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Maxwell Model
A Maxwell model 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. A generalization of the scalar relation to a tensor equation lacks motivation from more microscopic models and does not comply with the concept of material objectivity. However, these criteria are fulfilled by the Upper-convected Maxwell model. Definition The Maxwell model is represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. If, instead, we connect these two elements in parallel, we get the generalized model of a solid Kelvin–Voigt material. In Maxwell configuration, under an applied axial stress, the total stress, \sigma_\mathrm and the total strain, \varepsilon_\mathrm can be defined as follows: :\sigma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscoelastic
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both Viscosity, viscous and Elasticity (physics), elastic characteristics when undergoing deformation (engineering), deformation. Viscous materials, like water, resist both shear flow and Strain (materials science), strain linearly with time when a Stress (physics), 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 chemical bond, 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 James Clerk Maxwell, Ludwig Boltzm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell Deformation
Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (other) * Maxwell baronets, in the Baronetage of Nova Scotia * Maxwell (footballer, born 1979), Brazilian forward * Maxwell (footballer, born 1981), Brazilian left-back * Maxwell (footballer, born 1986), Brazilian striker * Maxwell (footballer, born 1989), Brazilian left-back * Maxwell (footballer, born 1995), Brazilian forward * Maxwell (musician) (born 1973), American R&B and neo-soul singer * Maxwell (rapper) (born 1993), German rapper, member of rap band 187 Strassenbande * Maxwell Jacob Friedman (born 1996), American professional wrestler * Maxwell Silva (born 1953), Sri Lankan Sinhala Catholic cleric, Auxiliary Bishop of Colombo Places United States * Maxwell, California * Maxwell, Indiana * Maxwell, Iowa * Maxwell, Nebraska * Maxwell, New Mexico * Maxwell, Texas * Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Linear Solid Model
The standard linear solid (SLS), also known as the Zener model after Clarence Zener, is a method of modeling the behavior of a viscoelastic material using a linear combination of springs and dashpots to represent elastic and viscous components, respectively. Often, the simpler Maxwell model and the Kelvin–Voigt model are used. These models often prove insufficient, however; the Maxwell model does not describe creep or recovery, and the Kelvin–Voigt model does not describe stress relaxation. SLS is the simplest model that predicts both phenomena. Definition Materials undergoing strain are often modeled with mechanical components, such as springs (restorative force component) and dashpots (damping component). Connecting a spring and damper in series yields a model of a Maxwell material while connecting a spring and damper in parallel yields a model of a Kelvin–Voigt material.David Roylance, "Engineering Viscoelasticity" (October 24, 2001) https://ocw.mit.edu/course ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oldroyd-B Model
The Oldroyd-B model is a constitutive model used to describe the flow of viscoelastic fluids. This model can be regarded as an extension of the upper-convected Maxwell model and is equivalent to a fluid filled with elastic bead and spring dumbbells. The model is named after its creator James G. Oldroyd. The model can be written as: \mathbf + \lambda_1 \stackrel = 2\eta_0 (\mathbf + \lambda_2 \stackrel) where: * \mathbf is the deviatoric part of the stress tensor; * \lambda_1 is the relaxation time; * \lambda_2 is the retardation time = \frac\lambda_1 ; * \stackrel is the upper-convected time derivative of stress tensor: \stackrel = \frac \mathbf + \mathbf \cdot \nabla \mathbf -( (\nabla \mathbf)^T \cdot \mathbf + \mathbf \cdot (\nabla \mathbf)) ; *\mathbf is the fluid velocity; *\eta_0 is the total viscosity composed of solvent and polymer components, \eta_0= \eta_s + \eta_p ; *\mathbf is the deformation rate tensor or rate of strain tensor, \mathbf = \frac \left boldsymbo ... [...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 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 varying time distribution. The Wiechert model shows this by having as many spring–dashpot Maxwell elements as are necessary to accurately represent the distribution. The figure on the right shows the generalised Wiechert model.Roylance, David (2001 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Dynamic Modulus
Dynamic modulus (sometimes complex modulusThe Open University (UK), 2000. ''T838 Design and Manufacture with Polymers: Solid properties and design'', page 30. Milton Keynes: The Open University.) is the ratio of stress to strain under ''vibratory conditions'' (calculated from data obtained from either free or forced vibration tests, in shear, compression, or elongation). It is a property of viscoelastic materials. Viscoelastic stress–strain phase-lag Viscoelasticity is studied using dynamic mechanical analysis where an oscillatory force (stress) is applied to a material and the resulting displacement (strain) is measured. *In purely elastic materials the stress and strain occur in phase, so that the response of one occurs simultaneously with the other. *In purely viscous materials, there is a phase difference between stress and strain, where strain lags stress by a 90 degree (\pi/2 radian) phase lag. *Viscoelastic materials exhibit behavior somewhere in between that of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell Relax Spectra
Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (other) * Maxwell baronets, in the Baronetage of Nova Scotia * Maxwell (footballer, born 1979), Brazilian forward * Maxwell (footballer, born 1981), Brazilian left-back * Maxwell (footballer, born 1986), Brazilian striker * Maxwell (footballer, born 1989), Brazilian left-back * Maxwell (footballer, born 1995), Brazilian forward * Maxwell (musician) (born 1973), American R&B and neo-soul singer * Maxwell (rapper) (born 1993), German rapper, member of rap band 187 Strassenbande * Maxwell Jacob Friedman (born 1996), American professional wrestler * Maxwell Silva (born 1953), Sri Lankan Sinhala Catholic cleric, Auxiliary Bishop of Colombo Places United States * Maxwell, California * Maxwell, Indiana * Maxwell, Iowa * Maxwell, Nebraska * Maxwell, New Mexico * Maxwell, Texas * Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Creep (deformation)
In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point. The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function – for example creep of a turbine blade could cause the blade to contact the casing, resulting in the failure of the blade. Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress Relaxation
In materials science, stress relaxation is the observed decrease in stress in response to strain generated in the structure. This is primarily due to keeping the structure in a strained condition for some finite interval of time hence causing some amount of plastic strain. This should not be confused with creep, which is a constant state of stress with an increasing amount of strain. Since relaxation relieves the state of stress, it has the effect of also relieving the equipment reactions. Thus, relaxation has the same effect as cold springing, except it occurs over a longer period of time. The amount of relaxation which takes place is a function of time, temperature and stress level, thus the actual effect it has on the system is not precisely known, but can be bounded. Stress relaxation describes how polymers relieve stress under constant strain. Because they are viscoelastic, polymers behave in a nonlinear, non-Hookean fashion.Meyers and Chawla. "Mechanical Behavior of Mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relaxation Time
Relaxation stands quite generally for a release of tension, a return to equilibrium. In the sciences, the term is used in the following ways: * Relaxation (physics), and more in particular: ** Relaxation (NMR), processes by which nuclear magnetization returns to the equilibrium distribution ** Dielectric relaxation, the delay in the dielectric constant of a material ** Vibrational energy relaxation, the process by which molecules in high energy quantum states return to the Maxwell-Boltzmann distribution ** Chemical relaxation methods, related to temperature jump ** Relaxation oscillator, a type of electronic oscillator In mathematics: :* Relaxation (approximation), a technique for transforming hard constraints into easier ones :* Relaxation (iterative method), a technique for the numerical solution of equations :* Relaxation (extension method), a technique for a natural extension in mathematical optimization or variational problems In computer science: :* Relaxation (com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
