# Hookes law and youngs modulus relationship test

### What is Poisson's ratio?

Young's modulus can be defined at any strain, but where Hooke's law is obeyed it is a This is a very useful relationship to understand when thinking about the. relationship between the modulus of rigidity—which I'll refer to as shear Hooke's law with a state of pure shear stress as occurs for, say, a torsion test. In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law: s = E e. That is, E is the slope of the stress-strain curve.

Analysis of effect of Poisson's ratio on compression of a layer. What about the effect of Poisson's ratio on constrained compression in the 1 or x direction? Constrained compression means that the Poisson effect is restrained from occurring. This could be done by side walls in an experiment.

Also, compression of a thin layer by stiff surfaces is effectively constrained. Moreover, in ultrasonic testing, the wavelength of the ultrasound is usually much less than the specimen dimensions. The Poisson effect is restrained from occurring in this case as well.

In Hooke's law with the elastic modulus tensor as Cijkl we sum over k and l, but, due to the constraint, the only strain component which is non-zero is e Let us find the physical significance of that tensor element in terms of engineering constants. One may also work with the elementary isotropic form for Hooke's law. There is stress in only one direction but there can be strain in three directions.

So Young's modulus E is the stiffness for simple tension, with the Poisson effect free to occur. The physical meaning of Cis the stiffness for tension or compression in the x or 1 direction, when strain in the y and z directions is constrained to be zero. The reason is that for such a constraint the sum in the tensorial equation for Hooke's law collapses into a single term containing only C The constraint could be applied by a rigid mold, or if the material is compressed in a thin layer between rigid platens.

Calso governs the propagation of longitudinal waves in an extended medium, since the waves undergo a similar constraint on transverse displacement. Therefore the constrained modulus Cis comparable to the bulk modulus and is much larger than the shear or Young's modulus of rubber.

Practical example - cork in a bottle. An example of the practical application of a particular value of Poisson's ratio is the cork of a wine bottle. The cork must be easily inserted and removed, yet it also must withstand the pressure from within the bottle. Rubber, with a Poisson's ratio of 0. Cork, by contrast, with a Poisson's ratio of nearly zero, is ideal in this application.

Practical example - design of rubber buffers. How does three-dimensional deformation influence the use of viscoelastic rubber in such applications as shoe insoles to reduce impact force in running, or wrestling mats to reduce impact force in falls?

## Young's modulus

Solution Refer to the above analysis, in which deformation under transverse constraint is analyzed. Rubbery materials are much stiffer when compressed in a thin layer geometry than they are in shear or in simple tension; they are too stiff to perform the function of reducing impact. Compliant layers can be formed by corrugating the rubber to provide room for lateral expansion or by using an elastomeric foam, which typically has a Poisson's ratio near 0. Corrugated rubber is used in shoe sneaker insoles and in vibration isolators for machinery.

Foam is used in shoes and in wrestling mats. Practical example - aircraft sandwich panels.

### Young’s modulus | Description, Example, & Facts | jingle-bells.info

The honeycomb shown above is used in composite sandwich panels for aircraft. The honeycomb is a core between face-sheets of graphite-epoxy composite. Such panels are usually flat. If curved panels are desired, the honeycomb cell shape must be changed from the usual regular hexagon shape, otherwise the cells will be crushed during bending. Several alternative cell shapes are known, including those which result in a negative Poisson's ratio.

Practical example - Interpreting compression tests on blocks of flexible material. The material is constrained at contact surfaces by the compression device, so the Poisson effect cannot freely occur.

We will learn exactly what the terms stress and strain describe as well as the relationship between them. After going through the lesson's material, I will pass out a handout with example problems.

**Young's modulus and the interatomic spring constant**

Work these to the best of your abilities independently first; then we will review the problems as a class. After becoming familiar with using the new equations, we will explore Hooke's law in an associated activity Applying Hooke's Law to Cancer Detection by experimentally determining an unknown proportionality constant.

After exploring Hooke's law, in the second portion of the activity, we will begin to apply what we've learned to develop a means of imaging body tissues and we will soon be able to detect malignant tumors! You will also practice graphing prepared data to depict cancerous tissue. After we have mastered this material, we will have a quiz on stress, strain and Hooke's law. Please take careful notes and be sure to ask any questions you have about the example problems we will be working through.

Referring back to the legacy cycle which we discussed in the previous lesson, today's lesson constitutes the research and revise phase.

Refer back to your initial thoughts notes and record any new information that applies to solving the challenge. Your goal today is to review, revise and expand your current knowledge! Now, let's learn how to detect cancer. Students begin to learn the basic concepts required for creating a strain graph to depict cancerous tissue.

Following this lesson, have students revise their initial thoughts and at the conclusion of the associated activity, students should have the skills necessary to Go Public with a solution.

The quiz serves as a formative assessment while the next lesson's Go Public phase provides a summative assessment.