Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.

Continuum Physics, Volume IV: Polar and Nonlocal Field Theories discusses the exposition of field theories for bodies which possess inner structure that can interact with mechanical and electromagnetic fields. This book provides precise presentations of exact continuum theories on materially non-uniform or non-simple bodies that can respond to short- and long-range inter-particle loads and fields. This volume consists of three parts. Part I is devoted to the study of continuum field theories for bodies having inner structure. All materials, to some extent, are composed of particles that behave like small rigid bodies or deformable particles, unlike the geometrical points of the classical continuum theory. The developments of nonlocal theories of nonpolar and polar continua are covered in Parts II and III. This publication is valuable to students and researchers interested in polar and nonlocal field theories.

Continuum Physics, Volume III: Mixtures and EM Field Theories discusses the field theories for bodies composed of different substances, such as mixtures and interaction of electromagnetic effects with the deformable bodies. This book aims to present the mathematical foundations of nonlinear mechanical, electrical, and magnetic phenomena that take place in mixtures and materially uniform bodies. This volume consists of three parts. Part I is devoted to the development of the theory of mixtures, including kinematics, balance laws, and constitutive equations for bodies consisting of several different substances. Part II is concerned with the mechanics of deformable bodies interacted by electromagnetic fields. The deformation produced by EM fields, EM fields resulting from the deformation of bodies, and plethora of other physical phenomena arising from mechanical and EM interactions are also covered. Micromagnetism is covered in Part III, including considerations arising from the interaction of strong magnetic fields with the inner structure of the body. This publication is valuable to students and researchers interested in mixtures and EM field theories.

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 book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.

Explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Including a comprehensive bibliography and historical review of the field, and a pedagogical mathematical treatment, it is ideal for graduate students and researchers in mechanical and civil engineering, and materials science.

This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.