On the Modelling and Computation of Magneto-Sensitive-Elastomers

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Magneto-sensitive-elastomers are smart materials which are composed of a rubber-like basis matrix filled with magneto-active particles. Due to the highly elastic properties of the rubberlike material, these compounds are able to deform significantly, i.e. geometrically non-linearly by the application of external magnetic fields. The rapid response, the high level of deformations that may be achieved, and the possibility of controlling these deformations by varying an external magnetic field, make these materials of special interest; e.g., for vibration and noise suppression. Thus, there is an urgent need for research on this novel material class in terms of modelling within the framework of geometrically nonlinear continuum physics and in the area of suitable computational methods in order to simulate technologically relevant benchmark problems. In this proposal, three main objectives are pursued: (i) the discussion and formulation of appropriate boundary conditions for the coupled magneto-elastic problem, in particular the correct acknowledgement of the influence of the magnetic field on the mechanical boundary conditions; (ii) the development of simple and at the same time realistic forms for the constitutive equations, respecting the microstructural features and including a careful analysis of the ellipticity (or infinitesimal rank-one convexity) condition; and, finally, an objective of utmost importance is (iii) to solve relevant nonlinear boundary value problems by resorting to a newly developed finite element method.