Krishnendu Haldar

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

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.

Stability Analysis of Magnetostatic Boundary Value Problems for Magnetic SMAs

Magnetic shape memory alloys have been the subject of much research in recent years as potential high actuation energy multifunctional materials. They can be considered as continua that deform under mechanical and magnetic forces. The constitutive magnetization response of such materials is highly non-linear with magnetic field. A boundary value problem where Maxwell’s equations of the magnetostatic problem are coupled with the non-linear constitutive behavior is solved using finite element analysis. The numerical simulation reveals localization zones of the field variables, which appear due to loss of ellipticity of the magnetostatic problem. Stability analysis is performed by considering the characteristics of the magnetostatic field equations.

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries.

A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.

Model predictions of strain and magnetization responses under magneto-thermo-mechanical loading paths in magnetic shape memory alloys

Magnetic shape memory alloys (MSMAs) have recently drawn considerable research interest due to their ability to produce magnetic field-induced strains (MFIS) , at least one order of magnitude higher than those of ordinary magnetostrictive materials. In the present work microstructure dependence of martensitic phase transformation and reorientation is taken into account by introducing internal variables into the model. The magneto-thermomechanical constitutive equations are derived in a thermodynamic consistent way. A 3-D stress-field-temperature phase diagram is predicted using the model for the case of field induced phase transformation (FIPT).

Constitutive modeling of magneto-mechanical coupling response of magnetic field-induced phase transformations in NiMnCoIn magnetic shape memory alloys

The unique characteristic of magnetic field induced phase transformation of NiMnCoIn magnetic shape memory alloys (MSMAs) lies in the generation of large transformation strains under high constant stress levels. Motivated by experiments, a constitutive model is proposed to take into account magnetic field induced phase transformation from austenitic to martensitic phase. The working principle of such materials is described by the deformation of continua due to mechanical and magnetic forces. The cross coupling of mechanical and magnetic variables is captured by introducing nonlinear kinematics. In the present work, microstructure dependence of martensitic phase transformation is taken into account by introducing internal variables into the model. The constitutive response is derived in a consistent thermodynamic way.

Stability of the magnetomechanical problem in magnetic shape memory alloys

In this work we study the unstable phenomena that occur on Magnetic Shape Memory Alloys (MSMAs) during compression tests. Solving the coupled magnetomechanical problem we observe that during the reorientation process the material presents strong non-uniformity, in the form of localized zones, in the distribution of the magnetic, the stress and the strain field. This non-uniformity is due to loss of ellipticity of the coupled problem during the martensitic reorientation and affects significantly the reorientation process. The identification of the stability conditions of the magnetomechanical problem is achieved by performing stability analysis.

Constitutive Modeling of Magneto-Thermo-Mechanical Response of Field-Induced Phase Transformations in NiMnCoIn Magnetic Shape Memory Alloys

In this work we model the magnetic field induced phase transformation (FIPT) of magnetic shape memory alloys (MS-MAs). The working principle of such materials is described by the cross coupling of mechanical, thermal and magnetic fields. The Thermo-magneto-mechanical constitutive equations are derived in a thermodynamic consistent way. A 3-D stress-field-temperature phase diagram is constructed using the model. The model is calibrated from the experimental data and the model predictions are compared with experimental results.Copyright

Magnetic Field-Induced Reversible Phase Transformation in Magnetic Shape Memory Alloys

Magnetic Shape Memory Alloys (MSMAs) are promising high-frequency active materials for actuation, sensing, shape control, vibration suppression and energy harvesting applications. The macroscopic functionality of MSMAs originates from the coupled evolution of highly heterogeneous magnetic and elastic domain microstructures. Microstructure dependence of phase transformations in MSMAs introduces internal variables into the model to account for strong effects of domain microstructure processes on MSMA properties and varying elastic and magnetic coupling. Selection of internal variables and their incorporation into constitutive modeling has been done for the problem of field-induced martensite reorientation. Introducing a new internal variable, the austenitic volume fraction, the study of field induced phase transformation between the parent and martensitic phases is performed.

Constitutive Modeling of Magnetic Field-Induced Phase Transformation in NiMnCoIn Magnetic Shape Memory Alloys

In this work we model the magnetic field induced phase transformation (FIPT) of magnetic shape memory alloys (MSMAs). The working principle of such materials is described by the deformation of continua due to mechanical and magnetic forces. The cross coupling of mechanical and magnetic variables is captured by introducing nonlinear kinematics. The mechanical and magnetic constitutive equations are derived by a thermodynamic consistent way. Finally, the model prediction followed by model calibration is compared with the experimental results.Copyright

Magneto-Mechanical Finite Element Analysis of Magnetic Shape Memory Alloys With Body Force and Body Couple

This work describes the coupling between the magnetostatic and mechanical problems. The aim is to investigate the influence of magnetic body force and magnetic body couple on the equilibrium equations. The magnetic body force and couple are computationally evaluated using finite element analysis over the domain of a magnetic shape memory alloy (MSMA) specimen with rectangular cross-section, subjected to applied magnetic and mechanical boundary conditions. The analysis presented in this paper studies the non uniform distribution of magnetic body force and body couple in the specimen and their impact on the Cauchy stress distribution.Copyright