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."

The book covers experiments and theory in the fields of ferroelectrics, ferromagnets, ferroelastics, and multiferroics. Topics include experimental preparation and characterization of magnetoelectric multiferroics, the modeling of ferroelectric and ferromagnetic materials, the formation of ferroic microstructures and their continuum-mechanical modeling, computational homogenization, and the algorithmic treatment in the framework of numerical solution strategies.

Giants of Engineering Science is a biographical monograph examining the life and works of ten of the world’s leading engineering scientists.

The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.

Microcontinuum field theories extend classical field theories to microscopic spaces and short time scales. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balance laws, and constitutive equations, and then discusses applications of the fundamental ideas to the theory of elasticity. The ideas developed here are important in modeling the fluid or elastic properties of porous media, polymers, liquid crystals, slurries, and composite materials.

This third volume describes continuous bodies treated as classical (Boltzmann) and spin (Cosserat) continua or fluid mixtures of such bodies. It discusses systems such as Boltzmann continua (with trivial angular momentum) and Cosserat continua (with nontrivial spin balance) and formulates the balance law and deformation measures for these including multiphase complexities. Thermodynamics is treated in the spirit of Müller–Liu: it is applied to Boltzmann-type fluids in three dimensions that interact with neighboring fluids on two-dimensional contact surfaces and/or one-dimensional contact lines. For all these situations it formulates the balance laws for mass, momenta, energy, and entropy. Further, it introduces constitutive modeling for 3-, 2-, 3-d body parts for general processes and materially objective variable sets and their reduction to equilibrium and non-equilibrium forms. Typical (reduced) fluid spin continua are liquid crystals. Prominent nematic examples of these include the Ericksen–Leslie–Parodi (ELP) formulation, in which material particles are equipped with material unit vectors (directors). Nematic liquid crystals with tensorial order parameters of rank 1 to n model substructure behavior better, and for both classes of these, the book analyzes the thermodynamic conditions of consistency. Granular solid–fluid mixtures are generally modeled by complementing the Boltzmann laws with a balance of fluctuation (kinetic) energy of the particles. The book closes by presenting a full Reynolds averaging procedure that accounts for higher correlation terms e.g. a k-epsilon formulation in classical turbulence. However, because the volume fraction is an additional variable, the theory also incorporates ‘k-epsilon equations’ for the volume fraction.

The book develops a cross-disciplinary approach to the phenomenon of linear and nonlinear wave propagation in piezoelectric crystals. Based on the rigorous presentation of nonlinear continuum mechanics and electromechanical interactions in anisotropic bodies, the work starts from primary principles, is progressive and develops the subject matter by means of worked out examples up to the most recent applications in signal processing, introducing the most efficient methods of applied mathematics. The attention is especially focused on phenomena such as the formation of shocks, the generation harmonics, the anisochronism of resonators, nonlinear surface waves, the convolution of signals by means of surface-wave guides, the nonlinear couling between the crystal and deformations, the compensation between dispersion and nonlinearity. The work should be of pedagogical and practical interest to graduate students and research workers in various fields of applied science and engineering. Request Inspection Copy