🔴 PHY103. ELASTICITY

 *ELASTICITY* 

 Elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed

 Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal

  Moving on, the physical reasons for elastic behavior can be quite different for different materials.

 In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system).

 But for rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied.

Let's look into Hooke's law

 *HOOKE'S LAW* 

Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of deformation, regardless of how large that distance becomes

 This is known as perfect elasticity, in which a given object will return to its original shape no matter how strongly it is deformed.

 This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs.

  So, in engineering, the elasticity of a material is determined by two types of parameters:

1.  The material's modulus and the material's elastic limit

2. The material's modulus, which measures the amount of force per unit area needed to achieve a given amount of deformation

 Note that‼️

A higher modulus typically indicates that the material is harder to deform.

 The SI unit of a modulus is the *pascal (Pa)*

 *Question*

 That means modulus is the same as pressure

Right?

 *Answer*

 Yeah

The material's modulus, which measures the (amount of force per unit area) needed to achieve a given amount of deformation

    More explanatory, you should know that when we pull the object to check it's elasticity, we are definitely applying Pressure to the object

The other one which is the material's elastic limit, is referred to the maximum stress that can arise in a material before the onset of permanent deformation.

 Its SI unit is also the *pascal (Pa).* 

 When describing the relative elasticities of two materials, both the modulus and the elastic limit have to be considered.

 So, if you forget everything, make sure to recall that when an elastic material is deformed due to an external force, it experiences internal resistance to the deformation and restores it to its original state if the external force is no longer applied.

 There are various elastic moduli, such as Young's modulus, the shear modulus, and the bulk modulus, all of which are measures of the inherent elastic properties of a material as a resistance to deformation under an applied load.

 The various moduli apply to different kinds of deformation

They are three:-

 For instance, *Young's modulus* applies to extension/compression of a body. 

The shear modulus applies to its shear

(N/b: Both Young and Shear modulus are only for solids)

We also have the *bulk modulus* which is for solids, liquids and gases.

 The elasticity of materials is described by a stress–strain curve, which shows the relation between stress (the average restorative internal force per unit area) and strain (the relative deformation)

 The curve is generally nonlinear, but it can (by use of a Taylor series) be approximated as linear for sufficiently small deformations (in which higher-order terms are negligible)

 If the material is isotropic, the linearized stress–strain relationship is called Hooke's law, which is often presumed to apply up to the elastic limit for most metals or crystalline materials whereas nonlinear elasticity is generally required to model large

 deformations of rubbery materials even in the elastic range.

 For even higher stresses, materials exhibit plastic behavior, that is, they deform irreversibly and do not return to their original shape after stress is no longer applied

 For rubber-like materials such as elastomers, the slope of the stress–strain curve increases with stress, meaning that rubbers progressively become more difficult to stretch, while for most metals, the gradient decreases at very high stresses, meaning that they progressively become easier to stretch

 Elasticity is not exhibited only by solids; non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions quantified by the Deborah number

  In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape.

 Under larger strains, or strains applied for longer periods of time, these fluids may start to flow like a viscous liquid.

  Because the elasticity of a material is described in terms of a stress–strain relation, it is essential that the terms stress and strain be defined without ambiguity.

 Typically, two types of relation are considered:-

1.  The first type deals with materials that are elastic only for small strains.

2.The second deals with materials that are not limited to small strains.

 Clearly, the second type of relation is more general in the sense that it must include the first typewriter as a special case.

 For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor, the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called the generalized Hooke's law.

 Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for the possibility of large rotations, large distortions, and intrinsic or induced anisotropy.

For more general situations, any of a number of stress measures can be used, and it generally desired (but not required) that the elastic stress–strain relation be phrased in terms of a finite strain measure that is work conjugate to the selected stress measure, i.e., the time integral of the inner product of the stress measure with the rate of the strain measure should be equal to the change in internal energy for any adiabatic process that remains below the elastic limit.

 But I'd task us to read on Taylor series, non newtonian fluids, Deborah number and Cauchy stress as they relate to Elasticity

By: Ms. Ojimadu David

✍️ *FLASHPEE EDUCATIONAL TEAM*