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The present study characterizes the effects of variations in the poling characteristics of the matrix and the fiber phase on the overall electromechanical behavior of a 1-3 piezocomposite. Upon identifying 15 types of 1-3 piezocomposites based on two factors: the spatial arrangement of the fibers and the relative orientation of the poling direction of one phase with respect to the second phase, a comprehensive finite-element-based numerical model that can fully capture the electromechanical response of all the 15 types of 1-3 piezocomposites is developed and the following principal results are obtained: (i) a judicious selection of the combination of poling characteristics of the individual constituents, that each exhibit unidirectional sensitivity, could lead to the development of a piezocomposite with significant bidirectional sensitivity; (ii) variations in the elastic, piezoelectric, and dielectric material constants with fiber volume fraction are in general nonlinear, while converging to the expected monolithic material limits at very low and very high volume fractions of the fiber phase in the piezocomposite; (iii) concentrations in mechanical stresses typically occur at the fiber-matrix interface and thus the location and conditions for the onset of mechanical failure in the piezocomposites could be predicted; (iv) highest efficiency in energy transfer from the mechanical to the electrical domain and vice versa is obtained in class I piezocomposites where the fiber phase and matrix phase are poled in a direction parallel to the fiber axis. However, a wide range of specific acoustic impedances are generated in a composite by a variation in the poling characteristics, thus enhancing the tunability of piezocomposites for specific applications.