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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 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] |
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] |
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. It is the simplest observer independent constitutive equation for viscoelasticity and further is able to reproduce first normal stresses. Thus, it constitutes one of the most fundamental models for rheology. 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 and the gradient of a vector follows the convention (\nabla)_ = \partial_i v_j. *\eta_0 is material viscosity at steady simple shear; *\mathbf is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James G
James may refer to: People * James (given name) * James (surname) * James (musician), aka Faruq Mahfuz Anam James, (born 1964), Bollywood musician * James, brother of Jesus * King James (other), various kings named James * Prince James (other) * Saint James (other) 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 Film and television * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * "James", a television episode of ''Adventure Time'' Music * James (band), a band from Manchester ** ''James'', U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (physics)
In continuum mechanics, stress is a physical quantity that describes Force, forces present during Deformation (physics), deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to Tension (physics), ''tensile'' stress and may undergo Elongation (materials science), elongation. An object being pushed together, such as a crumpled sponge, is subject to Compression (physics), ''compressive'' stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has Dimension (physics), dimension of force per area, with SI Units, SI units of newtons per square meter (N/m2) or Pascal (unit), pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while Strain (mechanics), ''strain'' is the measure of the relative deformation (mechanics), deformation of the material. For example, when a ... [...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 associated with 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; those components form an array, which can be thought of as a high-dimensional matrix. 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, quantum mechanics, fluid mechanics, moment of inertia, ...), electrodynamics ( electromagnetic ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retardation Time
Retardation is the delayed response to an applied force or stress, which can be described as "delay of the elasticity". Ideal elastic materials show an immediate deformation after applying a jump-like stress, and an immediate reformation after removing the stress afterwards in the jump-like form again. For viscoelastic samples, this elastic behaviour occurs with a certain time delay. The term "relaxation time" has been described. It is used in combination with tests presetting the strain (deformation) or strain rate (shear rate In physics, mechanics and other areas of science, shear rate is the rate at which a progressive shear strain is applied to some material, causing shearing to the material. Shear rate is a measure of how the velocity changes with distance. Simple ...), e.g., when performing relaxation tests. On the other hand, the term "retardation time" is used for tests when presetting the stress, e.g., when performing creep tests. See also * Creep-testing ma ... [...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 derivat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per metre squared, or pascal-seconds. Viscosity quantifies the internal friction, 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 center line than near its walls. Experiments show that some stress (physics), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal Strain Theory
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation. With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made. The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Flow
In solid mechanics, shear flow is the shear stress over a distance in a thin-walled structure.Higdon, Ohlsen, Stiles and Weese (1960), ''Mechanics of Materials'', article 4-9 (2nd edition), John Wiley & Sons, Inc., New York. Library of Congress CCN 66-25222 In fluid dynamics, shear flow is the flow ''induced'' by a force in a fluid. In solid mechanics For thin-walled profiles, such as that through a beam or semi-monocoque structure, the shear stress distribution through the thickness can be neglected. Furthermore, there is no shear stress in the direction normal to the wall, only parallel. In these instances, it can be useful to express internal shear stress as shear flow, which is found as the shear stress multiplied by the thickness of the section. An equivalent definition for shear flow is the shear force ''V'' per unit length of the perimeter around a thin-walled section. Shear flow has the dimensions of force per unit of length. This corresponds to units of newtons per meter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
