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Encyclopedia > Continuum mechanics

Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i.e., liquids and gases). The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Mechanics (Greek ) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. ... Look up continuum in Wiktionary, the free dictionary. ... In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ... A liquid will assume the shape of its container. ... A gas is one of the four main phases of matter (after solid and liquid, and followed by plasma), that subsequently appear as a solid material is subjected to increasingly higher temperatures. ...

The fact that matter is made of atoms and that it commonly has some sort of heterogeneous microstructure is ignored in the simplifying approximation that physical quantities, such as energy and momentum, can be handled in the infinitesimal limit. Differential equations can thus be employed in solving problems in continuum mechanics. Some of these differential equations are specific to the materials being investigated and are called constitutive equations, while others capture fundamental physical laws, such as conservation of mass or conservation of momentum. In fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made. Properties For other uses, see Atom (disambiguation). ... In classical mechanics, momentum (pl. ... In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ... In mathematics, the concept of a limit is used to describe the behavior of a function as its argument either gets close to some point, or as it becomes larger and larger; or the behavior of a sequences elements, as their index becomes larger and larger. ... Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In structural analysis, constitutive relations connect applied stresses or forces to strains or deformations. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... The law of conservation of mass/matter (The Lomonosov-Lavoisier law) states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ... The Knudsen number (Kn) is the ratio of the molecular mean free path length to a representative physical length scale. ...

The physical laws of solids and fluids do not depend on the coordinate system in which they are observed. Continuum mechanics thus uses tensors, which are mathematical objects that are independent of coordinate system. These tensors can be expressed in coordinate systems, for computational convenience. A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...

Continuum mechanics Solid mechanics. Solid mechanics is the study of the physics of continuous solids with a defined rest shape. Elasticity (physics), which describes materials that return to their rest shape after an applied stress.
Plasticity, which described materials that permanently deform (change their rest shape) after a large enough applied stress. Rheology Given that some materials are viscoelastic (a combination of elastic and viscous), the boundary between solid mechanics and fluid mechanics is blurry.
Fluid mechanics (including Fluid statics and Fluid dynamics), which deals with the physics of fluids. An important property of fluids is its viscosity, which is the force generated by a fluid in response to a velocity field. Non-Newtonian fluids
Newtonian fluids

Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ... There are separate articles about elasticity in economics, and about British rubber bands. ... Figure 1  Stress tensor A mature tree trunk may support a greater force than a fine steel wire but intuitively we feel that steel is stronger than wood. ... In physics and materials science, plasticity is a property of a material to undergo a non-reversible change of shape in response to an applied force. ... Rheology is the study of the deformation and flow of matter. ... A viscoelastic material is one in which: hysteresis is seen in the stress-strain curve. ... The hydrogeology is study about of water-bearing formation. ... Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ... Fluid dynamics is the subdiscipline of fluid mechanics that studies fluids (liquids and gases) in motion. ... The pitch drop experiment at the University of Queensland. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

See also

In physics and thermodynamics, an equation of state is a constitutive equation describing the state of matter under a given set of physical conditions. ... In continuum mechanics, finite deformation tensors are tensors that are used to measure deformation. ...

  General subfields within physics  v·d·e 

Classical mechanics | Electromagnetism | Thermodynamics | General relativity | Quantum mechanics  The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess the property of electric charge, and is in turn affected by the presence and motion of such particles. ... ‹ The template below has been proposed for deletion. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915 [1][2]. It unifies special relativity and Isaac Newtons law of universal gravitation with the insight that gravitation is not due to a force but rather is a manifestation of curved space and time... Fig. ...

Particle physics | Condensed matter physics | Atomic, molecular, and optical physics  Particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. ... Atomic, molecular, and optical physics is the study of matter-matter and light-matter interactions on the scale of single atoms or structures containing a few atoms. ...

  Results from FactBites:
Physics Today December 2003 - Reference Frame (0 words)
One of the oddities of contemporary physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum.
Continuum mechanics refers to field descriptions of mechanical phenomena, which are usually modeled by partial differential equations.
With exposure to the continuum way of thinking about mechanical phenomena, students would have access to many physical aspects of nature: laboratory and geophysical fluid dynamics, the dynamics of deformable materials, part of the growing fields of soft condensed matter physics and complex fluids, and much more.
ENGnetBASE: Engineering Handbooks Online (0 words)
The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics.
Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum.
Mastering the contents of Continuum Mechanics: Second Edition provides the reader with the foundation necessary to be a skilled user of today's advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships.
  More results at FactBites »



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