Analysis of nonlinear piezomagnetism for magnetostrictive terfenol-D composites

This study presents two micromechanics formulations to investigate the nonlinear piezomagnetism for magnetostrictive Terfenol-D composites subjected to large magnetic driving fields. A simplified unit-cell micromechanics method that hypothesizes the composite microstructure forming a periodic array is developed, and the well-known Mori-Tanaka micromechanics model is reformulated for nonlinear composite problems. This work elucidates the nature of the approximation in applying the unit-cell and Mori-Tanaka micromechanics models to magnetostrictive composites insofar as the concentration tensors are concerned. A first moment secant linearization but conventional tangent linearization is employed for nonlinear magneto-elastic constitutive laws in order to obtain a unified and linearized constitutive equation. Later, a homogenization process on the nonlinear responses of magnetostrictive composites is performed via numerical iterations in order to minimize errors from the linearization process. Different composites comprising of unidirectional Terfenol-D fiber, particle, and lamina reinforcements are studied, respectively. For nonlinear piezomagnetic strain responses simulated in this work, the predictions given by the unit-cell and Mori–Tanaka schemes are in good agreement with the experimental data available in the literature. Numerical results are also presented to illustrate the performance of each micromechanics model for common composite connectivity, i.e., 1–3, 0–3, and 2–2 types. Depending on Terfenol-D geometry, volume fraction, and applied magnetic field, the magnetostrictive composites could exhibit various degrees of nonlinear piezomagnetism. The presented micromechanics models can further be served as composite constitutive equations to analyze smart composite structures such as beams commonly utilized in sensor and actuator applications.