Electromechanical response and numerical analysis of d₃₁ piezoelectric macro-fiber composite based on microscopic characterization

We establish a representative volume element (RVE) model and investigate the electromechanical coupling between the electric and mechanical fields in d₃₁ piezoelectric macro-fiber composite (MFC) through numerical simulation methods. The average equivalent performance parameters characterization of d₃₁ MFC is formulated by following the finite element homogenization methodology previously proposed for shear d₁₅ MFC. When varying the direction of RVE constraints, the distribution of various physical fields (with a focus on stress, strain, electric displacement, electric field intensity, potential, and polarization field) is significantly affected. When the RVE is subjected to unidirectional constraints only, the distribution of each physical field is relatively uniform. However, when it is simultaneously subjected to constraints from two directions, there are significant differences in the variations of each physical field, exhibiting a non-uniform distribution. Based on the constitutive relationship of d₃₁ MFC provided in the reference framework, the equivalent performance parameters of d₃₁ MFC are evaluated in the RVE when the volume fraction of piezoceramic ranges from 20% to 80%. Specifically, the effects of interdigital electrodes and flexible substrates on the effective elastic modulus, piezoelectric coefficient, and dielectric coefficient are analyzed. These research works provide theoretical support for the preparation of d₃₁ MFC with different performance parameters.