Nonlinear magnetoelastic deformations of elastomers

• Published in: Acta mechanica Vol. 167; no. 1-2; pp. 13 - 28
• Main Authors: Dorfmann, A., Ogden, R.W.
• Format: Journal Article
• Language: English
• Published: Wien Springer 01.01.2004; New York, NY Springer Nature B.V
• Subjects: Elastomers; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Magnetic fields; Mechanical properties; Physics; Solid mechanics; Structural and continuum mechanics; Theory and numerical methods; Constitutive equation; Elastomer; Circular cylinder; Magnetomechanical properties; Cylindrical shell; Non linear effect; Modeling; Magnetoelastic effect; Lagrange equation; Smart materials; Strength
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-003-0061-2

Magneto-sensitive (MS) elastomers are 'smart materials' whose mechanical properties may be changed rapidly by the application of a magnetic field. Such materials typically consist of micron-sized ferrous particles dispersed within an elastomeric matrix. The equations governing deformations of these materials were discussed in a recent paper by the present authors and applied in a particular specialization of the constitutive model to the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field. In the present paper we develop the governing equations for a more general form of constitutive model and provide alternative forms of the equations, including a Lagrangian formulation. To illustrate the theory the problem of azimuthal shear of a circular cylindrical tube is formulated and then solved for a specific constitutive law with a magnetic field that is initially radial. The results, which show the stiffening of the azimuthal shear stress/strain response with increasing magnetic field strength, are illustrated graphically. [PUBLICATION ABSTRACT]