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This research is dedicated to the estimation of the effective elastic modulus of polymer concrete by a new micromechanical model. The capability of the equivalent inclusion methods have been proved by numerous researches. The Mori-Tanaka (M-T) model is the most used homogenization scheme for two-phase composite materials. The M-T model provides good estimates of the stiffness tensor for two-phase composites with low to moderate volume fraction of inclusions. However, when the volume fraction of reinforcing phase is high, M-T model is unable to predict the stiffness tensor accurately. The major disadvantage of M-T model is that when volume fraction is high, in the associated isolated inclusion medium (AIIM), the properties of the reinforcing phase does not affect the matrix properties. The idea of the proposed model is that in high volume fraction of the associated isolated inclusion medium, the matrix phase must be affected by the reinforcing phase properties. In order to evaluate this model, twelve components with two different compositions were manufactured and tested. Also, the results from other researches were used to evaluate this model. The validation of the proposed model with the experimental data and results by other researchers shows the remarkable predictive capability of this 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.

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In this work, the effect of carbon nanotube (CNT) size on the effective elastic properties of a hybrid composite reinforced by fuzzy fiber is investigated using a unit cell-based micromechanical approach. This hybrid nanocomposite is composed of the CNT, carbon fiber, polymer matrix and interphase created due to the non-bonded van der Waals interactions between the CNTs and polymer. The novel constructional feature of this hybrid nanocomposite is that the uniformly aligned CNTs are radially grown on the surface of the horizontal carbon fibers. The CNT and carbon fiber are modeled as a transverse isotropic solid, while the interphase and polymer matrix are assumed to be isotropic. The influence of CNT size on the overall behavior of polymer matrix nanocomposite (PMNC), composite fuzzy fiber (CFF) and hybrid composite reinforced with fuzzy fiber is examined. Results show that size of CNT is more significant for the transverse effective properties of the hybrid nanocomposites reinforced with fuzzy fiber. It has been found that the transverse effective properties of hybrid nanocomposite are improved with increasing the CNT size. The micromechanical model is also used to examine the influence of interphase on the overall behavior of the PMNC, CFF and hybrid composite reinforced with fuzzy fiber. The effective elastic properties of the hybrid composite obtained by the present micromechanical model demonstrate very good agreement with those predicted by the other researches.