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μ(I) Rheology
In granular mechanics, the ''μ''(''I'') rheology is one model of the rheology of a granular flow. Details The inertial number of a granular flow is a dimensionless quantity defined as I = \frac, where \dot\gamma is the shear rate tensor, , , \dot\gamma, , is its magnitude, ''d'' is the average particle diameter, ''P'' is the isotropic pressure and ''ρ'' is the density. It is a local quantity and may take different values at different locations in the flow. The ''μ''(''I'') rheology asserts a constitutive relationship between the stress tensor of the flow and the rate of strain tensor: \sigma_ = -P\delta_ + \mu(I)P \frac where the eponymous ''μ''(''I'') is a dimensionless function of ''I''. As with Newtonian fluids, the first term -''Pδ''''ij'' represents the effect of pressure. The second term represents a shear stress: it acts in the direction of the shear, and its magnitude is equal to the pressure multiplied by a coefficient of friction ''μ''(''I' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Granular Mechanics
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose granular material are large enough such that they are not subject to thermal motion fluctuations. Thus, the lower size limit for grains in granular material is about 1 μm. On the upper size limit, the physics of granular materials may be applied to ice floes where the individual grains are icebergs and to asteroid belts of the Solar System with individual grains being asteroids. Some examples of granular materials are snow, nuts, coal, sand, rice, coffee, corn flakes, salt, and bearing balls. Research into granular materials is thus directly applicable and goes back at least to Charles-Augustin de Coulomb, whose law of friction was originally stated for granular materials. Granular materials are commercially important in applications as di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rheology
Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied forcRheology is the branch of physics that deals with the deformation and flow of materials, both solids and liquids.W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon The term '' rheology'' was coined by Eugene C. Bingham, a professor at Lafayette College, in 1920 from a suggestion by a colleague, Markus Reiner.The Deborah Number The term was inspired by the aphorism of Heraclitus (often mistakenly attributed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Granular Flow
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose granular material are large enough such that they are not subject to thermal motion fluctuations. Thus, the lower size limit for grains in granular material is about 1 μm. On the upper size limit, the physics of granular materials may be applied to ice floes where the individual grains are icebergs and to asteroid belts of the Solar System with individual grains being asteroids. Some examples of granular materials are snow, nuts, coal, sand, rice, coffee, corn flakes, salt, and bearing balls. Research into granular materials is thus directly applicable and goes back at least to Charles-Augustin de Coulomb, whose law of friction was originally stated for granular materials. Granular materials are commercially important in applications as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inertial Number
The Inertial number I is a dimensionless quantity which quantifies the significance of dynamic effects on the flow of a granular material. It measures the ratio of inertial forces of grains to imposed forces: a small value corresponds to the quasi-static state, while a high value corresponds to the inertial state or even the "dynamic" state. It is given by: I = \frac, where \dot\gamma is the shear rate, d the average particle diameter, P is the pressure and \rho is the density. Generally three regimes are distinguished: * I<10^: quasi static flow * |
Dimensionless Quantity
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined Unit of measurement, units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific Unit of volume, units of volume used, such as in milliliters per milliliter (mL/mL). The 1, number one is recognized as a dimensionless Base unit of measurement, base quantity. Radians serve as dimensionless units for Angle, angular measurements, derived from the universal ratio of 2Ï€ times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constitutive Relationship
Constitutive may refer to: * In physics, a constitutive equation is a relation between two physical quantities * In ecology, a constitutive defense is one that is always active, as opposed to an inducible defense * Constitutive theory of statehood A sovereign state is a state that has the highest authority over a territory. It is commonly understood that a sovereign state is independent. When referring to a specific polity, the term "country" may also refer to a constituent country, or a ... * In biochemistry and pharmacology, a constitutively active receptor produces a biological response in the absence of a bound ligand * In genetics, a constitutive gene is always expressed – see constitutive expression {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Stress Tensor
In continuum mechanics, the Cauchy stress tensor (symbol \boldsymbol\sigma, named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration. The second order tensor consists of nine components \sigma_ and relates a unit-length direction vector e to the ''traction vector'' T(e) across an imaginary surface perpendicular to e: :\mathbf^ = \mathbf e \cdot\boldsymbol\quad \text \quad T_^= \sum_\sigma_e_i. The SI base units of both stress tensor and traction vector are newton per square metre (N/m2) or pascal (Pa), corresponding to the stress scalar. The unit vector is dimensionless. The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates. A graphical representation of this transformation law is the Mohr's circle for stress. The Cauchy stress tensor is used for stress analysis of mater ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newtonian Fluid
A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector. A fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is also isotropic (i.e., its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous shear deformation and continuous compression or expansion, respectively. Newtonian fluids are the easiest mathematical models of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Stress
Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. General shear stress The formula to calculate average shear stress or force per unit area is: \tau = ,where is the force applied and is the cross-sectional area. The area involved corresponds to the material face (geometry), face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force. Other forms Wall shear stress Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as:\tau_w := \mu\left.\frac\_,where is the dynamic viscosity, is the flow velocity, and is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called tribology, and has a history of more than 2000 years. Friction can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. It is known that frictional energy losses account for about 20% of the total energy expenditure of the world. As briefly discussed later, there are many different contributors to the retarding force in friction, ranging from asperity deformation to the generation of charges and changes in local structure. When two bodies in contact move relative to each other, due to these various ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectricity, ferroelectric materials, as well as in the deformation (mechanics), deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems, it is often associated with irreversible process, irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect. Hysteresis can be fou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Element Method
A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact, particle deformation and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, ice and rock mechanics. DEM has been extended into the Extended Discrete Element Method taking heat transfer, chemical reaction and coupling to CFD and FEM into account. Discrete element ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
