Constitutive Equations of Nonlinear Electromagnetic-Elastic Crystals

Continuum physics is concemed with the predictions of deformations, stress, temperature, and electromagnetic fields in deformable and fluent bodies. To that extent, mathematical formulation requires the establishment of basic balance laws and constitutive equations. Balance laws are the union of those of continuum thermomechanics and MaxweIl's equations, as coIlected in Chapter 1. To dose the theory it is necessary to formulate equations for the material response to extemal stimuli....
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Continuum physics is concemed with the predictions of deformations, stress, temperature, and electromagnetic fields in deformable and fluent bodies. To that extent, mathematical formulation requires the establishment of basic balance laws and constitutive equations. Balance laws are the union of those of continuum thermomechanics and MaxweIl's equations, as coIlected in Chapter 1. To dose the theory it is necessary to formulate equations for the material response to extemal stimuli. These equations bring into play the material properties of the media under consideration. In their simplest forms these are the constitutive laws, such as Hooke's law of dassical elasticity, Stokes' law of viscosity of viscous fluids, Fourier's law of heat conduction, Ohm's law of electric conduction, etc. For large deformations and fields in material media, the constitutive laws become very complicated, in vol ving all physical effects and material symmetry. The present work is concemed with the material symmetry regulations arising from the crystaIlographic symmetry of magnetic crystals. While there exist some works on the thirty-two conventional crystal dasses, exduding the linear case, there exists no study on the nonlinear constitutive equations for the ninty magnetic crystal dasses. Yet the interaction of strong electromagnetic fields with deformable solids cannot be explained without the material sym­ metry regulations relevant to magnetic crystals. In this monograph, we present a thorough discussion of magnetic symmetry by means of group theory. We consider onlyone scalar function which depends on one symmetric second-order tensor (e. g.