Nonlinear Magnetoelastic Deformations

Magneto-sensitive (MS) elastomers are materials that change their mechanical behavior in response to the application of magnetic fields. They have attracted considerable interest recently because of their potential for providing relatively simple and quiet variable-stiffness devices for use as rapid-response interfaces between electronic controls and mechanical systems. Applications include adaptive tuned vibration absorbers, stiffness tunable mounts and suspensions and automotive bushing. Typically, the magnetic response is achieved and optimized by distributing within an elastomeric matrix particles with a high magnetic saturation, such as an alloy of iron, and volume fractions between 0.1 and 0.5. The choice of the matrix material is based on its thermomechanical properties and, for example, silicone and other elastomers are also used.

We have developed several alternative formulations of the governing equilibrium equations for nonlinear magnetoelastic deformations of magneto-sensitive solids, and have applied the theory in the solution of several illustrative boundary-value problems. In our paper on Nonlinear Magnetoelastic Deformations (QJMAM 2004) we provide a new, rather elegant and simple formulation based on the use of a modified free-energy function with the referential magnetic induction vector as the independent magnetic variable. We also provided an alternative formulation with the magnetic field itself as the independent variable.

Publications:

Bustamante R., Dorfmann A., Ogden R.W.: Numerical solution of finite geometry boundary-value problems in nonlinear magnetoelasticity. International Journal of Solids and Structures 48 (2011), 874-883.

Bustamante R., Dorfmann A., Ogden R.W.: On Variational Formulations in Nonlinear Magnetoelastostatics, Mathematics and Mechanics of Solids 13 (2008), 725-745.

Bustamante R., Dorfmann A., Ogden R.W.: A Nonlinear Magnetoelastic Tube under Extension and Inflation in an Axial Magnetic Field: Numerical Solution, Journal of Engineering Mathematics 59 (2007), 139-153.

Bustamante R., Dorfmann A.: Ogden R.W., Universal Relations in Isotropic Nonlinear Magnetoelasticity, The Quarterly Journal of Mechanics and Applied Mathematics 59 (2006), 435-450

Dorfmann A., Ogden R.W.: Some Problems in Nonlinear Magnetoelasticity, Zeitschrift für Angewandte Mathematik und Physik (ZAMP)  56 (2005), 718-745.

Dorfmann A., Ogden R.W.: Nonlinear Magnetoelastic Deformations, The Quarterly Journal of Mechanics and Applied Mathematics 57 (2004), 599-622.

Dorfmann A., Ogden R.W. Saccomandi G.: Universal Relations for Magnetoelastic Solids, International Journal of Non-Linear Mechanics 39 (2004), 1699-1708.

Dorfmann A., Ogden R.W.: Magnetoelastic Modelling of Elastomers, European Journal of Mechanics - A/Solids 22 (2003), 497-507.

Brigadnov I.A., Dorfmann A.: Mathematical Modelling of Magneto-Sensitive Elastomers, International Journal of Solids and Structures 40 (2003), 4659-4674.