"Continuum mechanics, a branch of mechanics, deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. It is a mathematical framework for studying the transmission of force through and deformation of materials of all types. Of course, no real materials are actually continuous. We know from physics and chemistry that materials, such as solids, liquids and gases, are composed of molecules separated by space. Even at much larger size scales, materials may be composed of distinct grains, e.g., a sand, or of grains of different constituents, e.g., steel, or deformable particles such as blood. Nevertheless, treating material as continuous is a great advantage since it allows us to use the mathematical tools of continuous functions, such as differentiation. In addtion to being convenient, this approach works remarkably well. This is true even at size scales for which the justfication of treating the material as a continuum might be dubious. The ultimate justification is that extrapolations made using continuum mechanics are in harmony with observations and measurements. Continuum mechanics contracts with physical properties of solids and fluids which are liberated of any particular coordinate system in which they are observed. These physical properties are then represented by tensors, which are mathematical objects that have the required property of being independent of coordinate system. These tensors can be expressed in coordinate systems for computational convenience. Both the existence of a Newtonian reference frame, and the concept of a continuum, are mathematical idealizations. Experimental evidence suggest that the laws of motion based on these assumptions accurately approximate the behavior of most solid and fluid materials at length scales of order mm-km or so in engineering applications. In some cases continuum models can also approximate behavior at much shorter length scales (for volumes of material containing a few 1000 atoms), but models at these length scales often require different relations between internal forces deformation measures in the solid to those used to model larger volumes.
Two-Volume ‘Brig’s Handbook of Methods & Research in Continuum Mechanics and Theory of Materials’ covers the trends in development of the theory of material behavior and is an introduction to understand the advanced theories of mechanics. The primary objectives of this handbook are: to study the conservation principles in mechanics of continua and formulate the equations that describe the motion and mechanical behavior of materials; to present the applications of these equations to simple problems associated with flows of fluids, conduction of heat, and deformations of solid bodies. This handbook will be of valuable to students and researchers involved in materials science in engineering and in physics. The comprehensive work also helps engineers who depend on canned programs to analyze problems to interpret the results produced by such programs."