Continuum Modeling

Abstract

Common experience with the thermomechanical properties and behavior of matter is usually at the continuum level, i.e., observations concern such phenomena as elastic and inelastic deformation of solids, flow of fluids, and conduction of heat. Continuum descriptions of these phenomena are expressed in terms of partial differential equations representing the principles of balance of mass, momentum, and energy. Since the basic principles apply to all materials, it is apparent that they alone will not suffice for solving specific problems. The peculiarities of individual materials are expressed in terms of constitutive equations, of which Hooke's law of elasticity and Newton's law of viscosity are examples. For the most part, “continuum modeling” refers to the process of devising constitutive equations. This work requires exercise of physical insight at both the macroscopic and microscopic levels, consideration of experimental observations, and application of formal mathematical principles.Much of materials science is devoted to development and application of materials that have been selected for, or designed to have, useful properties different from those of existing materials. Many materials are of interest precisely because they have unusual properties. For example, paints and other coatings are often designed to flow easily when spread, but resist running afterward. Much work is devoted to analyzing manufacturing processes, whether they be processing of foodstuffs, forging metals, drawing films and fibers, or curing polymers. Properties and physical states of materials that are important during manufacture are often very different from those desired under service conditions.