Finite element analysis of the demagnetization effect and stress inhomogeneities in magnetic shape memory alloy samples

Abstract

This paper is concerned with the finite element analysis of boundary value problems involving nonlinear magnetic shape memory behavior, as might be encountered in experimental testing or engineering applications of magnetic shape memory alloys (MSMAs). These investigations mainly focus on two aspects: first, nonlinear magnetostatic analysis, in which the nonlinear magnetic properties of the MSMA are predicted by the phenomenological internal variable model previously developed by Kiefer and Lagoudas, is utilized to investigate the influence of the demagnetization effect on the interpretation of experimental measurements. An iterative procedure is proposed to deduce the true constitutive behavior of MSMAs from experimental data that typically reflect the shape-dependent system response of a sample. Secondly, the common assumption of a homogeneous Cauchy stress distribution in the MSMA sample is tested. This is motivated by the expectation that the influence of magnetic body forces and body couples caused by field matter interactions may not be negligible in MSMAs that exhibit blocking stresses of well below 10 MPa. To this end, inhomogeneous Maxwell stress distributions are first computed in a post-processing step, based on the magnetic field and magnetization distributions obtained in the magnetostatic analysis. Since the computed Maxwell stress fields, though allowing a first estimation of the influence of the magnetic force and couple, do not satisfy equilibrium conditions, a finite element analysis of the coupled field equations is performed in a second step to complete the study. It is found that highly non-uniform Cauchy stress distributions result under the influence of magnetic body forces and couples, with magnitudes of the stress components comparable to externally applied bias stress levels.

Keywords:

• magnetic shape memory alloys (MSMAs)
• magnetostatics
• demagnetization effect
• magneto-mechanical coupling
• coupled finite element analysis

Acknowledgements

The authors would like to acknowledge the financial support of the Army Research Office, Grant No. W911NF-06-1-0319 and the financial support of NSF-IIMEC (International Institute for Multifunctional Materials for Energy Conversion) under Grant No. DMR-0844082.

Notes

Note

1. The specific results presented here are based on solutions of 2-D boundary value problems and can thus only be used for a qualitative assessment. The procedure is the same for 3-D problems, which, however, are computationally much more involved.