# Mechanics of Materials II

## Objectives

Mechanics of Materials II objective is the study of the mechanical behavior of some important classes of materials not considered in the first unit, Mechanics of Materials I – these are essentially the fluids and the polymeric materials. The study of fluids is initiated in the unit of Physics I, at a very elementary level, and here we aim at giving the student a wider view about their mechanical behavior. As to the polymers, the knowledge already acquired in previous units is applied and developed, in the study of two phenomena of the utmost practical importance, as is the case with elasticity and viscoelasticity. The objective is the understanding by the student of these phenomena, and the molecular characteristics lying on its genesis, so that in their professional life, in a manufacturing environment, he or she will be able to judge and determine the physical-chemicalstructure that will better generate the properties envisaged for the material.

## General characterization

##### Code

10195

##### Credits

6.0

##### Responsible teacher

Maria Teresa Varanda Cidade

##### Hours

Weekly - 5

Total - Available soon

##### Teaching language

Português

### Prerequisites

It is required a convenient preparation in the areas of Physics - mainly Newtonian Mechanics, and Mathematics - mainly Euclidean geometry, Vector calculus and Differencial and integral calculus. A basic knowledge of Polymer physics is also required, although a general review on this topic is included in the program of the unit. The knowledge required in this areas is provided by some previous units of the Course, namely Análise Matemática I, II and III, Física I and Física de Polímeros.

### Bibliography

## W. Lai, David Rubin, Erhard Krempl, "Introduction to Continuum Mechanics", Butterworth Weinemann for Elseivier, USA, 1999.

I.M.Ward, J.Sweeney, “An introduction to the Mechanical Properties of Solid Materials”, John Wiley and Sons Ltd, 2004.~

R. C. Arridge, "Mechanics of Polymers", Clarendon Press, Oxford, 1975

N.Phan-Thien, “Understanding Viscoelasticity”, Springer-Verlag, Berlin, 2002

### Teaching method

Theoretical-practical classes and practical laboratory classes. In the former the subjects included in the program are transmited, with a focus on understanding the different topics, and resolution of exercises are performed to practice mathematical techniques used in Material Mechanics, as well as for ilustrating the physical phenomena involved in the flow of fluids, mainly non-Newtonian and in the elasticity and viscoelasticity of polymers. In the Laboratory, tensile and impact tests will be carried on, on different types of commercial thermoplastic polymers. In the evaluation, it is necessary to have a positive evaluation in the Laboratories, to gain frequency in the unit, as well as a positive result in the continuous evaluation or, alternatively, in the final exam. For the purposes of continuous assessment, two tests and 1 mini-test (evaluation of laboratory classes) are carried out throughout the semester. The result of the mini-test has a contribution of 20% for the final classification and the average of the two tests or the exam contribute to the remaining 80%.

### Evaluation method

The unit has a practical component, leading to a mark NP, and a theoretical-practical component, leading to a mark NT. Both range from 0 to 20 points. For approval in the unit, with a final mark N, a student needs a mark of at least 9.5 points in each component. N will be given by

N = 0,2 NP + 0,8 NT.

NP is the mark obtained in an individual quiz relative to two laboratory sessions, and NT can be obtained in two different ways: either by averaging the marks obtained in two written tests, or alternatively, it is the mark obtained in a final exam.

To perform the UC by continuous evaluation it is necessary that the grade of the 1st test is not lower than 7.5 values. Otherwise, the student is admitted to the exam, provided he obtained NP higher than 9.5 val..

The students must carry out all the lab sessions, otherwise they will be excluded.

## Subject matter

Chapter 1. Basic concepts of Tensor analysis.

Chapter 2. Tensions.

Chapter 3. Deformation and Deformation rate. Vorticity.

Chapter 4. General principles: conservation of mass, linear momentum, angular momentum and energy, second law of Thermodynamics.

Chapter 5. Constitutive equations of Elasticity.

Chapter 6. Mechanical behaviour of polymers.

Chapter 7. Viscoelasticity: viscoelastic models, master curves, time-temperature superposition principle, WLF equation.