Concept of Continuous Media

Continuum mechanics deals with forces (stresses) and motion (or deformation, strain) of solids, liquids and gases disregarding their molecular structure. It is assumed that continuous mathematical functions can describe the medium valid at all interior points of the body. This concept allows us to define stress, i.e., force/unit area at all points. This definition implies that mass density is continuous at all points

where are the coordinate position at time t, and is the mass identified with a volume

element of

Applications of the theory lead to the study of the theory of elasticity, plasticity and fluid mechanics.