A hierarchical multi-scale analytical approach for predicting the elastic behavior of short fiber reinforced polymers under triaxial and flexural loading conditions

This paper presents a computationally efficient multi-scale analytical framework for predicting the effective elastic response of short fiber reinforced polymers (SFRPs) under triaxial and flexural loading conditions where the details of microstructure such as core/shell thickness, volume fraction distribution, fiber misalignment and fiber length variation are objectively taken into account. To this end, the mean-field homogenization and finite element approaches are compared to calculate the elastic response of SFRPs at the microscopic level while the orientation averaging approach is used to address the effects of fiber misalignment. The obtained mechanical behavior is then linked to an enhanced laminate theory to predict the effective triaxial and bending macrostructural behavior considering the core/shell effects and variation of volume fraction through the thickness. Using the second-order homogenization technique, the numerical validation of the proposed analytical approach is investigated based on the micro- and meso-scale analyses. Furthermore, the potential of the proposed strategy is demonstrated for hybrid composites. Finally, the accuracy of the suggested model is thoroughly studied using the available experimental tests in literature where the statistical information about the details of SFRP microstructures is presented.