Bjoern Kiefer

ACCURATE INTERPRETATION OF MAGNETIC SHAPE MEMORY ALLOY EXPERIMENTS UTILIZING COUPLED MAGNETOSTATIC ANALYSIS

In order to build a reliable constitutive model for magnetic shape memory alloys (MSMAs) the availability of accurate experimental data for calibration and validation purposes is essential. However, the demagnetization effect and the resulting sample shape-dependent difference between the applied field and the internal field makes measurements of MSMAs properties difficult to interpret. Since for non-ellipsoidal specimen the internal magnetic field and thus the induced magnetization is nonuniform, standard demagnetization factors can not be applied without evaluation of the expected error. Following up on previous work by the authors this paper describes a methodology by which experimental data can be interpreted more accurately. The procedure involves the numerical solving of nonlinear magnetostatic boundary value problems for MSMAs in which the stress-dependent magnetic properties of the material are predicted by the constitutive model. New results of this analysis presented here include a parametric study of the sample shape dependence of the demagnetization effect when accounting for the nonlinear magnetization properties of MSMAs.Copyright

Finite element simulation of rate-dependent magneto-active polymer response

This contribution is concerned with the embedding of constitutive relations for magneto-active polymers (MAP) into finite element simulations. To this end, a recently suggested, calibrated, and validated material model for magneto-mechanically coupled and rate-dependent MAP response is briefly summarized in its continuous and algorithmic settings. Moreover, the strongly coupled field equations of finite deformation magneto-mechanics are reviewed. For the purpose of numerical simulation, a finite element model is then established based on the usual steps of weak form representation, discretization and consistent linearization. Two verifying inhomogeneous numerical examples are presented in which a classical plate with a hole geometry is equipped with MAP properties and subjected to different types of time-varying mechanical and magnetic loading.

A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts

A non-local gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a non-local free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush–Kuhn–Tucker conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with a non-local gradient enhancement. An important part of the present work is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the Karush–Kuhn–Tucker conditions in the multi-surface damage-plasticity setting. Response simulations for representative inhomogeneous boundary value problems are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity.

Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques

This paper presents an energy relaxation-based approach for the modeling of single crystalline magnetic shape memor)) alloy response under general two-dimensional magnetomechanical loading. It relies on concepts of energy relaxation in the context of non-convex free energy landscapes whose wells define preferred states of straining and magnetization. The constrained theory of magnetoelasticity developed by DeSimone and James [1] forms the basis for the model development. The key features that characterize the extended approach are (i) dissipative effects, accounted for in an incremental variational setting, and (ii) finite magnetocrystalline anisotropy energy. In this manner, important additional response features, e.g. the hysteretic nature, the linear magnetization response in the prevariant reorientation regime, and the stress dependence of the maximum field induced strain, can be captured, which are prohibited by the inherent assumptions of the constrained theory. The enhanced modeling capabilities of the extended approach are demonstrated by several representative response simulations and comparison to experimental results taken from literature. These examples particularly focus on the response of single crystals under cyclic magnetic field loading at constant stress, and cyclic mechanical loading at constant magnetic field. (Less)

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.

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