This 2006 book combines modern and traditional solid mechanics topics in a coherent theoretical framework.

The monograph "Micropolar Theory of Elasticity" is devoted to the asymmetric theory of elasticity and thermoelasticity, aiming at researchers and postgraduate students in solid mechanics and applied mathematics, as well as mechanical engineers. It offers various new results including the basic field equations, general methods of integration of basic equations, formulations of problems, as well as solutions to particular problems. The presented general solutions cover those of Galerkin, Green-Lamé and Papkovitch-Neuber type, whereas the formulations include the displacement-rotation problems as well as pure stress problems of asymmetric elastodynamics. Solutions to stationary 3D and 2D problems for a half-space, and singular solutions to 3D and 2D asymmetric elastodynamics and the thermoelasto-dynamics problems for an infinite space are given.

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 textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises.

Elastodynamics, Volume II: Linear Theory is a continuation of Volume I and discusses the dynamical theory of linear isotropic elasticity. The volume deals with the fundamental theorems regarding elastodynamics and the different mathematical methods of solution and their employment in one, two, and three dimensions. The text outlines the fundamentals of linear elastodynamics and explains basic equations, displacement formulation, stress formulation, and the uniqueness theorem of elastodynamics. The book also investigates elastodynamic problems involving one-space dimension in governing boundaries, equations, and initial conditions. The book then compares two-dimensional problems as being subject to more precise mathematical analysis compared to three-dimensional situations by using scalar wave equations. The text then analyzes elastodynamic problems in three space dimensions when the solution depends on the condition of separability of the vector wave equation and the satisfaction of the boundary conditions. The diffraction of elastic waves is also described using two approaches: the integral equation method or the Eigen function technique. The book can prove valuable to researchers and practitioners whose work involves advanced statistics, general physics, and thermodynamics.

Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. - Contains exercises for student engagement as well as the integration and use of MATLAB Software - Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of

This book is essentially made up of the lecture notes delivered by seven authors at the International Centre for Mechanical Sciences in Udine in June 1979. It attempts to provide an up-to-date and concise summary of the authors' understanding of micropolar materials. Both asymmetric elasticity and fluids are covered. The chapters range from the discussion of micropolar molecular models to the analysis of structure models, from linear to nonlinear theories and from electromagnetic, thermal, viscous effects to lattice defects. The subjects are treated from both theoretical and experimental points of view. Students with physics, mathematics and mechanical backgrounds as well as professionals will find this treatise useful for study and reference.