Constitutive modeling of magneto-viscoelastic polymers, demagnetization correction, and field-induced Poynting effect

Haldar, Krishnendu

doi:10.1016/j.ijengsci.2021.103488

Cited by 22 publications

(11 citation statements)

References 92 publications

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“…where (•) ,q denotes the derivative of (•) with respect to the qth component, we can rewrite the first variation (56) as…”

Section: Finite Element Formulation For Soft Mapsmentioning

confidence: 99%

“…Based on the seminal theoretical works of Pao and Nemat-Nasser [43], Eringen and Maugin [44], Maugin [45]; Dorfmann and Ogden [46][47][48] and Bustamante and co-workers [49][50][51] developed constitutive frameworks for magneto-mechanics taking into account the underlying isotropy and transverse isotropy for MAPs. Furthermore, Saxena et al [52,53], Nedjar [54], Haldar et al [55,56], Mukherjee et al [57] developed constitutive models that take into account the time-dependent behaviour of polymeric matrices. In contrast to phenomenologically-motivated ideas that are formulated in terms of strain or stretch invariants [58], few constitutive models have been proposed over the years that consider the micro-mechanical information of the MAPs' underlying microstructures.…”

Section: Introductionmentioning

confidence: 99%

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A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers

Kadapa¹,

Hossain²

2021

Preprint

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The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified into two groups: i) hard magnetic MAPs in which a large residual magnetic flux density sustains even after the removal of the external magnetic field, and ii) soft magnetic MAPs where the magnetisation of the filler particles disappear upon the removal of the external magnetic field. Polymeric materials are widely treated as fully incompressible solids that require special numerical treatment to solve the associated boundary value problem. Furthermore, both soft and hard magnetic particles-filled soft polymers are inherently viscoelastic. Therefore, the aim of this paper is to devise a unified finite element method-based numerical framework for magneto-mechanically coupled systems that can work for compressible and fully incompressible materials and from hard to soft MAPs, including the effects of the time-dependent viscoelastic behaviour of the underlying matrix. First, variational formulations for the uncoupled problem for hard MAPs and the coupled problem for soft MAPs are derived. The weak forms are then discretised with higher-order Bézier elements while the evolution equation for internal variables in viscoelastic models is solved using the generalised-alpha time integration scheme, which is implicit and second-order accurate. Finally, a series of experimentally-driven boundary value problems consisting of the beam and robotic gripper models are solved in magneto-mechanically coupled settings, demonstrating the versatility of the proposed numerical framework. The effect of viscoelastic material parameters on the response characteristics of MAPs under coupled magnetomechanical loading is also studied.

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“…where (•) ,q denotes the derivative of (•) with respect to the qth component, we can rewrite the first variation (56) as…”

Section: Finite Element Formulation For Soft Mapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers

Kadapa¹,

Hossain²

2021

Preprint

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“…Microstructural-based models have been reported to understand the underlying magneto-mechanical interactions, i.e., dipole-to-dipole and Zeeman interactions [25]. Also, energy-based phenomenological constitutive models can be found in [26], and full-field numerical homogenization modelling, in [51]. This latter approach provides understanding of microstructural mechanisms that govern the overall response from the consideration of the actual particle distribution and interactions with the matrix.…”

Section: Introductionmentioning

confidence: 99%

Effects of soft and hard magnetic particles on the mechanical performance of ultra-soft magnetorheological elastomers

Moreno-Mateos

López-Donaire

Hossain

et al. 2022

Smart Mater. Struct.

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Magnetorheological elastomers (MREs) mechanically respond to external magnetic stimuli by changing their mechanical properties and/or changing their shape. Recent studies have shown the great potential of MREs when manufactured with an extremely soft matrix and soft-magnetic particles. Under the application of an external magnetic field, such MREs present significant mechanical stiffening, and when the magnetic field is off, they show a softer response, being these alternative states fully reversible. Although soft-magnetic particles are suitable for their high magnetic susceptibility, they require the magnetic actuation to remain constant in order to achieve the magneto-mechanical stiffening. Here, we present an alternative solution based on hard-magnetic MREs to provide stiffening responses that can be sustained along time without the need of keeping the external magnetic field on. To this end, we manufacture novel extremely soft hard-magnetic MREs (stiffness in the order of 1~kPa) and characterise them under magneto-mechanical shear and confined magnetic expansion deformation modes, providing a comparison framework with the soft-magnetic counterparts. The extremely soft nature of the matrix allows for easily activating the magneto-mechanical couplings under external magnetic actuation. In this regard, we provide a novel approach by setting the magnetic actuation below the fully magnetic saturating field. In addition, free deformation tests provide hints on the microstructural transmission of torques from the hard-magnetic particles to the viscoelastic carrier matrix, resulting in macroscopic geometrical effects and complex functional morphological changes.

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“…Balance equations are treated, e.g., in [ 1 , 2 ], while interesting constitutive equations are developed in, e.g., [ 3 , 4 ]. Updated lists of references are given in [ 5 , 6 , 7 ]. Despite the various approaches and procedures developed in the literature, the subject deserves further attention, hopefully to create simpler models.…”

Section: Introductionmentioning

confidence: 99%

“…While balance equations are used as the standard in the literature (see, e.g., [ 6 , 10 , 11 ]), constitutive equations are placed in quite new settings. The modelling through memory functionals involves constitutive equations with a joint dependence on the present values and thermal, deformation, and magnetic field histories so that, at time t, the response of the material is determined by the present values of the temperature

, the deformation gradient

, the magnetic field

, and the temperature gradient

as well as the histories, up to time t ,

…”

Section: Introductionmentioning

confidence: 99%

Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

Giorgi

Morro

2022

Materials

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The properties of viscoelastic solids subject to a magnetic field are modelled within two thermodynamically consistent approaches that are typical of models with a non-instantaneous response. One is based on memory functionals: the reversible changes are described by the instantaneous response, while the dissipativity is expressed by the dependence on histories. The other approach involves objective rate equations. While memory functionals lead to the difficulty of determining thermodynamically consistent free energy functionals, rate equations result in a simpler scheme. The greater simplicity allows the discovery of, in particular, models of magneto-hyperelastic materials, magneto-hypoelastic materials, and various forms of magneto-viscoelastic behaviour. The novelty of the procedure is based on two features: a representation formula, originating from the entropy inequality, and the use of the entropy production as a constitutive function. Relations with other approaches in the literature are examined in detail.

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Constitutive modeling of magneto-viscoelastic polymers, demagnetization correction, and field-induced Poynting effect

Cited by 22 publications

References 92 publications

A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers

A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers

Effects of soft and hard magnetic particles on the mechanical performance of ultra-soft magnetorheological elastomers

Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

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