Continuum Mechanics

the branch of mechanics devoted to the study of the motion and equilibrium of gases, liquids, and deformable solids. Subdivisions of continuum mechanics include hydroaeromechanics, gas dynamics, elasticity theory, and plasticity theory. The main assumption of continuum mechanics is that matter can be considered as a continuous medium with its molecular (atomic) structure disregarded and that the distribution of all the characteristics of the medium (including density, stresses, and velocities of particles) can also be considered to be continuous. This is justified by the negligibility of the dimensions of molecules in comparison with the dimensions of the particles that are considered in theoretical and experimental studies in continuum mechanics. Therefore, the apparatus of higher mathematics, which has been well developed for continuous functions, may be employed in continuum mechanics.

The following are the basic equations in the study of any medium in continuum mechanics: (1) the equations of motion or equilibrium for the medium, which are obtained as a consequence of the fundamental laws of mechanics; (2) the continuity equation for the medium, which is a consequence of the law of conservation of mass; and (3) the energy equation. The distinctive features of each specific medium are taken into account by the equation of state or by the rheological equation; the latter establishes for a given medium the form of the relation among the stresses or their rates of change and the strains or their rates of change for the particles. The characteristics of the medium may also depend on the temperature and other physicochemical parameters; the form of these dependences must be established independently. Moreover, the initial and boundary conditions, whose form also depends on the features of the medium, must be specified in solving each particular problem.

Continuum mechanics has an enormous number of important applications in various fields of physics and engineering.