which builds on the micromodel proposed by [PERSON] [110]. Experimental verifications validate the theoretical ones in this case as well. The off-axis creep response of hybrid polymer matrix composites (HPMCs) reinforced with unidirectional carbon fibers and silica nanoparticles is predicted using a multi-step homogenization technique [111].