Editing Continuum mechanics (section)

==Concept of a continuum==
The concept of a continuum underlies the mathematical framework for studying large-scale forces and deformations in materials. Although materials are composed of discrete atoms and molecules, separated by empty space or microscopic cracks and [[crystallographic defects]], physical phenomena can often be modeled by considering a substance distributed throughout some region of space. A continuum is a body that can be continually sub-divided into [[infinitesimal]] elements with local material properties defined at any particular point. Properties of the bulk material can therefore be described by continuous functions, and their evolution can be studied using the mathematics of [[calculus]].

Apart from the assumption of continuity, two other independent assumptions are often employed in the study of continuum mechanics. These are [[homogeneity (physics)|homogeneity]] (assumption of identical properties at all locations) and [[isotropy]] (assumption of directionally invariant vector properties).{{sfn|Malvern|1969|p=2}} If these auxiliary assumptions are not globally applicable, the material may be segregated into sections where they are applicable in order to simplify the analysis. For more complex cases, one or both of these assumptions can be dropped. In these cases, computational methods are often used to solve the [[differential equation]]s describing the evolution of material properties.