A continuum body is defined as a body whose material points are identifiable with the geometric points of a regular region of physical space, and which is endowed with mass for which there is a mass density function that can represent its measure.
The continuum body is a phenomenological model that includes both solids and fluids, hence it is specifically referred to as solid mechanics and fluid mechanics, and is associated with the concept of a deformable body in that its parts undergo changes in shape and volume during motion. A limiting case of a continuum body is the rigid body, the study of which, developed by rational mechanics, is defined on the basis of a finite number of degrees of freedom and leads to systems of ordinary differential equations. Deformable continua, on the other hand, can be thought of as systems with infinite degrees of freedom, and their mechanical equations take the form of partial differential equations.
A classification of continuum body models can be made on the basis of the size of the region of space they occupy. The three-dimensional models include the Cauchy continuum, which is the best-known and most important continuum body model in the discipline, so much so that the term continuum mechanics is often used synonymously with Cauchy continuum mechanics. The three-dimensional models also include the polar Cosserat continuum model, which has a richer local structure than the point structure of the Cauchy model, also expressed in terms of the orientation of its material points.
Both two-dimensional continua, such as plates, slabs, and shells, and one-dimensional continua, such as the beam model studied in structural engineering, are widely used in structural mechanics because of their greater simplicity.