Information about Continuum Mechanics
| Continuum mechanics | |
) | |
| Key topics | |
| Conservation of mass Conservation of momentum Navier-Stokes equations | |
| Classical mechanics | |
| Stress Strain Tensor | |
| Solid mechanics | |
| Solids Elasticity Plasticity Hooke's law Rheology Viscoelasticity | |
| Fluid mechanics | |
| Fluids Fluid statics Fluid dynamics Viscosity Newtonian fluids Non-Newtonian fluids Surface tension | |
| Scientists | |
| Newton Stokes | others |
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 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.
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.
| Continuum mechanics | Solid mechanics is the study of the physics of continuous solids with a defined rest shape. | Elasticity (physics) describes materials that return to their rest shape after removal of an applied force. | |
| Plasticity describes materials that permanently deform (change their rest shape) after a large enough applied force. | Rheology: Given that some materials are viscoelastic (exhibiting a combination of elastic and viscous properties), the boundary between solid mechanics and fluid mechanics is blurry. | ||
| Fluid mechanics (including Fluid statics and Fluid dynamics) deals with the physics of fluids. An important property of fluids is viscosity, which is the force generated by a fluid in response to a velocity gradient. | Non-Newtonian fluids | ||
| Newtonian fluids | |||
See also
The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system will remain constant, regardless of the processes acting inside the system.
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The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances such as liquids and gases. These equations establish that changes in momentum in infinitesimal volumes of fluid are simply the sum of dissipative
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Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies.
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Stress is a measure of force per unit area within a body. It is a body's internal distribution of force per area that reacts to external applied loads. Stress is often broken down into its shear and normal components as these have unique physical significance.
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strain is the geometrical expression of deformation caused by the action of stress on a physical body. Strain is calculated by first assuming a change between two body states: the beginning state and the final state.
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The term tensor has slightly different meanings in mathematics and physics. In the mathematical fields of multilinear algebra and differential geometry, a tensor is a multilinear function.
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Solid mechanics is the branch of physics and mathematics that concerns the behavior of solid matter under external actions (e.g., external forces, temperature changes, applied displacements, etc.). It is part of a broader study known as continuum mechanics.
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A solid object is in the states of matter characterized by resistance to deformation and changes of volume. At the microscopic scale, a solid has these properties :
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- The atoms or molecules that comprise the solid are packed closely together.
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Elasticity is a branch of physics which studies the properties of elastic materials. A material is said to be elastic if it deforms under stress (e.g., external forces), but then returns to its original shape when the stress is removed.
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plasticity is a property of a material to undergo a non-reversible change of shape in response to an applied force. For example, a solid piece of metal or plastic being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself.
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Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress).
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Rheology is the study of the deformation and flow of matter under the influence of an applied stress, which might be shear stress or extensional stress. Rheology dealing with shear stress is called shear rheology.
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Viscoelasticity, also known as anelasticity, is the study of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied.
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Fluid mechanics is the study of how fluids move and the forces on them. (Fluids include liquids and gases.) Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion.
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FLUID (Fast Light User Interface Designer) is a graphical editor that is used to produce FLTK source code. FLUID edits and saves its state in text .fl files, which can be edited in a text editor for finer control over display and behavior.
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Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject.
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Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion).
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Viscosity is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow.
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A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its stress versus rate of strain curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.
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A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. As a result, non-Newtonian fluids may not have a well-defined viscosity.
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Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. It allows insects, such as the water strider (pond skater, UK), to walk on water.
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Sir Isaac Newton
Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
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Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
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George Stokes
Sir George Gabriel Stokes, 1st Baronet
Born 13 July 1819
Skreen, County Sligo, Ireland
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Sir George Gabriel Stokes, 1st Baronet
Born 13 July 1819
Skreen, County Sligo, Ireland
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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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For other uses, see Mechanic (disambiguation).
Mechanics (Greek Μηχανική
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Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.
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A solid object is in the states of matter characterized by resistance to deformation and changes of volume. At the microscopic scale, a solid has these properties :
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- The atoms or molecules that comprise the solid are packed closely together.
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FLUID (Fast Light User Interface Designer) is a graphical editor that is used to produce FLTK source code. FLUID edits and saves its state in text .fl files, which can be edited in a text editor for finer control over display and behavior.
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Liquid is one of the four principal states of matter. A liquid is a fluid that can freely form a distinct surface at the boundaries of its bulk material.
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Characteristics
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Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape. Compared to the solid and liquid states of matter a gas has lower density and a lower viscosity.
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