A form-finding strategy for magneto-elastic actuators

Ciambella, Jacopo; Tomassetti, Giuseppe

doi:10.1016/j.ijnonlinmec.2019.103297

Cited by 16 publications

(17 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our theoretical results supplemented by the discrete simulation are in excellent agreement with the experimental results. Moreover, the magnetic Kirchhoff rod equations reproduce the previous results on the planar deformation of hard magnetic beams or elastica [28,30,32,35]. We confirmed that the force and moment balance equations in our theory for hard magnetic rods reduce to those of Refs.…”

Section: Discussionsupporting

confidence: 90%

“…In Sec. 3.4, we show that our framework reproduces previous works on the planar deformation of hard magnetic beams and elastica [28,31,32,35], whereas in Sec. 6 we will employ our framework to study cases where the deformation is three-dimensional.…”

Section: Theory Of a Kirchhoff-like Equation For Hard Magnetic Elastic Rodssupporting

confidence: 83%

“…Combining the fact that our framework reproduces the previous results on the planar deformation (Sec. 3.4) [28,31,32,35] and the results presented in this subsection, the magnetic Kirchhoff equation ( 20) and ( 21) correctly predict the large deformation of naturally straight hard MRE rods. Next, we focus on the deformation of hard MRE rods that are naturally curved .…”

Section: Twist Instability Of a Straight Magnetic Rod Under Magnetic Loadingmentioning

confidence: 63%

See 2 more Smart Citations

A Kirchhoff-like theory for hard magnetic rods under three-dimensional geometrically nonlinear deformation

Sano¹

2020

Preprint

View full text Add to dashboard Cite

Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric (soft) matrix. By applying a strong magnetic field, one can magnetize the structure to program its deformation under the subsequent application of an external field. There is a variety of types of MREs depending on the value of their coercivity (i.e. the necessary field strength to erase the magnetization) that can be broadly classified into soft or hard MREs. Hard MREs, whose coercivities are large, have been receiving particular attention because the programmed magnetization remains unchanged upon actuation. Hence, once a structure made of a hard MRE is magnetized, it can be regarded as magnetized permanently. Motivated by a new realm of applications, there have been significant theoretical developments in the continuum (3D) description of hard MREs. By reducing the 3D description into 1D or 2D via dimensional reduction, several theories of hard magnetic slender structures such as linear beams, elastica, and shells have been recently proposed. In this paper, we derive an effective theory for MRE rods (slender, mono-dimensional structures) under geometrically nonlinear 3D deformation. Our theory is based on reducing the 3D magneto-elastic energy functional for the hard MREs into a 1D Kirchhoff-like description (centerline-based). Restricting the theory to 2D, we reproduce previous works on planar deformations. For further validation in the general case of 3D deformation, we perform precision experiments with both naturally straight and curved rods under either constant or constant-gradient magnetic fields. Our theoretical predictions are in excellent agreement with both discrete simulations and precision-model experiments. Finally, we discuss some limitations of our framework, as highlighted by the experiments, where longrange dipole-dippole interactions, which are neglected in the theory, can play a role.

show abstract

Section: Discussionsupporting

confidence: 90%

Section: Theory Of a Kirchhoff-like Equation For Hard Magnetic Elastic Rodssupporting

confidence: 83%

Section: Twist Instability Of a Straight Magnetic Rod Under Magnetic Loadingmentioning

confidence: 63%

See 1 more Smart Citation

A Kirchhoff-like theory for hard magnetic rods under three-dimensional geometrically nonlinear deformation

Sano¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Our proposed model augments the set of emerging reduced models for slender structures, for planar beams (Yan et al, 2021;Wang et al, 2020;Ciambella et al, 2018;Ciambella and Tomassetti, 2020) and Kirchhoff-like rods (Sano et al, 2021). Moreover, our reduced model extends the shell model presented in (Yan et al, 2020), which was restricted to axisymmetric deformations, now to non-axisymmetric configurations.…”

Section: Conclusion and Discussionmentioning

confidence: 86%

A geometrically exact model for thin magneto-elastic shells

Pezzulla,

Yan,

Reis

2021

Preprint

View full text Add to dashboard Cite

We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love assumption, we derive a reduced two-dimensional magneto-elastic energy that can be minimized through numerical analysis. In parallel, we simplify the reduced energy by expanding it up to the second order in the displacement field and provide a physical interpretation. Our theoretical analysis allows us to identify and interpret the two primary mechanisms dictating the magneto-elastic response: a combination of equivalent magnetic pressure and forces at the first order, and distributed magnetic torques at the second order. We contrast our reduced framework against a three-dimensional nonlinear model by investigating three test cases involving the indentation and the pressure buckling of shells under magnetic loading. We find excellent agreement between the two approaches, thereby verifying our reduced model for shells undergoing nonlinear and non-axisymmetric deformations. We believe that our model for magneto-elastic shells will serve as a valuable tool for the rational design of magnetic structures, enriching the set of reduced magnetic models.

show abstract

“…The theory of bulk magneto-elasticity was studied in the 1950s with the pioneering works of Brown [3], Truesdell, Toupin and Tiersten [35] and later formulated in the context of large strain elasticity by Dorfmann and Ogden [16] and Kankanala and Triantafyllidis [25]. The advantage of structural theories with magnetic forcing terms lies in their analytical tractability which allows, for instance, to study closed form solution for buckling and postbuckling regimes as well as inverse problems related to shape optimization [9,18,27,32].…”

Section: Introductionmentioning

confidence: 99%

A theory of magneto-elastic nanorods obtained through rigorous dimension reduction

Ciambella¹,

Kružík²,

Tomassetti³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Starting from a two-dimensional theory of magneto-elasticity for fiber-reinforced magnetic elastomers we carry out a rigorous dimension reduction to derive a rod model that describes a thin magneto-elastic strip undergoing planar deformations. The main features of the theory are the following: a magneto-elastic interaction energy that manifests itself through a distributed torque; a penalization term that prevent local interpenetration of matter; a regularization that depends on the second gradient of the deformation and models microstructure-induced size effects. As an application, we study a problem involving magnetically-induced buckling and we show that the intensity of the field at the onset of the instability increases if the length of the rod is decreased. Finally, we assess the accuracy of the deduced model by performing numerical simulations where we compare the two-dimensional and the one-dimensional theory in some special cases and we observe excellent agreement.

show abstract

A form-finding strategy for magneto-elastic actuators

Abstract: Non-linear mechanics problems with emphasis on hysteretic and stochastic behavior aspects.

Cited by 16 publications

References 29 publications

A Kirchhoff-like theory for hard magnetic rods under three-dimensional geometrically nonlinear deformation

A Kirchhoff-like theory for hard magnetic rods under three-dimensional geometrically nonlinear deformation

A geometrically exact model for thin magneto-elastic shells

A theory of magneto-elastic nanorods obtained through rigorous dimension reduction

Contact Info

Product

Resources

About