By Luis Dorfmann, Ray W. Ogden
This book offers a unified concept on nonlinear electro-magnetomechanical interactions of soppy fabrics in a position to huge elastic deformations. The authors contain an overview of the elemental rules of the vintage idea of electromagnetism from the basic notions of element fees and magnetic dipoles via to distributions of cost and present in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize suitable theories of continuum mechanics, required to account for the deformability of fabric and current a constitutive framework for the nonlinear magneto-and electroelastic interactions in a hugely deformable fabric. The equations contained within the e-book formulate and remedy quite a few consultant boundary-value difficulties for either nonlinear magnetoelasticity and electroelasticity.
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Extra resources for Nonlinear Theory of Electroelastic and Magnetoelastic Interactions
0 and then dividing by ıs and letting ıs ! e. t E D 0. 167)1 follows. Now consider a cylinder (or ‘pill box’) of infinitesimal height ıh and crosssectional area ıS D nıS straddling the surface S , as depicted in Fig. 6. 170) V where ˙ is the bounding surface of the cylinder. Since ıh is infinitesimal and the flux of D across the lateral surface of the cylinder becomes negligible as ıh ! 0, the only contributions to the surface integral come from the top and bottom surfaces of the cylinder. 170) is the total free charge in V , which consists of the surface charge f ıS .
76) Now consider a circuit C of finite dimensions carrying current I , as depicted in Fig. 3. Let S be any regular surface that is bounded by C . Imagine that a fine network of curves is constructed on S such that each mesh is infinitesimal, 26 2 Electromagnetic Theory m = IdS S C Γ Fig. 3 An open surface S bounded by a closed circuit C carrying current I . On S is shown a network of curves made up of small current loops with current I corresponding to magnetic dipoles with magnetic moment m D I dS, where dS is the directed area element on S related to the direction of the current by the right-hand screw rule.
X0 / within a volume V , vanishing outside V . 148) has again been used. 158) where the skew-symmetry of M has been used. 63) shows that, for a distribution of dipoles, curl M behaves like a current density and therefore has the interpretation 42 2 Electromagnetic Theory indicated above. 89) for J D Jb . 162) which shows that only the free electric current density Jf remains in Maxwell’s equation. The term @D=@t , the time derivative of the electric displacement, plays a role similar to a current density and is known as the displacement current.