Continuum Mechanics


Also found in: Wikipedia.

continuum mechanics

[kən′tin·yə·wəm mə′kan·iks]

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.

REFERENCES

Landau, L. D., and E. M. Lifshits. Mekhanika sploshnykh sred, 2nd ed. (Series Teoreticheskaia fizika. ) Moscow, 1954.
Sedov, L. I. Mekhanika sploshnoi sredy, vols. 1–2. Moscow, 1973.

S. M. TARG

References in periodicals archive ?
The main approaches used to describe the small-scale effect in the analysis of nanostructures include nonlocal continuum mechanics and the atomic theory of lattice dynamics [1].
Hence, the extension of the continuum mechanics to accommodate the size dependence of nanostructures is a topic of major concern.
Some of the most commons are: Finite Difference Methods, developed in the 1950s; Boundary Element Methods, developed in the 1970s and principally used in linear continuum mechanics problems; Discrete Element Methods, developed in the 1970s and used mainly with granular materials problems; Meshfree Methods, recently propagated and it has its primary uses in fracture and crack propagation analysis; and the Finite Element Method, originated in the 1950s by the necessity for solving complex structural analysis problems.
The goal of this proposal is to unravel the mechanisms of tissue growth in native valves and TEHVs by integrating advanced continuum mechanics and cell biology, in order to develop predictive models of valve growth that can guide and optimize tissue engineering of heart valves.
Researchers from the Oxford Silk Group, along with collaborators in Oxford's Department of Engineering Science and Universidad Carlos III de Madrid's Department of Continuum Mechanics and Structural Analysis, have studied the links between web vibration and web silk properties.
We are very delighted partnering with MultiMechanics, experts in the fields materials science, continuum mechanics, and software engineering," said Zakir Hussain, Director, Lanika Solutions.
compressive and tensile strength) make the assumption of homogeneousness and continuity is not consistent with the actual situation; for some extreme cases, the state-of-the-art strength theory of rock based on continuum mechanics also confronts severe problems challenging the researchers' best knowledge [2].
Defect theory has been the subject of investigation since the first half of the XXth century and is a well-developed discipline in continuum mechanics [9-14].
Based on the theory of continuum mechanics and irreversible thermodynamics, macro damage mechanics (CDM) assumes that the media, which contains various defects and structures, is a continuum.
The classical continuum mechanics are augmented with additional equations that account for conservation of microinertia moments and balance of first stress moments that arises due to consideration of the microstructure in a material.
One can conclude that the finite element method--being an orthodox daughter of continuum mechanics, where the notion of a point force is forbidden since it leads to singularity--would give infinite displacements for infinitely fine mesh.
The initial value MSSE based on continuum mechanics has been considered using the relationships of analytical nonlinear theory of elasticity and plasticity in increments.