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Magnetodeformation effect of the elastomer with the magnetized
polydisperse spherical inclusions

A. A. Pan’kov

State National Research Politechnical University of Perm

**The paper is
received on
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M**arch 18, 2015**

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**Abstract.
O**n the basis of two-level
structural mathematical models of mechanics of composites the magnetodeformation effect of unique ability of elastomers with magnetic
microparticles to fast and controlled considerable deformations in magnetic
fields is investigated. The exact analytical decision for the macroscopic and
structural magnetodeformation fields arising at a bend of a cylindrical hollow
console core with polydisperse structure from unidirectionally magnetized
spherical inclusions in an elastomer in an external quasistatic magnetic field
is received. The new analytical decision for residual magnetization of a
composite and the decision for a deformation field in an elastomer of a
compound spherical cell from action on inclusion of the rotating magnetic
moment is given. Statement of a boundary-value problem of elasticity theory for
finding of macro-level fields of deformation with the formulation of boundary
conditions is proved and given in tension on face, internal and external
lateral surfaces of a hollow cylindrical console core with uniform effective
elastic properties. Settlement schemes for the solution of this problem on the
elasticity theory and are provided in the simplified look for a curved axis of
a hollow core. The analysis of influence of a volume fraction of the magnetized
spherical inclusions on a flexural deformativnost of a composite core is
carried out. Nonmonotonic nature of this dependence is established and optimum
values of a volume fraction of inclusions are defined. The conclusion is drawn
on need of a choice of an elastomer with high magnetic permeability and small
rigidity on stretching.

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****Key
words:
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magnetic field, magnetooperated elastomer,
magnetized structure, composite, effective properties.