Finite element simulation of rate-dependent magneto-active polymer response

Abstract

This contribution is concerned with the embedding of constitutive relations for magneto-active polymers (MAP) into finite element simulations. To this end, a recently suggested, calibrated, and validated material model for magneto-mechanically coupled and rate-dependent MAP response is briefly summarized in its continuous and algorithmic settings. Moreover, the strongly coupled field equations of finite deformation magneto-mechanics are reviewed. For the purpose of numerical simulation, a finite element model is then established based on the usual steps of weak form representation, discretization and consistent linearization. Two verifying inhomogeneous numerical examples are presented in which a classical 'plate with a hole' geometry is equipped with MAP properties and subjected to different types of time-varying mechanical and magnetic loading.

Limit points in the free inflation of a magnetoelastic toroidal membrane

“…By appropriately considering the micromechanical constitution of magnetoelastic polymers, formulations for coupled field equations using homogenisation techniques have been proposed by Castañeda and Galipeau (2011);Galipeau and Castañeda (2013) and Chatzigeorgiou et al (2014), among others. Phenomenon of energydissipation due to viscoelasticity has been modelled by Saxena et al (2013), Ethiraj and Miehe (2016), and Haldar et al (2016); and anisotropic structure of magnetoelastic polymers has been accounted in the models by Bustamante (2010), Danas et al (2012a), and Saxena et al (2014). However, in this work, we restrict our attention to isotropic and conservative magnetoelastic systems.…”

Finite deformations and incremental axisymmetric motions of a magnetoelastic tube

“…To work with the governing equations (29) and (28) in the presence of an azimuthal magnetic field, the non-zero components of the magnetoelastic tensors are A 0iiii , A 0iijj , A 0ijij , A 0ijji , C 0ii2 , C 0i2i , K 0ii for i, j ∈ {1, 2, 3} and i = j. Explicit formulas for these components for the Mooney-Rivlin magnetoelastic material are given in the Appendix.…”

“…Since both EAPs and MREs are polymer based composites, the deformation process is usually dissipative. The effect of the magnetic field on the viscoelasticity has been studied by Bellan and Bossis [24], the effect on the Mullin’s effect studied by Coquelle and Bossis [25], magneto-viscoelasticity of isotropic and anisotropic MREs was studied by Saxena et al [26, 27] and Haldar et al [28] and a micromechanical approach to study magneto-viscoelasticity has been undertaken by Ethiraj and Miehe [29]. A similar case of dissipation in the electro-viscoelastic case has been studied by Ask et al [30], Saxena et al [31] and Denzer and Menzel [32].…”

Magnetoelastic deformation of a circular membrane: Wrinkling and limit point instabilities

“…Several advanced techniques have been proposed to model additional features of the particle-filled magnetoelastic smart elastomers. For example, Castañeda and Galipeau (2011); Castaneda and Siboni (2012) and Chatzigeorgiou et al (2014) formulated the field equations by coupling magneto-mechanical phenomena at the microscopic level and the use of homogenization; Saxena et al (2013); Ethiraj and Miehe (2016) and Haldar et al (2016) modelled the energy dissipation due to coupled polymer magneto-viscoelasticity; Bustamante (2010); Danas et al (2012) and Saxena et al (2014Saxena et al ( , 2015 modelled the inherent anisotropy and resulting changes in the magneto-mechanical response of these polymers. Several of the above-mentioned models have been useful in computational analysis of instabilities in magnetoelastic bulk media reported by Otténio et al (2008); Kankanala and Triantafyllidis (2008); Rudykh and Bertoldi (2013); Danas and Triantafyllidis (2014); Saxena (2017), and Goshkoderia and Rudykh (2017).…”