What is isotropic elasticity?

A material is said to be isotropic if its properties do not vary with direction. Isotropic materials therefore have identical elastic modulus, Poisson’s ratio, coefficient of thermal expansion, thermal conductivity, etc. In order to define the isotropic elastic properties, you must define the elastic modulus Ex .

What are the 4 basic elasticity equations?

Also one might have been exposed to four equations connecting these four concepts, namely strain-displacement equation, constitutive equation, equilibrium equation and compatibility equation.

What is the formula of elasticity in physics?

In equation form, Hooke’s law is given by F=kΔL F = k Δ L , where ΔL is the change in length. Elasticity is a measure of how difficult it is to stretch an object. In other words it is a measure of how small k is. Very elastic materials like rubber have small k and thus will stretch a lot with only a small force.

What is elasticity matrix?

The elasticity matrix for homogeneous materials is defined simply by the poisson’s ratio “v” or “n” and the modulus of elasticity “E”.

What are stiffness constants?

Any one of the coefficients of the relations in the generalized Hooke’s law used to express stress components as linear functions of the strain components. Also known as elastic constant. Elastic stiffness constant is associated with the different compositions of system stress and strain.

What are the 3 modulus of elasticity?

The modulus of elasticity is simply the ratio between stress and strain. Elastic Moduli can be of three types, Young’s modulus, Shear modulus, and Bulk modulus.

What are isotropic materials?

Isotropic materials are materials whose properties remain the same when tested in different directions. Common isotropic materials include glass, plastics, and metals. On the other hand, fiber-reinforced materials such as composites and natural materials such as wood tend to display anisotropic properties.

What are the 4 types of elasticity?

Four types of elasticity are demand elasticity, income elasticity, cross elasticity, and price elasticity.

How do you calculate price elasticity?

Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. It is computed as the percentage change in quantity demanded (or supplied) divided by the percentage change in price.

What is the SI unit of elasticity?

pascal
The material’s elastic limit or yield strength is the maximum stress that can arise before the onset of plastic deformation. Its SI unit is also the pascal (Pa).

What is unit of modulus of elasticity?

The units of modulus of elasticity are pressure units, as it is defined as stress (pressure units) divided by strain (dimensionless). Most commonly the units are Pascals (Pa) which is the SI unit, or pounds per square inch (psi) depending on the industry or geographical location.

How to find the elastic constants for isotropic materials?

The two elastic constants are usually expressed as the Young’s modulus E and the Poisson’s ratio n. However, the alternative elastic constants K ( bulk modulus) and/or G ( shear modulus) can also be used. For isotropic materials, G and K can be found from E and n by a set of equations, and vice-versa.

What are the equations of elasticity for an infinitesimal element?

1. Equilibrium 2. Strain – Displacement 3. Stress – Strain Relations ( Constitutive Relations) Consider each: 1. Equilibrium (3) • Σ F i = 0, Σ M i = 0 • Free body diagrams • Applying these to an infinitesimal element yields 3 equilibrium equations Figure 4.1 Representation of general infinitesimal element Paul A. Lagace © 2001

Which is a constitutive equation for a linear elastic material?

CONSTITUTIVE EQUATIONS \ \ 1 E 1^ = 2 E\2 Figure 3.1: Stress-strain curve for a linear elastic material subject to uni-axial stress ˙(Note that this is not uni-axial strain due to Poisson e\ect) In this expression, Eis Young’s modulus.

How to calculate Hooke’s law for isotropic materials?

Hooke’s law for isotropic materials in compliance matrix form is given by, Some literatures may have a factor 2 multiplying the shear modulii in the compliance matrix resulting from the difference between shear strain and engineering shear strain, where , etc.