Nonlinear mechanical behavior and multi-field coupling characteristics in polymer-based multiferroic composites under combined tension and bending

Polymer-based multiferroic composites simultaneously exhibit ferroelasticity, ferroelectricity, and ferromagnetism, supporting applications in flexible electronics, biomimetics, and biomedicine. Their macroscopic properties are influenced by averaging, synergy, antagonism, and product interactions. This study investigates these behaviors by incorporating nonlinear hysteresis, interface polarization, and leakage effects, integrating a crystal phase transformation model with two-step homogenization theory. A theoretical framework is developed to analyze nonlinear mechanical responses and magnetoelectric (ME) effects under combined tension and bending, based on Kirchhoff thin plate theory and tension-bending control equations. Analytical expressions are derived for natural frequencies, vibration modes, displacements, and ME coefficients. Results reveal that increasing ferromagnetic particle content enhances ferromagnetism but causes dielectric relaxation, percolation, and leakage, reducing piezoelectricity. Moderate content promotes β-phase formation, enhancing piezoelectric performance. The composite shows multiple natural frequencies, with resonance at specific ones. The ME properties exhibit hysteresis, significantly amplified under combined deformation. Theoretical predictions of magnetization, polarization, piezoelectric coefficient, leakage current, and ME coefficient closely match experimental results, validating the model’s accuracy and applicability. To address leakage at high particle fractions, two strategies are proposed. Under optimal conditions, the ME coefficient improves by 2.4 times, establishing a solid basis for the design and optimization of polymer-based multiferroic composites.