| 1. |
- Bartel, Thorsten, et al.
(författare)
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An energy-relaxation-based framework for the modelling of magnetic shape memory alloys—Simulation of key response features under homogeneous loading conditions
- 2020
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 182-183, s. 162-178
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Tidskriftsartikel (refereegranskat)abstract
- In this contribution we present a constitutive modelling framework for magnetic shape memory alloys (MSMA) that builds on a global variational principle. The approach relies on concepts of energy relaxation and generalised notions of convexity to compute effective energy hulls to the non-convex energy landscape associated with the underlying multi-phase solid, from which the prediction of microstructure evolution results. In this sense it fundamentally distinguishes itself from MSMA models that essentially follow phenomenological concepts of classical plasticity (Kiefer and Lagoudas, 2005; 2009). The microstructure is not spatially resolved, but micro-scale quantities are taken into account in an effective sense by additional state variables—such as volume fractions or interface orientations—and appropriate mixture rules. The model allows all mechanisms central to MSMA behaviour—i.e. variant switching, magnetisation rotation away from easy axes, and magnetic domain evolution—to occur simultaneously. The authors have previously been able to demonstrate that such a modelling approach can quantitatively capture the key characteristics of single-crystalline MSMA response under standard loading scenarios (Kiefer et al., 2015). The modelling framework presented here is now further able to predict much more general response features, such as variant switching diagrams, magnetic field-biased pseudo-elasticity and the influence of specimen shape anisotropy. Moreover, the global variational framework is formulated in a manner that lends itself to finite element implementation. In this work, however, numerical examples are considered in which the nonlocal nature of the demagnetisation field is taken into account in an approximate sense through appropriate shape factors.
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| 2. |
- Buckmann, Karsten, et al.
(författare)
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Rank-One Convexification Approach for the Modeling of Magnetic Shape Memory Response
- 2015
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Ingår i: PAMM - Proceedings in Applied Mathematics and Mechanics. - : Wiley. - 1617-7061. ; 15, s. 311-312
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Buckmann, Karsten, et al.
(författare)
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Simulation of magnetised microstructure evolution based on a micromagnetics-inspired FE framework : application to magnetic shape memory behaviour
- 2019
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Ingår i: Archive of Applied Mechanics. - : Springer Science and Business Media LLC. - 0939-1533 .- 1432-0681. ; 89:6, s. 1085-1102
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Kiefer, Bjoern, et al.
(författare)
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Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques
- 2014
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Ingår i: Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. - 9780791846148 ; 1, s. 2014-7436
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 5. |
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