Plasticity coupled with thermo-electric fields: Thermodynamics framework and finite element method computations

Moreno-Navarro, Pablo; Ibrahimbegović, Adnan; Pérez-Aparicio, José L.

doi:10.1016/j.cma.2016.10.038

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…where V * is the variation of V , which should take zero value at the Dirichlet boundary V * | Γ V = 0. The standard choice of finite element discrete approximation is suitable for this variational formulation [32].…”

Section: Single Field Electrostatic Formulation With Scalar Potentialmentioning

confidence: 99%

“…Thus, the vast majority of works on coupled mechanics and electromagnetism turned toward extending the philosophy specialized for their particular field to all the other fields computations. The current approach by mechanics experts relies upon the standard isoparametric finite element approximations and the simplest case of using a scalar potential for electric and magnetic fields [32], [33], which can accommodate, for instance, piezoelectric or piezomagnetic devices. This type of approach is further extended to higher order approximations, large displacement and homogenization techniques always using the finite element approximation for all fields; see [15], [40] and [27], among others.…”

Section: Introductionmentioning

confidence: 99%

“…Attempts to generalize the cell method approach to solve the problems with more complicated mechanics models have not been recorded, and furthermore, they seem very difficult to imagine. Namely, plasticity coupled with electric field [32] requires precise localization of the plastic zone that keeps changing throughout computations, making a global constitutive equation impossible to describe. However, a few authors have used the exterior calculus formalism to adapt it to finite element method philosophy such as [3] As for theoretical aspects of the problem, the electromagnetics community also evaluated a potential energy-type of variational formulation [35], [20], [21], which is no different from mechanical approach in, for instance, [22].…”

Section: Introductionmentioning

confidence: 99%

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Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

2019

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In this paper we propose different multi-field variational formulations for electrostatics and magnetostatics, which can provide optimal discrete approximation of any particular vector field. The proposed formulations are constructed by appealing to mechanics point of view amenable to using general constitutive equations, which is quite different from electrostatics and magnetostatics formulations typical of physics and electrical engineering focusing on the corresponding global form suitable only for linear case. In particular, the formulations we propose can be combined with mixed discrete approximations that can ensure the continuity of tangential component of electric or magnetic field and normal component of electric displacement and magnetic flux even for low order interpolations. The choice of this kind is quite different from currently favorite choice of high order finite element interpolations used for coupling electromagnetism with mechanics. The discrete approximation is based upon Whitney's interpolations representing the vector fields in terms of corresponding differential forms, with electric and magnetic fields as one-form and electric displacement and magnetic flux as two-form. The implementation of interpolations of this kind is made for 3D tetrahedron elements with non-standard approximation parameters defined not only at vertices (for zero-form), but at edges (for one-form) and at facets (for two-form). The results of several numerical simulations are presented to illustrate the performance of different formulations proposed herein.

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Section: Single Field Electrostatic Formulation With Scalar Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

2019

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“…The stresses of the other materials can be high due to their high relative stiffness, entering in plastic regime and affecting the TE in their junctions. This plasticity is ignored in the present work, but in an article recently published [20] it is considered in all materials of the cell.…”

Section: Finite Element Modelmentioning

confidence: 99%

Optimization of pulsed thermoelectric materials using simulated annealing and non-linear finite elements

Moreno-Navarro

Pérez-Aparicio

Gómez‐Hernández

2017

Applied Thermal Engineering

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The objective of this work is to determine the optimal shape, gains and duration of an electric pulse applied to a Peltier cell, together with the length of the thermoelectric to maximize cooling while minimizing electric consumption. For this purpose, a fully coupled, multiphysics, dynamic finite-element model, which solves for the thermal, electric and mechanical fields is used. Because of the demanding computing requirements of the optimization process, a special mesh is designed and a convergence analysis is carried out before using the multiphysics model. The highly nonlinear optimization is done by simulated annealing, a heuristic algorithm in the Markov chain Monte-Carlo family. A preliminary parametric investigation is presented, analyzing the impact of some of the parameters. The results of this preliminary analysis help to understand the effect of the different shapes in the evolution of the cold face temperature. Some of these results are expected and have already been discussed elsewhere, but others can only be explained after further analysis and a full system modeling. Pulse optimization is multiobjective and multiparametric, i.e., it can consider several targets such as maximizing the cooling temperature, the cooling duration or others. The trade-offs between the different targets are studied. In all cases, stresses inside the thermoelement are examined at all points, and the pulses must meet the restriction that an equivalent stress is not above the allowable value.

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Numerical experiment based on non-linear micropolar finite element to study micro-rotations generated by the non-symmetric Maxwell stress tensor

2023

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The main aim of the present work is to investigate the role of the Maxwell stress tensor in the study of active materials. Despite the importance of this tensor in modeling mechatronic devices used in sophisticated applications, its non–symmetry still generates controversies in the literature, probably because classical continuum mechanics assumes a symmetric Cauchy stress, although the sum of Cauchy and Maxwell stresses is non–symmetric. In the framework of generalised continuum mechanics–a more advanced formalism than the classical one–, each material point has an associated microstructure so that the micro–rotations of the electric/magnetic dipoles present in real active materials may be simulated. To this end, a modified total stress formulation, including an angular momentum balance, is developed and implemented into a finite element research code using a complex–step formulation. It is concluded that generalised mechanics allows for incorporating both symmetric and non–symmetric contributions of the Maxwell tensor. Consequently, the rotations generated by the electromagnetic field may be analysed. The influence of the complete Maxwell tensor in a magnetostrictive actuator is studied by several magneto–mechanical numerical experiments of a Terfenol–D rod encircled by air, and several conclusions are highlighted.

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Plasticity coupled with thermo-electric fields: Thermodynamics framework and finite element method computations

Cited by 8 publications

References 13 publications

Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

Optimization of pulsed thermoelectric materials using simulated annealing and non-linear finite elements

Numerical experiment based on non-linear micropolar finite element to study micro-rotations generated by the non-symmetric Maxwell stress tensor

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