Abstract
In this series of lectures, after an introduction of the most basic elements and some historical perspective on the matter, an exposition of electromagnetic source terms to be taken into account in the Galilean invariant continuum thermodynamics of deformable continua is first given. The emphasis here is placed on the notions of ponderomotive force and couple, of which the latter already hints at some generalization of usual continua by the necessity to envisage nonsymmetric Cauchy stress tensors. Then the notion of magnetic continua endowed with a dynamic magnetic structure, such as in ferromagnets and antiferromagnets, is envisioned. The corresponding modelling can be made by exploiting different methods, among these a direct model of magneto-mechanical interactions in the manner of H. F. Tiersten but also an application of a generalized version of the principle of virtual power, or that of a Hamiltonian variational principle in the absence of dissipation. Such approaches allow one to exhibit a strict analogy with the equations that govern generalized, purely mechanical, continua such as micropolar or oriented media in the manner of the Cosserat brothers or Eringen, by introducing the notions of spin and couple stress. A parallel approach is given for electro-deformable media endowed with permanent electric polarization, e.g., ferroelectrics. Then analogies are established between the resonance couplings arising in certain structures (plates, shells) as shown by Mindlin in classical studies, and those existing for coupled magnetoelastic and electroelastic waves of different types. Finally, the contribution of these electromagnetic microstructures in the computation of configurational forces (e.g., driving forces acting on cracks) is shown to be quite similar to the terms due to a mechanical microstructure.
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Maugin, G.A. (2013). Electromagnetism and Generalized Continua. In: Altenbach, H., Eremeyev, V.A. (eds) Generalized Continua from the Theory to Engineering Applications. CISM International Centre for Mechanical Sciences, vol 541. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1371-4_6
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