A new nonlinear multiscale magnetostrictive approach for FEM modelling of magnetoelectric composites under magneto-thermo-elastic loading

A magneto-elastic multiscale approach based on analytical solution in accounting for the temperature dependence is proposed to model the behavior of magne-tostrictive material under magnetic, stress and thermal loading. The approach is based on the anhysteretic magneto-elastic Gibbs free energy model. However, the implementation of the original form of this model in numerical modeling such as the finite element method is cumbersome. To alleviate this difficulty, we propose a general extension of the model and compute the necessary magneto-elastic parameters from specific derivation of the partition function of the average energy. To consider the temperature dependence, the model is coupled with an extension of the temperature Bloch law relation. The model is implemented into a Finite Element code to simulate the behavior of laminated magnetoelectric composites constituted of PZT-5A and Terfenol-D layers under magneto-thermo-elastic loading.