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In this work, an analytical micromechanical model based on unit-cell approach is used to study the effect of interphase on the non-linear viscoelastic response of multiphase polymer composites. The representative volume element of composite consists of three phases including unidirectional fibers, polymer matrix and fiber/matrix interphase. Perfect bonding conditions are applied between the constituents of composites. The Schapery viscoelastic constitutive equation is used to model the nonlinear viscoelastic matrix. Prediction of the presented micromechanical model for the creep response of polymer material and two-phase composites shows good agreement with available experimental data. Furthermore, the predicted overall elastic behavior of three-phase composites demonstrates close agreement with other numerical results available. The effects of material and thickness of interphase on the creep-recovery strain curves of three-phase composites are studied in details. Results show that the interphase thickness and material properties have significant effect on the creep-recovery strain responses of the three-phase composites under transverse loading. According to micromechanical modeling results, it is found that the interphase negligibly affects the nano-linear viscoelastic behavior of three-phase composites under axial loading. Effects of the different stress levels and the variation of fiber volume fraction on the creep-recovery strain curves of three-phase composites are also investigated.

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A micro-mechanical model based on the representative volume element (RVE) is presented to study the time-dependent and creep behavior of fibrous composite material. To this aim a finite element model is presented for analysis of creep behavior of material in multi-axial creep are presented. The generalized plane strain condition is employed to model the behavior of the RVE in axial and transverse normal loading. The governing equations of the problem in the RVE are discretized using the presented finite element method and the stiffness and force matrixes are presented. Appropriate boundary conditions are implied to the RVE in order to consider the transverse and axial loading conditions including creep behavior. The Euler explicit method is employed to solve the discretized equations in the time domain. The distribution of micro-stresses and the effect of creep in re-distribution of the stresses are studied. The steady state creep behavior of composite in macro-mechanical scale is investigated by analysis of the micromechanical behavior of the RVE. The macro-mechanical creep behavior of metal matrix composite in axial and transverse loading are predicted from the presented micromechanical model.

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The use of porous scaffolds for repairing the damaged bone tissues has been increased in recent years. As exploration of the mechanical properties of the scaffolds on the basis of experiments is time consuming and uneconomic, mathematical models are increasingly being introduced into the field, but most of them rely on finite element method and theoretical studies are rarely found in the literature. In this paper, different micromechanical models are presented for obtaining the effective elastic properties of bone scaffolds. Using these models, the mechanical properties of different scaffolds, including ceramic and composite bone scaffolds, are investigated. Single scale and multi-scale modeling approaches are used to simulate the ceramic and composite scaffolds, respectively. Furthermore, because of the wide application of hydroxyapatite in fabrication of bone scaffolds, the mechanical properties of hydroxyapatite scaffolds in different porosities are obtained in the current study by means of the presented methods. Results show that Dewey, self-consistent and differential schemes are the best methods in calculation of the value of Young’s modulus of these scaffolds in porosity ranges of less than 30 %, 30 to 60 % and more than 60 %, respectively. Moreover, self-consistent scheme gives good estimation of the value of Poisson’s ratio of hydroxyapatite scaffolds in different porosities. By obtaining the values of the mechanical properties of the scaffolds in different porosities by these models and using the statistical analysis, the mathematical relationship between the porosity and the mechanical properties of this kind of scaffolds (Young’s modulus and Poisson’s ratio) is obtained.