By Luis Dorfmann, Ray W. Ogden
This book offers a unified concept on nonlinear electro-magnetomechanical interactions of soppy fabrics able to huge elastic deformations. The authors comprise an overview of the fundamental rules of the vintage thought 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 proper 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 various consultant boundary-value difficulties for either nonlinear magnetoelasticity and electroelasticity.
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Additional info for Nonlinear Theory of Electroelastic and Magnetoelastic Interactions
The speed of electromagnetic effects in free space). 134) is the source term. 131)2 , we may write B D curl A, A being a time-dependent vector potential. e. 140) Since there is flexibility in the definition of A (as noted in Sect. 141) should be adopted. 86) to the timevarying situation and known as the Lorenz condition (Ludwig Valentin Lorenz, 1829–1891). Note that Lorentz and Lorenz are different. x0 /; where t 0 is the retarded time t over to the dynamic situation. 143) R R=c. 2 Polarization and Magnetization in Materials In Sects.
55) As we shall see in Sect. 55) is one of Maxwell’s equations, and it applies within material media, with e then replaced by the free charge density f (to be defined in Sect. 4), as well as in vacuum (where e D 0), and also when there is time dependence. 56) are equivalent, but, as we shall see in Chap. 4, their counterparts are not equivalent in polarizable media. 21), for example. Magnetism is fundamentally different since the analogue of a point charge (a magnetic monopole) does not exist. The basic 22 2 Electromagnetic Theory unit of magnetism is the magnetic dipole, but magnetic fields are generated by moving charges and a magnetic dipole is equivalent to an idealized small currentcarrying circuit.
5. The sides AB and CD of are parallel to t and have lengths ıs. The sides BC and DA are parallel to n and have lengths ıh. 169) @t Taking the limit as ıh ! 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 !