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This quantity provides a cutting-edge review of the continuum concept of either electro- and magneto-sensitive elastomers and polymers, together with mathematical and computational points of the modelling of those fabrics from the viewpoint of fabric houses and, specifically, the "smart-material" keep watch over in their mechanical homes.

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**Additional resources for Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials (CISM International Centre for Mechanical Sciences)**

**Sample text**

Because of our special interest in fracture and the evaluation of energyrelease rates, the equation of energy associated with equations (179)–(181) is most relevant. To that purpose we note that TF = E ⊗ E − 1 −1 F E·E , 2 E := JF F−1 · E. (183) It is checked that divR TF = −(∇R · Π) E, (184) where we recognize in the quantity within parentheses a so-called polarization charge density. With an objective energy density for a homogeneous material, per unit reference volume, W = W C, E , we have the mechanical and electric constitutive equations S=2 ∂W , ∂C Π=− ∂W ∂E , (185) corresponding to the energy equation (no dissipation of any kind) ˙ ˙ − Π · E.

Between, the ordered array of atoms and magnetic spins in a perfect ferromagnetic crystal and the iron-nickel plates used in building transformers. Easily identiﬁable scales in this problem are those of the atomic structure (10−9 meters), of the magnetic domain, of the grain-monocrystal (10−6 meters), of the representative volume element (RVE) of a polycrystal (10−3 meters), and the industrial scale of the order of 10−1 –100 meters. Basic physical mechanisms are really at the smallest scale having a quantum-physical justiﬁcation (without which magnetism would not exist at all).

Finally, Eshelbian mechanics and the theory of material inhomogeneities as viewed by the author provide an eﬃcient means to formulate the relevant problems of fracture and propagation of ﬁeld discontinuities (Section 6). Electromagnetics in Deformable Solids 51 Bibliography A. N. Abd-Alla and G. A. Maugin. Nonlinear magnetoacoustic equations. J. Acoust. Soc. Am. 82:1746–1752, 1987. E. Bassiouny, A. F. Ghaleb, and G. A. Maugin. Thermodynamical formulation for coupled electromechanical hysteresis eﬀects – basic equations.