| 1. |
- Bartel, Thorsten, et al.
(författare)
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An energy-relaxation-based framework for the modeling of magnetic shape memory alloys—Simulation of three-dimensional effects under homogeneous loading conditions
- 2021
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 208-209, s. 221-234
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Tidskriftsartikel (refereegranskat)abstract
- It is known from experimental findings that three-dimensional effects can have a strong influence on magnetic shape memory behavior. Such phenomena are, however, often neglected in MSMA constitutive models, as they only become meaningful under complex loading conditions. The extensions of our original modeling framework, cf. Bartel et al. (2020), to include 3D-effects is threefold: (i) vector-valued microstructural variables are now elements in R3, i.e. no longer parameterizable in polar coordinates, (ii) a third tetragonal martensite variant may form/vanish by switching from/back into both other variants, and (iii) a more general and robust algorithmic treatment is necessary. The latter includes the implementation of a staggered Augmented Lagrangian scheme to handle the now much larger and numerically more advanced sets of equality and inequality constraints. In this context, two extended model formulations are presented. The first considers a first-order, two-variant laminate approach (rank-one convexification), in which domain magnetizations, interface orientations etc. are now three-dimensional vectors. The second model is based on a convexification approach, for which the incorporation of the third martensitic variant is quite natural. Numerical examples are investigated to test the generalized modeling framework. Firstly, it is confirmed that both extended models recover the solution of the previously established two-dimensional model for a simple loading case. Secondly, response predictions for more complex loading scenarios (non-proportional bi-axial stresses, orthogonal magnetic field), motivated by experiments, are investigated. It is found that capturing the formation, elimination and mutual interaction of all martensitic variants as well as general three-dimensional magnetization vector orientations is of key importance under these conditions. The extended convexification model and modified algorithmic formulation are shown to reliably handle even such general cases.
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| 2. |
- 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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| 3. |
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| 4. |
- Hernandez, Edwin A. Peraza, et al.
(författare)
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Analytical investigation of structurally stable configurations in shape memory alloy-actuated plates
- 2015
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 69-70, s. 442-458
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Tidskriftsartikel (refereegranskat)abstract
- Strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface-like engineering structures. Shape memory alloys (SMAs) are active materials that provide a significant amount of strain under large stresses, a characteristic of great utility in such morphing structures. In this work, an analytical approach to approximate the deformation of plates with SMA constituents is developed via the Rayleigh-Ritz method. An additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field. The total potential energy is then calculated using the displacement field, loading conditions, and constitutive relations for the plate layer(s) composed of SMA wire meshes, dense SMA films, and/or elastic material. The unknown coefficients are then found via minimization of the total potential energy. This approach provides closed-form expressions for the approximate deformation of the plates including multistable configurations. The response of circular SMA-based plates is studied herein. The results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate Gaussian curvature is determined by the direction of the temperature gradient. An alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape. The obtained closed-form expressions show good agreement with detailed non-linear finite element analysis simulations. The proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of SMA-based plates under given loading conditions. Knowledge of such stable configurations is very valuable in the design of SMA-based morphing structures. (C) 2015 Elsevier Ltd. All rights reserved.
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| 5. |
- Kiefer, Bjoern, et al.
(författare)
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A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts
- 2018
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Ingår i: International Journal of Damage Mechanics. - : SAGE Publications. - 1056-7895 .- 1530-7921. ; 27:2, s. 253-295
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- 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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| 7. |
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