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Burgers Material
A Burgers material is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the Dutch physicist Johannes Martinus Burgers. Overview Maxwell representation Given that one Maxwell material has an elasticity E_1 and viscosity \eta_1, and the other Maxwell material has an elasticity E_2 and viscosity \eta_2, the Burgers model has the constitutive equation : \sigma + \left( \frac + \frac \right) \dot\sigma + \frac \ddot\sigma = \left( \eta_1 + \eta_2 \right) \dot\varepsilon + \frac \ddot\varepsilon where \sigma is the stress and \varepsilon is the strain. Kelvin representation Given that the Kelvin material has an elasticity E_1 and viscosity \eta_1, the spring has an elasticity E_2 and the dashpot has a viscosity \eta_2, the Burgers model has the constitutive equation : \sigma + \left( \frac + \frac + \frac \right) \dot\sigma + \frac \ddot\sigma = \eta_2\dot\varepsilon + \frac \ddot\varepsilon where \sigma is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscoelastic
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscosity is the result of the diffusion of atoms or molecules inside an amorphous material.Meyers and Chawla (1999): "Mechanical Behavior of Materials", 98-103. Background In the nineteenth century, physicists such as Maxwell, Boltzmann, and Kelvin researched and experimented with creep and recovery of glasses, metals, and rubbers. Viscoelasticity was further examined in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly proportional to the distanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Martinus Burgers
Johannes (Jan) Martinus Burgers (January 13, 1895 – June 7, 1981) was a Dutch physicist and the brother of the physicist Wilhelm G. Burgers. Burgers studied in Leiden under Paul Ehrenfest, where he obtained his PhD in 1918. He is credited to be the father of Burgers' equation, the Burgers vector in dislocation theory and the Burgers material in viscoelasticity. Jan Burgers was one of the co-founders of the International Union of Theoretical and Applied Mechanics (IUTAM) in 1946, and was its secretary-general from 1946 until 1952. In 1931 he became member of the Royal Netherlands Academy of Arts and Sciences, in 1955 he became foreign member. Early life and education Burgers was born in Arnhem, Netherlands. There he attended both primary and secondary school. He attended Leiden University from 1914 until 1917. Burgers became a Doctor of Mathematical and Physical Sciences in 1918, writing a thesis entitled "Het Atoommodel van Rutherford-Bohr" (The Model of the Atom accor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burgers Model 2
Burger or Burgers may refer to: Food and drink Foods * Hamburger, a sandwich consisting of one or more cooked beef patties, placed inside a sliced bread roll or bun roll. ** Cheeseburger, a hamburger with added cheese(s) * Ground beef, minced beef used to make hamburgers ** Patty, a portion of ground meat, often round, used to make burgers * Steak burger, a burger consisting of steak * Rice burger, uses compressed rice cakes instead of hamburger buns * Turkey burger, a burger involving a deli turkey or a turkey patty * Veggie burger, a burger made with plant-based meat substitute * Afghani burger, an Afghan fast food wrap consisting of a piece of Afghan bread rolled around french fries, along with chutney and other condiments, vegetables, and often sausages or other meat. Drinks * Burger (grape), a Californian wine grape * Gouais blanc, a French wine grape that is also known as Burger * Elbling, a German wine grape that is also known as Burger People * Burger (surname) * Burg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constitutive Equation
In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations. Some constitutive equations are simply phenomenological; others are derived from first principles. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as electrical conductivity or a spring constant. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burgers Model
A Burgers material is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the Dutch physicist Johannes Martinus Burgers. Overview Maxwell representation Given that one Maxwell material has an elasticity E_1 and viscosity \eta_1, and the other Maxwell material has an elasticity E_2 and viscosity \eta_2, the Burgers model has the constitutive equation : \sigma + \left( \frac + \frac \right) \dot\sigma + \frac \ddot\sigma = \left( \eta_1 + \eta_2 \right) \dot\varepsilon + \frac \ddot\varepsilon where \sigma is the stress and \varepsilon is the strain. Kelvin representation Given that the Kelvin material has an elasticity E_1 and viscosity \eta_1, the spring has an elasticity E_2 and the dashpot has a viscosity \eta_2, the Burgers model has the constitutive equation : \sigma + \left( \frac + \frac + \frac \right) \dot\sigma + \frac \ddot\sigma = \eta_2\dot\varepsilon + \frac \ddot\varepsilon where \sigma is the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Three Four Element Models
Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree. Where characteristics are different, the differences may then be evaluated to determine which thing is best suited for a particular purpose. The description of similarities and differences found between the two things is also called a comparison. Comparison can take many distinct forms, varying by field: To compare things, they must have characteristics that are similar enough in relevant ways to merit comparison. If two things are too different to compare in a useful way, an attempt to compare them is colloquially referred to in English as "comparing apples and oranges." Comparison is widely used in society, in science and in the arts. General usage Comparison is a natural activity, which even animals engage in when deci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Maxwell Model
The Generalized Maxwell model also known as the Maxwell–Wiechert model (after James Clerk Maxwell and E WiechertWiechert, E (1889); "Ueber elastische Nachwirkung", Dissertation, Königsberg University, GermanyWiechert, E (1893); "Gesetze der elastischen Nachwirkung für constante Temperatur", Annalen der Physik, Vol. 286issue 10, p. 335–348anissue 11, p. 546–570/ref>) is the most general form of the linear model for viscoelasticity In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearl .... In this model several Maxwell elements are assembled in parallel. It takes into account that the relaxation does not occur at a single time, but in a set of times. Due to the presence of molecular segments of different lengths, with shorter ones contributing less than longer ones, there is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin–Voigt Material
A Kelvin-Voigt material, also called a Voigt material, is the most simple model viscoelastic material showing typical rubbery properties. It is purely elastic on long timescales (slow deformation), but shows additional resistance to fast deformation. It is named after the British physicist and engineer William Thomson, 1st Baron Kelvin, Lord Kelvin and German physicist Woldemar Voigt. Definition The Kelvin-Voigt model, also called the Voigt model, is represented by a purely viscosity, viscous damper and purely elasticity (physics), elastic spring connected in parallel as shown in the picture. If, instead, we connect these two elements in series we get a model of a Maxwell material. Since the two components of the model are arranged in parallel, the strains in each component are identical: : \varepsilon_\text = \varepsilon_S = \varepsilon_D. where the subscript D indicates the stress-strain in the damper and the subscript S indicates the stress-strain in the spring. Similarl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell Material
A Maxwell material is the most simple model viscoelastic material showing properties of a typical liquid. It shows viscous flow on the long timescale, but additional elastic resistance to fast deformations. It is named for James Clerk Maxwell who proposed the model in 1867. It is also known as a Maxwell fluid. Definition The Maxwell model is represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. In this configuration, under an applied axial stress, the total stress, \sigma_\mathrm and the total strain, \varepsilon_\mathrm can be defined as follows: :\sigma_\mathrm=\sigma_D = \sigma_S :\varepsilon_\mathrm=\varepsilon_D+\varepsilon_S where the subscript D indicates the stress–strain in the damper and the subscript S indicates the stress–strain in the spring. Taking the derivative of strain with respect to time, we obtain: :\frac = \frac + \frac = \frac + \frac \frac where ''E'' is the elastic modul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
