Static Greens Functions In Anisotropic Media

This book presents the theory on static Green's functions in anisotropic magnetoelectroelastic media and their detailed derivations via different methods.

This book presents basic theory on static Green's functions in general anisotropic magnetoelectroelastic media including detailed derivations based on the complex variable method, potential method, and integral transforms. Green's functions corresponding to the reduced cases are also presented including those in anisotropic and transversely isotropic piezoelectric and piezomagnetic media, and in purely anisotropic elastic, transversely isotropic elastic and isotropic elastic media. Problems include those in three-dimensional, (two-dimensional) infinite, half, and biomaterial spaces (planes). While the emphasis is on the Green's functions related to the line and point force, those corresponding to the important line and point dislocation are also provided and discussed. This book provides a comprehensive derivation and collection of the Green's functions in the concerned media, and as such, it is an ideal reference book for researchers and engineers, and a textbook for both students in engineering and applied mathematics.

Displacement Green's function is the building block for some semi-analytical methods like Boundary Element Method (BEM), Distributed Point Source Method (DPCM), etc. In this thesis, the displacement Greeǹs function in anisotropic media due to a time harmonic point force is studied. Unlike the isotropic media, the Green's function in anisotropic media does not have a closed form solution. The dynamic Green's function for an anisotropic medium can be written as a summation of singular and non-singular or regular parts. The singular part, being similar to the result of static Green's function, is in the form of an integral over an oblique circular path in 3D. This integral can be evaluated either by a numerical integration technique or can be converted to a summation of algebraic terms via the calculus of residue. The other part, which is the regular part, is in the form of an integral over the surface of a unit sphere. This integral needs to be evaluated numerically and its evaluation is considerably more time consuming than the singular part. Obtaining dynamic Green's function and its spatial derivatives involves calculation of these two types of integrals. The spatial derivatives of Green's function are important in calculating quantities like stress and stain tensors. The contribution of this thesis can be divided into two parts. In the first part, different integration techniques including Gauss Quadrature, Simpson's, Chebyshev, and Lebedev integration techniques are tried out and compared for evaluation of dynamic Green’s function. In addition the solution from the residue theorem is included for the singular part. The accuracy and performance of numerical implementation is studied in detail via different numerical examples. Convergence plots are used to analyze the numerical error for both Green's function and its derivatives. The second part of contribution of this thesis relates to the mathematical derivations. As mentioned above, the regular part of dynamic Green's function, being an integral over the surface of a unit sphere, is responsible for the majority of computational time. From symmetry properties, this integration domain can be reduced to a hemisphere, but no more simplification seems to be possible for a general anisotropic medium. In this thesis, the integration domain for regular part is further reduced to a quarter of a sphere for the particular case of transversely isotropic material. This reduction proposed for the first time in this thesis nearly halves the number of integration points for the evaluation of regular part of dynamic Green's function. It significantly reduces the computational time.

This book reviews the mathematical modeling and experimental study of systems involving two or more different length scales. The effects of phenomena occurring at the lower length scales on the behavior at higher scales are of intrinsic scientific interest, but can also be very effectively used to determine the behavior at higher length scales or at the macro-level. Efforts to exploit this micro- and macro-coupling are, naturally, being pursued with regard to every aspect of mechanical phenomena. This book focuses on the changes imposed on the dynamics, strength of materials and durability of mechanical systems by related multiscale phenomena. In particular, it addresses: 1: the impacts of effective dissipation due to kinetic energy trapped at lower scales 2: wave propagation in generalized continua 3: nonlinear phenomena in metamaterials 4: the formalization of more general models to describe the exotic behavior of meta-materials 5: the design and study of microstructures aimed at increasing the toughness and durability of novel materials

Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. The book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances and new applications in piezoelectricity.

Dyadic Green's Function (DGF) for layered anisotropic media is essential for the electromagnetic field analysis of several problems. With the goal of deriving the DGF of a two-layer biaxially anisotropic medium we derive in this report the DGF of a corresponding unbounded problem. Using the Fourier transform method, an auxiliary dyadic Green's (ADGF) is first derived. The DGF is then obtained by performing a simple linear transformation on the ADGF. It is expressed in a compact dyadic form in terms of two characteristic waves, viz., the a-wave and the b-wave. Some features of the DGF are discussed by comparing our results with those of a corresponding uniaxial problem. Green's function, Electromagnetic waves, Anisotropic medium.

Nano-scale materials have unique electronic, optical, and chemical properties that make them attractive for a new generation of devices. In the second edition of Modeling, Characterization, and Production of Nanomaterials: Electronics, Photonics, and Energy Applications, leading experts review the latest advances in research in the understanding, prediction, and methods of production of current and emerging nanomaterials for key applications. The chapters in the first half of the book cover applications of different modeling techniques, such as Green’s function-based multiscale modeling and density functional theory, to simulate nanomaterials and their structures, properties, and devices. The chapters in the second half describe the characterization of nanomaterials using advanced material characterization techniques, such as high-resolution electron microscopy, near-field scanning microwave microscopy, confocal micro-Raman spectroscopy, thermal analysis of nanoparticles, and applications of nanomaterials in areas such as electronics, solar energy, catalysis, and sensing. The second edition includes emerging relevant nanomaterials, applications, and updated modeling and characterization techniques and new understanding of nanomaterials. Covers the close connection between modeling and experimental methods for studying a wide range of nanomaterials and nanostructures Focuses on practical applications and industry needs through a solid outlining of the theoretical background Includes emerging nanomaterials and their applications in spintronics and sensing

The book teaches engineers many new things about a classical topic which suddenly is again in the center of interest because of its relevance for finite element analysis, for the accuracy of computational methods. It shows that influence functions play a fundamental role in the finite element analysis of structures and practically all of linear computational mechanics. It also strives to add new and important insights into modern structural analysis and into computational mechanics by establishing the central role of influence functions for the numerical analysis and to lay a new foundation to the energy and variational principles.

Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.