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

by jppelteret

Authors: J-P. V. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann

In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media. [1]

[1] [doi] J-P. V. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann, “Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space,” International Journal for Numerical Methods in Engineering, vol. 108, iss. 11, pp. 1307-1342, 2016.
[Bibtex]
@Article{pelteret2016a-preprint,
author = {Pelteret, J-P. V. and Davydov, D. and McBride, A. and Vu, D. K. and Steinmann, P.},
title = {Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space},
journal = {International Journal for Numerical Methods in Engineering},
year = {2016},
volume = {108},
number = {11},
pages = {1307--1342},
abstract = {In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media.},
comment = {PREPRINT},
doi = {10.1002/nme.5254},
file = {pelteret2016a-preprint.pdf:PDF/pelteret2016a-preprint.pdf:PDF},
keywords = {Nonlinear electro-/magneto-elasticity; quasi-incompressible media; free space; finite strain},
owner = {Jean-Paul Pelteret},
timestamp = {2016.03.21},
}

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},
}