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In this paper, the absolute nodal coordinate formulation (ANCF) is applied to simulate the magnetic shape memory effect. Using the absolute nodal coordinate formulation makes it possible to describe complicated or large deformation cases. The nonlinear bidirectional coupling terms between the mechanical and magnetic field are taken into account in...
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Citations
... In many cases that is done by introducing internal variables that describe alloy microstructures: the volume ratio of different variants, the volume ratio of the magnetic domains, and the orientations of the magnetization vectors [31], [32], [33], [34], [35], [36], [37]. Many of these models were successfully implemented using numerical finite element techniques [34], [37], [38], including non-conventional ones, such as the absolute nodal coordinate formulation [39].A development of the model to study the quasi-static movement of TBs based on internal variables was reported in [40], and recent work [41] presents a numerical algorithm for studying the dynamic magnetomechanical response of MSM alloys. ...
Smart structures based on the magnetic shape memory (MSM) effect feature giant magnetic field-induced strains and an ultra-fast response. MSM alloys could be used in a variety of applications such as digital hydraulics, microfluidic systems, soft robotics. However, practical implementation of the MSM effect is complicated by a lack of precise engineering simulation tools suitable for designing structures using the MSM alloys. Presented here is an approach to calculating the difference in free energy across twin boundaries, which is the driving force for structural transformations in MSM alloys. The approach, based on 3D finite element simulations, makes it possible to consider an entire specimen while accounting for complex inner and outer non-homogeneous magnetic fields. Based on the simulation results obtained, conclusions are offered regarding the effect of different modeling approaches and experimental setups on free energy differences across twin boundaries.
This paper presents an overview of the finite-element (FE) absolute nodal coordinate formulation (ANCF), provides justifications for its use, and discusses issues relevant to its proper computer implementation and interpretation of its numerical results. The paper discusses future research directions for using ANCF finite elements in new areas such as soft tissues and materials relevant to broader areas of computational engineering and science. Selection of coordinates, definitions of forces and moments, geometric interpretation of the position gradients, and noncommutativity of finite rotations are among the topics discussed. To address concerns associated with finite-rotation noncommutativity and definition of moments in flexible-body dynamics, the paper demonstrates that the interpolation order is not preserved when the finite-rotation sequence is changed. Position gradients, on the other hand, are unique and preserve the highest interpolation order. It is shown that, while the spin tensor used to define the ANCF generalized forces due to moment application is associated with a rigid frame defined by the polar decomposition theorem, explicit polar decomposition of the matrix of position-gradient vectors is not required. ANCF elements have features that distinguish them from conventional finite elements and make them suited for large-displacement analysis of multibody systems (MBS). Their displacement fields, which allow increasing interpolation order without increasing number of nodes or using noncommutative finite rotations, are the basis for developing lower-dimension consistent rotation-based formulations (CRBF) without lowering the interpolation order. Nonetheless, the continuum-kinematic description of fully parameterized ANCF elements cannot be ignored when interpreting the ANCF numerical results. This issue is particularly important when comparing ANCF results with solutions obtained using semi-continuum conventional beam and plate models and simplified analytical approaches.
