# Continuum Mechanics

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## continuum mechanics

[kən′tin·yə·wəm mə′kan·iks]
(physics)

## 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 ?
Among his topics are solid continuum mechanics, the finite element method, the wave equation for solids, the simulation of strong ground motion, elasto-plasticity and fracture mechanics, the analysis of faulting, the simulation of faulting with the boundary element method, multi-agent simulation for evacuation process analysis, high performance computing application, and meta-modeling theory for the construction of numerical analysis models.
She recruits grad students for her lab from a class she teaches in continuum mechanics. "It's the first class graduate students should take in mechanics, and we use a lot of differential equations and calculus," she says.
(Sears and Batra 2006) proposed a comprehensive buckling analysis of single-walled and multi-walled carbon nanotubes by molecular mechanics simulations and continuum mechanics models.
This use of quantum mechanics to solve problems within the continuum mechanics domain shows a well known direct interchangeability of the systems in one direction.
Kim, "Mechanics of an elastic solid reinforced with bidirectional fiber in finite plane elastostatics: complete analysis," Continuum Mechanics and Thermodynamics, vol.
The continuous recognition of progress in understanding the mechanical properties of rock has led investigators to propose a variety of constitutive models by means of a subsequent viscoelastic plastic theory of continuum mechanics, such as that put forward by Liu et al.
The theoretical tools can be divided into three categories [12]: atomistic modeling, continuum mechanics (CM), and the hybrid method.
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.
Several methodologies of analysis have been developed in the research field of geometric continuum mechanics [14, 15], limit analysis [16-19], homogenization [20], elastodynamics [21-25], thermal problems [26-28], random composites [29-32], and nonlocal and gradient formulations [33-38].

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