Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton's principle: The numerical algorithm

This paper is the second part of a variational modeling work on the dynamic magneto mechanical response of magnetic shape memory alloys (MSMA). In the first part of this series work, the governing equations system for modeling the dynamic response of MSMA samples has been derived based on Hamilton's principle, which contains the Maxwell's equations, the magneto-mechanic equations, the evolution equations of internal variables and the twin interface motion criteria. In this paper, we aim to conduct comprehensive numerical simulations on the dynamic magneto-mechanical response of MSMA samples. To solve the governing system, the space-time finite element method is applied and a double-loop iterative numerical algorithm is proposed. By using this algorithm, the independent variables in the governing system and the motion of twin interfaces in the MSMA sample can be determined separately and iteratively. Besides that, a specific discretization of the sample is adopted to simplify the calculation of variant state distribution in the sample. To show the efficiency of the numerical algorithm, the magneto-mechanical response of a MSMA sample in stress-assisted dynamic field loading tests and field-assisted dynamic mechanical loading tests are studied. Based on the numerical results, some global response curves of the MSMA sample are plotted, which show good consistency with the experimental results. Furthermore, the current configuration of the sample and the distributions of some important physical fields in the sample can be simulated. The current work will be helpful for the design of novel actuators or energy harvesters with MSMA.