This paper deals with the structural analysis of composite materials with non-homogenous orientation of the reinforcement. During this research, a short fiber-reinforced polymer matrix composite is studied. In this case, inhomogeneity of the reinforcement orientation caused by injection molding manufacturing process is analyzed. The main objective of the paper is the investigation of an influence of process-induced orientation of the reinforcement on mechanical properties of the material in comparison with unidirectional and random reinforcement orientation. In particular, natural frequencies and transient response of an exemplary composite component are investigated. To specify effective properties of the composite, Mori-Tanaka's micromechanical model is assumed. Orientation distribution of the reinforcement is determined by injection molding simulation. To determine elastic material properties dependent on non-homogenous orientation of the reinforcement, an orientation averaging procedure is taken into account. Therefore, during this study, effectiveness of the orientation averaging procedure and different closure approximations influence on the results are studied. Orientation averaging results are compared with numerical results obtained by finite element-based homogenization of composites with prescribed second-order orientation tensor. Finally, the obtained material parameters were applied into a macroscale finite element model, and numerical simulation with different boundary conditions was conducted.

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

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