Optimization of magnetoelectric composites using convolutional neural networks

Magnetoelectric (ME) composites are known for their ability to convert an external magnetic stimulus into an electrical response and vice versa, which is accomplished indirectly through the transfer of mechanical strain between the ferromagnetic and ferroelectric constituents. They are widely used in the design of sensors, actuators, and devices for energy harvesting, where high ME coupling coefficients are desirable. To be able to observe the ME effect in a composite, electrical poling of its ferroelectric phase is a prerequisite, a process that activates the piezoelectric behavior by aligning the electric dipoles. In this work, we develop deep-learning surrogate models based on convolutional neural networks (CNNs) to explore optimal microstructural morphologies of ME composites that enhance their effective piezoelectric properties following the electrical poling process. The dataset required for developing the surrogates is generated in silico through the finite-element-based solution of a variational saddle-point principle governing the computational homogenization of magneto-electro-mechanically coupled boundary value problems. For selected microstructural configurations that lead to high effective piezoelectric coefficients, we then investigate the effective ME modulus as a function of the applied magnetic field strength for different volume fractions of the constituents. The trends are consistent with those observed in experiments.