# Continuum Mechanics (250952) – Course 2024/25 PDF

# Syllabus

## Learning Objectives

This is a complete course in nonlinear continuum mechanics for engineers. It carries out a deep review of the fundamental concepts, including motion, deformations, strains, stresses, governing laws of balance, variational principles and an introduction to the Mechanics of solids and of fluids. * The students will be able to understand and assimilate the foundations of the mechanics of solids, identifying the most important aspects of material modeling, and dissipation mechanisms associated with nonlinear behaviour. * They have to be able to interpret the physical meaning of the material properties and properly identify the numerical methods for the solution of problems of solid mechanics, with its application to elasticity, and learn the foundations of fluid mechanics. * The students will develop practical skills to work with tensors and formulate and develop analysis of diverse problems of solids in engineering. * Tensor algebra (definitions, invariants, gradients, divergences, rotational, integral theorems). * Kinetics: deformationºº and strain (strain tensors). * Small deformations and compatibility. * Stress tensors. * Governing laws * Constitutive Laws (laws of thermodynamics, deformation energy, elasticity) * Boundary value problems in linear elasticity (2D) * Introduction to plasticity (Von Mises, Tresca, Mohr, Coulomb) * Ideal and potential flows. * Viscous incompressible flow (with an introduction to turbulent flow) * Learning resources: o Bonet, J, Gil AJ, Wood RD, Nonlinear Solid Mechanics for Finite Element Analysis - Statics, Cambridge University Press o Bonet, J, Gil AJ, Wood RD, Nonlinear Solid Mechanics for Finite Element Analysis - Dynamics, Cambridge University Press o Holzapel, G.A., Nonlinear solid mechanics, a continuum approach for engineering, Wiley, 2000 o Currie, The main objectives of the course are the presentation, understanding and mastery of the basic fundamentals of nonlinear continuum mechanics and their application to solid mechanics and fluid mechanics.

## Total hours of student work

Hours | Percentage | |||
---|---|---|---|---|

Supervised Learning | Large group | 25.5h | 56.67 % | |

Medium group | 9.8h | 21.67 % | ||

Laboratory classes | 9.8h | 21.67 % | ||

Self Study | 80h |

## Teaching Methodology

The course consists of 40 hours of class, taught semi-intensively, intensively from Monday to Friday over the first two weeks and then one day per week. The classes include theory, problems and guided activities. For each subject, the necessary theoretical concepts are first introduced, then some examples and exercises are solved by the professor. The students will solve some additional problems during the class time under the supervision of the professor. On the other hand, students will solve some additional assignments as homework. The student has a basic teaching material for monitoring and understanding of the course: (1) the files in pdf format with the updated content of the classes; (2) video recordings of classroom lectures given during 2012-2013; basic and supplementary bibliographic references. Although most of the sessions will be given in the language indicated, sessions supported by other occasional guest experts may be held in other languages.

## Grading Rules

The evaluation calendar and grading rules will be approved before the start of the course.

The course grade is obtained from the ratings of the continuous assessment (30%) and final exam (70%). Continuous assessment: The student has to solve along the course and supervised by the professor, several exercises and problems, both in the classroom (during school hours), and beyond. Final exam: The final exam consists of some questions and problems similar to those that have been raised and resolved in class.

## Test Rules

Continuous assessment: Failure to perform a continuous assessment activity in the scheduled dates will result in a zero mark in that activity. Final exam: The final exam will be an open book exam.

## Office Hours

Negotiable

## Bibliography

### Basic

- Bonet, J, Gil, AJ, Wood RD. Nonlinear Solid Mechanics for Finite elemenet Analysis - Statics. Cambridge University Press,
- Bonet, J.; Wood, R.D. Nonlinear continuum mechanics for finite element analysis. Cambridge: Cambridge University Press, 2008. ISBN 9780521838702.
- Bonet, J, Gil AJ, Wood RD. Nonlinear Solid Mechanics for Finite Element Analysis - Dynamics.

### Complementary

- Holzapfel, G.A. Nonlinear solid mechanics: a continuum approach for engineering. Chichester: John Wiley & Sons, 2000. ISBN 0471823198.
- Oliver, X.; Agelet de Saracibar, C. Continuum mechanics for engineers: theory and problems. 2nd ed. Barcelona: els autors, 2017.
- Oliver Olivella, X.; Agelet de Saracíbar, C. Mecánica de medios continuos para ingenieros. 2a ed. Barcelona: Edicions UPC, 2002. ISBN 848301582X.
- González, O.; Stuart, A.M. A first course in continuum mechanics. Cambridge: Cambridge University, 2008. ISBN 9780521886802.
- Marsden,J.E.; Hugues, T.J.R. Mathematical foundations of elasticity. New York: Dover, 1994. ISBN 0486678652.
- Truesdell, C.; Noll, W. The non-linear field theories of mechanics. 3rd ed. Berlin: Springer-Verlag, 2004. ISBN 3540027793.