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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 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 ... [...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 examin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper-convected Maxwell Model
The upper-convected Maxwell (UCM) model is a generalisation of the Maxwell material for the case of large deformations using the upper-convected time derivative. The model was proposed by James G. Oldroyd. The concept is named after James Clerk Maxwell. The model can be written as: : \mathbf + \lambda \stackrel = 2\eta_0 \mathbf where: * \mathbf is the stress tensor; * \lambda is the relaxation time; * \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 material viscosity at steady simple shear; *\mathbf is the deformation rate tensor. Case of the steady shear For this case only two components of the shear stress became non-zero: :T_=\eta_0 \dot \gamma \, and :T_=2 \eta_0 \lambda ^2 \, where \dot \gamma is the shear rate. Thus, the upper-convected Maxwell model predicts for the simple s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James G
James is a common English language surname and given name: *James (name), the typically masculine first name James * James (surname), various people with the last name James James or James City may also refer to: People * King James (other), various kings named James * Saint James (other) * James (musician) * James, brother of Jesus Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Arts, entertainment, and media * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * James the Red Engine, a character in ''Tho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (physics)
In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elongation which is also known as deformation, like the stretching of an elastic band, it is called tensile stress. But, when the forces result in the compression of an object, it is called compressive stress. It results when forces like tension or compression act on a body. The greater this force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Therefore, stress is measured in newton per square meter (N/m2) or pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics ( stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics ( electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity (stress–energy tenso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper-convected Time Derivative
In continuum mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, is the rate of change of some tensor property of a small parcel of fluid that is written in the coordinate system rotating and stretching with the fluid. The operator is specified by the following formula: : \stackrel = \frac \mathbf - (\nabla \mathbf)^T \cdot \mathbf - \mathbf \cdot (\nabla \mathbf) where: * is the upper-convected time derivative of a tensor field \mathbf *\frac is the substantive derivative *\nabla \mathbf=\frac is the tensor of velocity derivatives for the fluid. The formula can be rewritten as: : _ = \frac + v_k \frac - \frac A_ - \frac A_ By definition, the upper-convected time derivative of the Finger tensor is always zero. It can be shown that the upper-convected time derivative of a spacelike vector field is just its Lie derivative by the velocity field of the continuum. The upper-convected derivativ ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
