Numerical solution of finite geometry boundary-value problems in nonlinear magnetoelasticity

This paper provides examples of the numerical solution of boundary-value problems in nonlinear magnetoelasticity involving finite geometry based on the theoretical framework developed by Dorfmann and co-workers. Specifically, using a prototype constitutive model for isotropic magnetoelasticity, we c...

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Bibliographic Details
Published in:International journal of solids and structures 2011-03, Vol.48 (6), p.874-883
Main Authors: Bustamante, R., Dorfmann, A., Ogden, R.W.
Format: Article
Language:English
Subjects:
74B20
74F15
74G15
Blocking
Boundary value problems
Deformation
Exact sciences and technology
Finite deformation
Fundamental areas of phenomenology (including applications)
Magnetic fields
Magnetoelasticity
Mathematical analysis
Mathematical models
Nonlinear elasticity
Nonlinearity
Numerical solution
Physics
Shear stress
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
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Summary:This paper provides examples of the numerical solution of boundary-value problems in nonlinear magnetoelasticity involving finite geometry based on the theoretical framework developed by Dorfmann and co-workers. Specifically, using a prototype constitutive model for isotropic magnetoelasticity, we consider two two-dimensional problems for a block with rectangular cross-section and of infinite extent in the third direction. In the first problem the deformation induced in the block by the application of a uniform magnetic field far from the block and normal to its larger faces without mechanical load is examined, while in the second problem the same magnetic field is applied in conjunction with a shearing deformation produced by in-plane shear stresses on its larger faces. For each problem the distribution of the magnetic field throughout the block and the surrounding space is illustrated graphically, along with the corresponding deformation of the block. The rapidly (in space) changing magnitude of the magnetic field in the neighbourhood of the faces of the block is highlighted.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2010.11.021