Nonlinear magnetoelastic deformations

Dorfmann, Luis

doi:10.1093/qjmam/57.4.599

Cited by 175 publications

(226 citation statements)

References 0 publications

Supporting

Mentioning

220

Contrasting

Unclassified

Order By: Relevance

“…For the constitutive law we again use the notation Ω for the energy density function, per unit volume in B 0 , but now it is a function of F and B l : Ω(F, B l ) [24]. This yields the Lagrangian relations…”

Section: Magnetostaticsmentioning

confidence: 99%

“…where K l is as defined following (24), σ E as in (15), and V s = F −1 v s . The boundary (jump) conditions associated with equations (40) are…”

Section: Lagrangian Formulationmentioning

confidence: 99%

“…They appear to have been used first by McCarthy [19,20], in the context of acceleration wave propagation, and an independent derivation was give by Lax and Nelson [21]; see also Maugin [5], for example. The Lagrangian equations have an important role, in particular in the context of configurational forces (see, for example, [16], [22,23]), and have also led, at least in the static context, to rather elegant general formulations of the constitutive laws and the accompanying equilibrium equations for magnetoelastic [24] and electroelastic [25] solids capable of undergoing finite deformations. Such formulations have facilitated the solution of a number of boundary-value problems for both magnetoelasticity and electroelasticity (see, for example, [26,27,28]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Ogden¹

2009

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.

show abstract

Section: Magnetostaticsmentioning

confidence: 99%

“…where K l is as defined following (24), σ E as in (15), and V s = F −1 v s . The boundary (jump) conditions associated with equations (40) are…”

Section: Lagrangian Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Ogden¹

2009

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

show abstract

“…Other constitutive models for nonlinear magnetoelastic response have been suggested in [2,3,5]. The associated thermodynamically-consistent constitutive relations follow from (1) and the general relations P t = ∂ Fψ * and −B = ∂ Hψ * as …”

Section: An Invariant Formulation Of Isotropic Nonlinear Finite Magnementioning

confidence: 99%

“…Recently, the field of non-linear magnetoelasticity has received considerable interest [1][2][3][4][5]. In this paper we discuss the necessity of accounting for free space contributions in constitutive modeling and the solving of boundary value problems in magnetomechanics.…”

Section: Introductionmentioning

confidence: 99%

Geometrical Aspects of the Incorporation of Free Space in Magnetomechanics at Finite Strains

Kiefer

Rosato

Miehé

2009

Proc Appl Math and Mech

View full text Add to dashboard Cite

This paper addresses the modeling of finite magnetoelasticity with a particular focus on the incorporation of free space energy storage and magnetic body forces. First, a coordinate-invariant formulation of an extended Neo-Hookean model with magnetostrictive coupling is presented. Then, a finite element model for finite magnetomechanics based on a variational stationarity principle is formulated. The influence of magnetic body forces is studied in an exemplary boundary value problem.

show abstract

The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

Saber

2023

Adv Eng Mater

View full text Add to dashboard Cite

The magnetorheological elastomers (MREs) are novel multifunctional materials wherein their viscoelastic properties can be varied instantly under an application of applied magnetic field. Due to their field‐dependent stiffness and damping properties, MREs are widely used in the development and design of MRE‐based adaptive vibration isolators and absorbers and also biomedical engineering. Moreover, MREs due to their inherent magnetostriction effect have enormous potential for the development of soft actuators. The dynamic behavior of MREs is affected by various material parameters (e.g., matrix and particle types, particle concentration, additives) as well as mechanical and magnetic loading parameters (e.g., frequency, amplitude, temperature, magnetic flux density). Understanding and predicting the effect of materials and loading parameters on the response behavior of MREs are of paramount importance for the design of MRE‐based adaptive structures and systems. This review paper mainly aims to provide a comprehensive study of material constitutive models to predict the nonlinear magnetomechanical behavior of MREs. Particular emphasis is paid to physics‐based models including continuum‐ and microstructure‐based models. Moreover, phenomenological models describing the dynamic magnetoviscoelastic behavior of MREs as well as the effect of temperature on the magnetomechanical behavior of such materials are properly addressed.

show abstract

Nonlinear magnetoelastic deformations

Cited by 175 publications

References 0 publications

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Geometrical Aspects of the Incorporation of Free Space in Magnetomechanics at Finite Strains

The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

Contact Info

Product

Resources

About