**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 Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ...
Image File history File links File links The following pages link to this file: Bernoullis equation ...
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 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. ...
The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ...
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. ...
Stress is a measure of force per unit area within a body. ...
This article is about the deformation of materials. ...
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. ...
Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ...
For other uses, see Solid (disambiguation). ...
For other uses, see Plasticity. ...
Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...
Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...
Viscoelasticity, also known as anelasticity, describes materials that exhibit both viscous and elastic characteristics when undergoing plastic deformation. ...
| *Fluid mechanics* | Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids Non-Newtonian fluids Surface tension | *Scientists* | Newton · Stokes · *others* Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ...
Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ...
For other uses, see Viscosity (disambiguation). ...
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. ...
Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...
Sir George Gabriel Stokes, 1st Baronet (13 August 1819â€“1 February 1903) was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes theorem). ...
| This box: view • talk • edit | **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. The amount of deformation is called the strain. In engineering mechanics, deformation is a change in shape due to an applied force. ...
Stress is a measure of force per unit area within a body. ...
In physics, force is anything that can cause a massive body to accelerate. ...
This article is about the deformation of materials. ...
## Modeling elasticity
The elastic regime is characterized by a linear relationship between stress and strain, denoted linear elasticity. This idea was first stated by Robert Hooke in 1676 as an anagram, then in 1678 in Latin, as *Ut tensio, sic vis*, which means: // Linear elasticity The linear theory of elasticity models the macroscopic mechanical properties of solids assuming small deformations. ...
Robert Hooke, FRS (July 18, 1635 â€“ March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ...
“ | As the extension, so the force. | ” | This linear relationship is called Hooke's law. The classic model of linear elasticity is the perfect spring. Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor, when considering simple situations of higher symmetry such as a rod in one dimensional loading, the relationship may often be reduced to applications of Hooke's law. Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...
Helical or coil springs designed for tension A spring is a flexible elastic object used to store mechanical energy. ...
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. ...
Sphere symmetry group o. ...
Because most materials are only elastic under relatively small deformations, several assumptions are used to linearize the theory. Most importantly, higher order terms are generally discarded based on the small deformation assumption. In certain special cases, such as when considering a rubbery material, these assumptions may not be permissible. However, in general, elasticity refers to the linearized theory of the continuum stresses and strains.
## Transitions to inelasticity Above a certain stress known as the elastic limit or the yield strength of an elastic material, the relationship between stress and strain becomes nonlinear. Beyond this limit, the solid may deform irreversibly, exhibiting plasticity. A stress-strain curve is one tool for visualizing this transition. The elastic limit is the maximum stress a material can undergo at which all strains are recoverable. ...
Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ...
For other uses, see Plasticity. ...
A stress-strain curve is a graph derived from measuring load (stress - Ïƒ) versus extension (strain - Îµ) for a sample of a material. ...
Furthermore, not only solids exhibit elasticity. Some non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow, exhibiting viscosity. A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
Viscoelasticity, also known as anelasticity, describes materials that exhibit both viscous and elastic characteristics when undergoing plastic deformation. ...
For other uses, see Viscosity (disambiguation). ...
## See also Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. ...
An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substances tendency to be deformed when a force is applied to it. ...
// Linear elasticity The linear theory of elasticity models the macroscopic mechanical properties of solids assuming small deformations. ...
3-D elasticity is one of three methods of structural analysis. ...
Pseudoelasticity, or sometimes called super elasticity, is an elastic (impermanent) response to relatively high stress caused by a phase transformation between the austenitic and martensitic phases of a crystal. ...
## References - W.J. Ibbetson (1887),
*An Elementary Treatise on the Mathematical Theory of Perfectly Elastic Solids*, McMillan, London, p.162 - L.D. Landau, E.M. Lifshitz (1986),
*Course of Theoretical Physics: Theory of Elasticity* Butterworth-Heinemann, ISBN 0-7506-2633-X - J.E. Marsden, T.J. Hughes (1983),
*Mathematical Foundations of Elasticity*, Dover, ISBN 0-486-67865-2 - P.C. Chou, N. J. Pagano (1992),
*Elasticity: Tensor, Dyadic, and Engineering Approaches*, Dover, ISBN 0-486-66958-0 - R.W. Ogden (1997),
*Non-linear Elastic Deformation*, Dover, ISBN 0-486-69648-0 |