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. Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... 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 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. ... 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. ... Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ... In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... 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. ... Hookes law accurately models the physical properties of common mechanical springs. ... Rheology is the study of the deformation and flow of matter. ... The hydrogeology is study about of water-bearing formation. ... A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ... 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 Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances like liquids and gases. ... The pitch drop experiment at the University of Queensland. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... In engineering mechanics, deformation is a change in shape due to an applied force. ... 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, force is that which changes or tend to change the state of rest or motion of a body. ... In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ...

Modeling elasticity

Under small stresses many solids' strains are roughly proportional to the stresses they are undergoing. The constant of proportionality (sometimes known as the elasticity), is given by the inverse of Young's modulus of elasticity, which is a measure of stiffness. Thus, elasticity is typically modeled using a linear relationship between stresses and strain (see "Linear elasticity"). The classic theoretical example of linear elasticity is the perfect spring, whose behavior is described by Hooke's law. Linear elasticity, however, is an approximation; real materials exhibit some degree of non-linear behavior. Whether working with linear or non-linear models, the relationship between stress and strain is often described using tensors. In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ... In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ... This article is about a physical property. ... Stiffness is the resistance of an elastic body to deflection by an applied force. ... The word linear comes from the Latin word linearis, which means created by lines. ... 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 any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ... // Linear elasticity The linear theory of elasticity models the macroscopic mechanical properties of solids assuming small deformations. ... It has been suggested that Coil spring be merged into this article or section. ... Hookes law accurately models the physical properties of common mechanical springs. ... It has been suggested that this article or section be merged with estimation. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... The word linear comes from the Latin word linearis, which means created by lines. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... 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. ...

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 breaks down. Beyond this limit, the solid may deform irreversibly, exhibiting plasticity. This phenomenon is often observed using stress-strain curves. The tensile strength of a material is the maximum amount of tensile stress that it can be subjected to before it breaks. ... Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ... 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. ... A stress-strain curve is a graph derived from measuring load (stress - σ) versus extension (strain - ε) 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. ... A viscoelastic material is one in which: hysteresis is seen in the stress-strain curve. ... The pitch drop experiment at the University of Queensland. ...

See also

• Stiffness
• Elastic modulus
• Linear elasticity
• 3-D Elasticity

Stiffness is the resistance of an elastic body to deflection by an applied force. ... ... // 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. ...

References

• L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics: Theory of Elasticity Butterworth-Heinemann, ISBN 0-7506-2633-X
• J.E. Marsden, T.J. Hughes, Mathematical Foundations of Elasticity, Dover, ISBN 0-486-67865-2
• P.C. Chou, N. J. Pagano, Elasticity: Tensor, Dyadic, and Engineering Approaches, Dover, ISBN 0-486-66958-0
• R.W. Ogden, Non-linear Elastic Deformation, Dover, ISBN 0-486-69648-0