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Microstructure evolution in magnetic materials is typically a non-local effect, in the sense that the behaviour at a material point depends on the magnetostatic energy stored within the demagnetisation field in the entire domain. To account for this, we propose a finite element framework in which the internal state variables parameterising the magnetic and crystallographic microstructure are treated as global fields, optimising a global potential. Contrary to conventional micromagnetics, however, the microscale is not spatially resolved and exchange energy terms are neglected in this approach. The influence of microstructure evolution is rather incorporated in an effective manner, which allows the computation of meso- and macroscale problems. This approach necessitates the development and implementation of novel mixed finite element formulations. It further requires the enforcement of inequality constraints at the global level. To handle the latter, we employ Fischer–Burmeister complementarity functions and introduce the associated Lagrange multipliers as additional nodal degrees-of-freedom. As a particular application of this general methodology, a recently established energy-relaxation-based model for magnetic shape memory behaviour is implemented and tested. Special cases—including ellipsoidal specimen geometries—are used to verify the magnetisation and field-induced strain responses obtained from finite element simulations by comparison to calculations based on the demagnetisation factor concept. [ABSTRACT FROM AUTHOR]

Phenomenological constitutive models of inelastic responses based on the methods of classical plasticity provide several advantages, especially in terms of computational efficiency. For this reason, they are attractive for the analysis of complex boundary value problems comprising large computational domains. However, for the analysis of problems dominated by single crystal behavior (e.g., inclusion, granular interaction problems or inter-granular fracture), such approaches are often limited by the symmetry assumptions inherent in the stress invariants used to form yield-type criteria. On the other hand, the high computational effort associated with micro-mechanical or crystal plasticity-type models usually prevents their use in large structural simulations, multi-scale analyses, or design and property optimization computations. The goal of the present work is to establish a modeling strategy that captures micro-scale single-crystalline sma responses with sufficient fidelity at the computational cost of a phenomenological macro-scale model. Its central idea is to employ an anisotropic transformation yield criterion with sufficiently rich symmetry class—which can directly be adopted from the literature on plasticity theory—at the single crystal level . This approach is conceptually fundamentally different from the common use of anisotropic yield functions to capture tension-compression asymmetry and texture-induced anisotropy in poly-crystalline SMAs. In our model, the required anisotropy parameters are calibrated either from experimental data for single crystal responses, theoretical considerations or micro-scale computations. The model thus efficiently predicts single crystal behaviors and can be applied to the analysis of complex boundary value problems. In this work we consider the application of this approach to the modeling of shape memory alloys (SMAs), though its potential utility is much broader. Example analyses of SMA single crystals that include non-transforming precipitates and poly-crystalline aggregates are considered and the effects of both elastic and transformation anisotropy in these materials are demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: This contribution deals with a micromechanical model for the simulation of the magnetomechanical behaviour of magnetic shape memory alloys which captures effects such as martensite variant switching, domain wall motion, and the rotations of local magnetisations. It is revealed, however, that the implementation into micromagnetics‐inspired Finite Element schemes cannot be realized in a standard fashion but requires the treatment of state variables via macroscopic fields. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this contribution we present a variational framework which is suitable for the finite element implementation of energy-relaxation based magnetostriction models. Our recent work [1] has shown that energy-relaxation based models are able to capture all key response characteristics of multi-ferroic magnetic shape memory alloys (MSMA). In order to simulate the response behavior of arbitrarily shaped samples we are switching to a micromagnetically inspired finite element framework [3], where the magnetization inside the magnetic material and the nonlocal demagnetization field are spatially resolved. First results compare the magnetization responses for FE-simulations and calculations using the demagnetization tensor concept. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We present an incremental energy minimization model for magnetic shape memory alloys (MSMAs) whose derivation departs from the constrained theory of magnetoelasticity [1], but additionally accounts for elastic deformations, magnetization rotation, and dissipative mechanisms. The minimization of the proposed incremental energy yields the evolution of the internal state variables. In this sense, the presented modeling concept clearly distinguishes itself from standard phenomenological approaches to MSMA modeling [4]. The extended model is applied to simulate the response of single crystalline Ni2MnGa. It is shown to accurately capture the nonlinear, anisotropic, hysteretic, and highly stress level-dependent features of MSMA behavior, based on just a few fundamental material parameters, which is validated by comparison to experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]