Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure

Abstract

Saxena, P., Pelteret, J.-P. and Steinmann, P. (2015) Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure. AbstractMagneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.

The Magneto-Mechanical Behavior of Active Components in Iron-Elastomer Composite

“…Both factors result in the extension of the linear viscoelastic regime to larger strain amplitudes and lead to higher shear storage and loss of moduli values [21,22]. The particle-particle dipolar interaction is explained in the schematic diagram (Figure 16) based on the various vector and angular positions that play the active role in the dipolar moment, contributing to the magneto-rheological effect in the MRE sample in the presence of a magnetic field [23], and also according to the continuum based model proposed in the literature [24][25][26][27].…”

Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space

“…In the absence of free charges, the governing equations for electro‐statics as given by Faraday's law of induction and Gauss's law in terms of referential quantities are Here, and respectively denote the electric field and displacement (sometimes called the electric induction) vectors, as defined in the material configuration. Alternatively, assuming that the material is electrically non‐conductive and that there exist no free currents, then the static form of Maxwell's equations are defined by Ampére's law and Gauss's law dictating that no magnetic monopoles are present , that is, The referential magnetic field and induction vectors are given by and respectively. The continuity conditions on are given by either of …”

“…Fundamentally, a different behaviour is demonstrated by MAPs, with either magnetostriction or magneto-elongation developing depending on the arrangement of their microstructure [8][9][10][11][12]. Analysis of the constitutive response of such materials [13][14][15][16][17][18] typically assumes that the body is incompressible.…”

“…Numerous examples of finite-strain-coupled numerical models of EAPs [19][20][21][22][23][24][25] and MAPs [18,26,27] can be found in the literature. In the context of electro-elastic problems, mixed variational principals have been used by Ortigosa and Gil [28], Rodríguez-Ramos et al [29], Yang and Batra [30] and Zwecker et al [21].…”

“…Here, E and D respectively denote the electric field and displacement (sometimes called the electric induction) vectors, as defined in the material configuration. Alternatively, assuming that the material is electrically non-conductive and that there exist no free currents, then the static form of Maxwell's equations are defined by Ampére's law and Gauss's law dictating that no magnetic monopoles are present [18,41,43,44], that is,…”