Mechanics Of Granular Materials Analysis Engineering Essay

Mechanics Of Granular Materials Analysis Engineering Essay

The survey of farinaceous stuffs comes from a field of natural philosophies known as nonlinear kineticss, which is the survey of entropy within physical systems. An illustration of nonlinear kineticss is a theoretical account of the way a marble will fall if pushed off a balanced place on the caput of a pin ( Clark, 1999 ) . Nonlinear kineticss helps us to understand more clearly the random procedure in farinaceous stuffs and besides to understand how the forces are distributed against the walls of a container keeping the farinaceous stuffs.

This chapter focuses on the forces of interaction and other physical measures moving on the atoms while fluxing inside the bed.

2.1 Farinaceous Materials

A farinaceous stuff is a mixture of distinct solids, chiefly macroscopic atoms characterized by a loss of energy during atom interactions. Some illustrations of farinaceous stuffs are nuts, coal, sand, java, cereals and ball bearings. Powders are besides farinaceous stuffs and there little sizes make them more cohesive.

We can province that farinaceous stuffs do non represent of a individual stage of affair but have features of solids, liquids and gases depending on the energy of the atoms.

When the mean energy of the farinaceous stuff is reasonably low, such that the atoms are comparatively stationary with each other, the farinaceous stuff Acts of the Apostless as a solid.

When the farinaceous stuff is in gesture such that the atoms are non stationary relation to each other, the farinaceous stuff is said to fluidize and come in a liquid like province. As the farinaceous stuff flow even more freely, it get flow features about indistinguishable to that of Newtonian fluids but farinaceous stuffs dissipate energy rapidly.

When the farinaceous stuff is driven even harder such that there is about no contact between the atoms, stuff is said to come in a gaseous province. However, the atoms in the farinaceous stuff will be given to organize bunchs, unlike gases. hypertext transfer protocol: //en.wikipedia.org/wiki/Granular_material

2.2 Forces moving on the atoms

A force can be described as a push or a pull playing on an object doing the object to alter its speed and hence accelerate or doing distortion to flexible objects. hypertext transfer protocol: //en.wikipedia.org/wiki/Force

2.2.1 Weight

The weight of the atoms act downwards, due to the pull of gravitation moving on the them and is equal to the merchandise of the mass of the atoms with the gravitative force of attractive force ( 9.81N ) .

2.2.2 Elastic force

This force arises due to the distortion of the solid depending on the organic structure ‘s instantaneous distortion ( hypertext transfer protocol: //encyclopedia2.thefreedictionary.com/elastic+force ) . For illustration, a spring acquires elastic force when stretched enabling it to return to its original length. ( hypertext transfer protocol: //en.wikipedia.org/wiki/Force # Elastic_force )

2.2.3 Coulomb clash

This frictional force occurs chiefly in mechanical systems when surfaces come into skiding contact with each other. Its magnitude depends on the forces in contact and its way is opposite to the comparative speed of the atoms in contact.

2.2.4 Friction torsion

The torsion produced due to the frictional force between the farinaceous stuffs in contact with each other doing the atoms to revolve.

2.3 Poisson ‘s ratio

Poisson ‘s ratio, ( named after Simeon Poisson ) , is the ratio of the contraction or strain moving perpendicular to the applied burden to the extension or strain in the way of the applied burden, when an object is stretched.

The Poisson Effect occurs when a compacting force applied on an object, makes the object to spread out in the two waies perpendicular to the way of compaction.

The Poisson ration values for most stuffs lie between 0.0 and 0.5. Hence, the Poisson ration value used in our computational simulations was taken to be 0.2, which is about the same value for sand, concrete and glass. hypertext transfer protocol: //en.wikipedia.org/wiki/Poisson % 27s_ratio

2.4 Coefficient of clash

Besides known as the ‘frictional coefficient ‘ , is denoted by the Grecian missive Aµ . It is a dimensionless scalar value stand foring the ration of the frictional force between two organic structures and the force pressing them together. Its value depends on the stuffs in contact with each other.

It may hold values runing from about zero to greater than one. The value for the coefficient of clash in our computational simulation was taken to be 0.3, which is about the same value for wood which lies between 0.2 and 0.6. hypertext transfer protocol: //en.wikipedia.org/wiki/PoissonHYPERLINK “ hypertext transfer protocol: //en.wikipedia.org/wiki/Poisson’s_ratio ” ‘HYPERLINK “ hypertext transfer protocol: //en.wikipedia.org/wiki/Poisson’s_ratio ” s_ratio

2.5 Coefficient of damages

This is the ratio of the velocity of an object before hit to the velocity of the object after hit. For elastic hits, the coefficient of damages is 1 whereas for inelastic hit it has a value less than 1. The value for the coefficient of damages, for two clashing objects a and B is given by the expression:

Where: is the concluding speed of object B

is the concluding speed of object a

is the initial speed of object a

is the initial speed of object B

hypertext transfer protocol: //en.wikipedia.org/wiki/Coefficient_of_restitution

2.6 Inelastic hit

It is a type of hit whereby the entire kinetic energy is non conserved and gets converted into vibrational and heat energy. The farinaceous stuffs are assumed to clash inelastically and therefore dispersing energy. hypertext transfer protocol: //en.wikipedia.org/wiki/Inelastic_collision

2.7 Dynamicss of atoms falling freely in a rectangular bed

Case 1: See a atom, with radius R, falling freely at an angle with the horizontal.

Y

ya

Xa – X0 = breadth of bed

left right ya – yo = tallness of bed

yo

X0 underside Xa

at t = 0, speed of atom, and place of atom S0 =

acceleration moving on atoms,

at t = t1, place of atom, S1 =

at left wall, SL =

when S1 = SL, impact occurs: =

Case 2: See 2 similar atoms, I± and I? , both of radius R, falling freely at an angle of I? and O with the horizontal severally.

Y

ya I± I?

I? O xa – xo = breadth of bed

left VI? VO right ya – yo = tallness of bed

yo

xo underside xa

at t = 0, place of I± , = and place of I? ,

acceleration moving on both atoms,

speed of atom I± , and speed of atom I? ,

at t = t1, place of atom I± , =

and place of atom I? ,

For hit to happen, must be equal to

Or