Finite element analysis of Hall effect and magnetoresistance

Brauer, J.R.; Ruehl, J.J.; MacNeal, B.E.; Hirtenfelder, F.

doi:10.1109/16.370061

Cited by 9 publications

(2 citation statements)

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“…For these reasons, several numerical formulations have emerged in the last two decades. The finite difference method was applied in [105], [104] and the FEM was used to study the Hall effect in [23]. The mentioned FEM formulation is very simple and not fully coupled, consisting on an electric element with anisotropic electric conductivity and magnetic-dependency of the conductivity tensor introduced as data.…”

Section: Other Interactionsmentioning

confidence: 99%

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

Pérez-Aparicio

Palma

Taylor

2015

Arch Computat Methods Eng

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Combining several theories this paper presents a general multiphysics framework applied to the study of coupled and active materials, considering mechanical, electric, magnetic and thermal fields. The framework is based on thermodynamic equilibrium and nonequilibrium interactions, both linked by a two-temperature model.The multi-coupled governing equations are obtained from energy, momentum and entropy balances; the total energy is the sum of thermal, mechanical and electromagnetic parts. The momentum balance considers mechanical plus electromagnetic balances; for the latter the Abraham representation using the Maxwell stress tensor is formulated. This tensor is manipulated to automatically fulfill the angular momentum balance. The entropy balance is formulated using the classical Gibbs equation for equilibrium interactions and non-equilibrium thermodynamics. For the non-linear finite element formulations, this equation requires the transformation of thermoelectric coupling and conductivities into tensorial form.The two-way thermoelastic Biot term introduces damping: thermomechanical, pyromagnetic and pyroelectric converse electromagnetic dynamic interactions. Ponderomotrix and electromagnetic forces are also considered.The governing equations are converted into a variational formulation with the resulting four-field, multicoupled formalism implemented and validated with two custom-made finite elements in the research code FEAP. Standard first-order isoparametric eight-node elements with seven degrees of freedom (dof) per node (three displacements, voltage and magnetic scalar potentials plus two temperatures) are used. Non-linearities and dynamics are solved with Newton-Raphson and Newmark-β algorithms, respectively.Results of thermoelectric, thermoelastic, thermomagnetic, piezoelectric, piezomagnetic, pyroelectric, pyromagnetic and galvanomagnetic interactions are presented, including non-linear dependency on temperature and some second-order interactions.

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Section: Other Interactionsmentioning

confidence: 99%

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

Pérez-Aparicio

Palma

Taylor

2015

Arch Computat Methods Eng

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“…[5][6][7][8][9] In the latter case, the influence of geometry on the overall response has been explicitly known for simply connected two-dimensional structures with pointlike contacts exposed to a homogeneous magnetic field B. 1,9,[11][12][13][14][15][16] Whatever their mathematical basis, these methods implement some procedure to solve the transport problem in the sample at B 0, which implies its own challenges. 1,9,[11][12][13][14][15][16] Whatever their mathematical basis, these methods implement some procedure to solve the transport problem in the sample at B 0, which implies its own challenges.…”

Section: Explicit Connection Between Sample Geometry and Hall Responsementioning

confidence: 99%