Journal ArticleDOI
Equilibrium theory for magnetic elastomers and magnetoelastic membranes
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TLDR
In this paper, a theory for the equilibrium response of magnetoelastic membranes under pressure and applied magnetic fields is formulated on the basis of three-dimensional magneto-elasticity.Abstract:
A theory for the equilibrium response of magnetoelastic membranes under pressure and applied magnetic fields is formulated on the basis of three-dimensional magnetoelasticity. A variational principle admitted by the three-dimensional theory is used to generate a model for membranes regarded as thin three-dimensional bodies. Minimum energy considerations in the presence of applied magnetic fields are used to motivate a direct theory of magnetoelastic membranes which does not require information about bulk properties. The theory is applicable to conventional elastomers magnetized through infusion with uniformly dispersed ferrous particles.read more
Citations
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Journal ArticleDOI
Analytical continuum mechanics à la Hamilton-Piola least action principle for second gradient continua and capillary fluids
TL;DR: In this article, a Lagrangian action is proved to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments.
Journal ArticleDOI
Nonlinear magnetoelastic deformations of elastomers
A. Dorfmann,Ray W. Ogden +1 more
TL;DR: In this paper, the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field was formulated and then solved for a specific constitutive law with a magnetic field that is initially radial.
Journal ArticleDOI
Computational homogenization in magneto-mechanics
TL;DR: A geometrically nonlinear homogenization framework for composites with magneto-mechanical behavior whereby the composite can be subject to large deformation processes is presented in this article.
Journal ArticleDOI
On Variational Formulations in Nonlinear Magnetoelastostatics
TL;DR: In this article, two new variational principles for nonlinear magnetoelastostatics are derived based on use of two independent variables: the deformation function and the magnetostatic vector potential.
Journal ArticleDOI
Transversely isotropic nonlinear magneto-active elastomers
TL;DR: In this paper, the authors provided a theoretical basis for the description of the nonlinear properties of a particular class of these materials, namely transversely isotropic magneto-active elastomers, and developed a general form of the constitutive law for such magnetoelastic solids.
References
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Book
Nonlinear Functional Analysis
TL;DR: A survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis can be found in this article, with extensive commentary, many examples, and interesting, challenging exercises.
Book
An introduction to continuum mechanics
Morton E. Gurtin,W. J. Drugan +1 more
TL;DR: In this paper, the NavierStokes Equations are used to define linear elasticity for tensor analysis, and the invariance of material response is established. But the analysis is restricted to finite elasticity and cannot be extended to infinite elasticity.
Journal ArticleDOI
Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber
R. S. Rivlin,D. W. Saunders +1 more
TL;DR: In this paper, it was shown that the load-deformation curves obtained for certain simple types of deformation of vulcanized rubber test-pieces in terms of a single stored energy function can be interpreted on the basis of the theory of large elastic deformations of incompressible isotropic materials.
Book ChapterDOI
Large Elastic Deformations of Isotropic Materials
TL;DR: In this paper, the equilibrium of a cube of incompressible, neo-Hookean material, under the action of three pairs of equal and oppositely directed forces f 1, f 2, f 3, applied normally to, and uniformly distributed over, pairs of parallel faces of the cube, is studied.