A variational, finite‐deformation constitutive model for piezoelectric materials

Mota, Alejandro; Zimmerman, Jonathan A.

doi:10.1002/nme.2993

Cited by 8 publications

(2 citation statements)

References 29 publications

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“…Compared with recent works on the same theme (e.g. [14]) the inclusion of the magnetic field, the derivation of novel electro-magnetic wave equations and the generalization of the boundary conditions were the major contributions. Further improvements in the number of ingredients and depth of numerical tests are being performed.…”

Section: Discussionmentioning

confidence: 99%

Damage-based fracture with electro-magnetic coupling

et al. 2012

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A coupled elastic and electro-magnetic analysis is proposed including finite displacements and damage-based fracture. Piezo-electric terms are considered and resulting partial differential equations include a non-classical wave equation due to the specific constitutive law. The resulting wave equation is constrained and, in contrast with the traditional solutions of the decoupled classical electromagnetic wave equations, the constraint is directly included in the analysis. The absence of free current density allows the expression of the magnetic field rate as a function of the electric field and therefore, under specific circumstances, removal of the corresponding magnetic degrees-offreedom. A Lagrange multiplier field is introduced to exactly enforce the divergence constraint, forming a three-field variational formulation (required to include the wave constraint). No vector-potential is required or mentioned, eliminating the need for gauges. The classical boundary conditions of electromagnetism are specialized and a boundary condition involving the electric field is obtained. The spatial discretiza-

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Section: Discussionmentioning

confidence: 99%

Damage-based fracture with electro-magnetic coupling

et al. 2012

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“…where A I is the I-th component of the vector potential and is an arbitrary scalar potential in the reference configuration. The non-uniqueness of the potentials is averted by applying a Coulomb gauge condition [27,44,45], stated as:…”

Section: Governing Equations In the Reference Configuration (Lagrangimentioning

confidence: 99%

Wavelet transformation induced multi-time scaling (WATMUS) model for coupled transient electro-magnetic and structural dynamics finite element analysis

Yaghmaie

Guo

Ghosh

2016

Computer Methods in Applied Mechanics and Engineering

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Multi-functional devices that integrate electromagnetic and mechanical fields are gaining importance in a wide variety of applications. The combined mechanical and electromagnetic regimes, encompassed in these structures, make it necessary to develop e ective multi-physics analysis tools at a range of temporal scales. An important consideration is that the di erent fields governing multi-physics response may have large frequency discrepancies, e.g. the ultra-high electromagnetic frequencies and moderate vibration frequencies. Computational analyses of these discrepant frequency problems using conventional time integration schemes can become intractable. This paper develops a framework for coupling transient electromagnetic and dynamic fields to predict the evolution of electric and magnetic fields and their fluxes in a vibrating substrate undergoing finite deformation. It addresses the issue of time integration with large frequency ratios, by introducing a novel wavelet transformation induced multi-time scaling (WATMUS) method in the finite element framework. The method significantly enhances the computational e ciency in comparison with conventional single time scale integration methods. An adaptive enhancement of WATMUS scheme allows for the optimal wavelet bases in the transformation and integration step sizes. The accuracy and e ciency of the proposed WATMUS scheme is verified by comparing

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A finite element model for coupled 3D transient electromagnetic and structural dynamics problems

Guo

Ghosh

2014

Comput Mech

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A variational, finite‐deformation constitutive model for piezoelectric materials

Cited by 8 publications

References 29 publications

Damage-based fracture with electro-magnetic coupling

Damage-based fracture with electro-magnetic coupling

Wavelet transformation induced multi-time scaling (WATMUS) model for coupled transient electro-magnetic and structural dynamics finite element analysis

A finite element model for coupled 3D transient electromagnetic and structural dynamics problems

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