An Eshelby–Mori–Tanaka-Based Micromechanical Model for Piezoelectric Polymer Composites with Spatially and Randomly-Oriented Inclusions in Orthotropic Matrix

A mean-field micromechanics model based on the Eshelby–Mori–Tanaka approach is used to investigate the effect of spatial orientation of reinforcements on the effective elastic, dielectric, and piezoelectric properties of a polymer composite, with an orthotropic matrix and a transversely isotropic reinforcement. The analysis is also performed for composites with random orientation of the piezoelectric reinforcements and with different shapes of spheroidal reinforcements ranging from aspect ratios of 2–1000. The effect of orientation on the effective axial and transverse Young’s moduli is not prominent at a low aspect ratio of 2, while the effective properties do not change significantly as functions of volume fraction for aspect ratios of 100 and above. The results also confirm that the random composites show significantly poorer properties than their perfectly-aligned counterparts. The results also allow us to obtain the specific orientation angles that would provide the highest elastic, piezoelectric, and dielectric properties for a given reinforcement volume fraction.