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3 Articles

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

by jppelteret

Authors: P. Saxena, J-P. V. Pelteret, and P. Steinmann

Magneto-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. [1]

[1] [pdf] [doi] P. Saxena, J-P. V. Pelteret, and P. Steinmann, “Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure,” European Journal of Mechanics A/Solids, vol. 50, pp. 132-151, 2015.
[Bibtex]
@Article{saxena2015a-preprint,
author = {Saxena, P. and Pelteret, J-P. V. and Steinmann, P.},
title = {Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure},
journal = {European Journal of Mechanics A/Solids},
year = {2015},
volume = {50},
pages = {132--151},
month = {March--April},
abstract = {Magneto-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.},
doi = {10.1016/j.euromechsol.2014.10.005},
file = {saxena2015a-preprint.pdf:PDF/saxena2015a-preprint.pdf:PDF},
keywords = {Nonlinear magnetoelasticity; Anisotropy; Chain dispersion},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Magnetic force and torque on particles subject to a magnetic field

by jppelteret

Authors: F. Vogel, J-P. V. Pelteret, S. Kaessmair, and P. Steinmann

Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier. [1]

[1] [pdf] [doi] F. Vogel, J-P. V. Pelteret, S. Kaessmair, and P. Steinmann, “Magnetic force and torque on particles subject to a magnetic field,” European Journal of Mechanics A/Solids, vol. 48, pp. 23-31, 2014.
[Bibtex]
@Article{vogel2014a-preprint,
author = {Vogel, F. and Pelteret, J-P. V. and Kaessmair, S. and Steinmann, P.},
title = {Magnetic force and torque on particles subject to a magnetic field},
journal = {European Journal of Mechanics A/Solids},
year = {2014},
volume = {48},
pages = {23--31},
month = {November--December},
abstract = {Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier.},
doi = {10.1016/j.euromechsol.2014.03.007},
file = {vogel2014a-preprint.pdf:PDF/vogel2014a-preprint.pdf:PDF},
keywords = {Magnetoactive materials; Magnetoelasticity; Finite-element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Comparison of several staggered atomistic-to-continuum concurrent coupling strategies

by jppelteret

Authors: D. Davydov, J-P. V. Pelteret, and P. Steinmann

In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented. Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance. [1]

[1] [pdf] [doi] D. Davydov, J-P. Pelteret, and P. Steinmann, “Comparison of several staggered atomistic-to-continuum concurrent coupling strategies,” Computer Methods in Applied Mechanics and Engineering, vol. 277, pp. 260-280, 2014.
[Bibtex]
@Article{davydov2014a-preprint,
author = {Davydov, D. and Pelteret, J-P. and Steinmann, P.},
title = {Comparison of several staggered atomistic-to-continuum concurrent coupling strategies},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2014},
volume = {277},
pages = {260--280},
month = {August},
abstract = {In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented.
Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance.},
doi = {10.1016/j.cma.2014.04.013},
file = {davydov2014a-preprint.pdf:PDF/davydov2014a-preprint.pdf:PDF},
keywords = {Concurrent multiscale methods; Atomic-to-continuum coupling methods; Molecular mechanics; Irving-Kirkwood-Noll procedure; Finite elements; Large strain},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}