Mechanics of Continuous Media

Recommended Prerequisites

General Physics I, Mechanics I, Linear Algebra and Analytical Geometry

Teaching Methods

Theoretical lessons: include a detailed explanation using audio-visual equipment, of the concepts, principals and fundamental theories, being simultaneously introduced practical exercises to illustrate the topic.

Theoretical-practical lessons: the students are request to solve proposed exercises for direct application of the acquired knowledge under guidance of the professor.

Learning Outcomes

C1) provide the student with the basic knowledge for structural analysis, namely for the Strength of Materials and Structures Theory, and also for Fluid and Soil Mechanics; C2) to provide the equations of internal equilibrium, compatibility conditions; C3) to introduce constitutive laws for different continuum solids and fluids; C4) to understand the behavior of the material and evaluate its safety using different criteria.

Work Placement(s)

No

Syllabus

q1 – Introduction and general information: General considerations, Fundamental definitions.

q2 - The Stress Tensor: Equilibrium conditions, Stresses in an inclined facet, Principal stresses and principal directions, Octahedral stresses, Two-dimensional analysis of the stress tensor.

q3 – The Strain Tensor: Components of the Strain Tensor, Pure deformation and rigid body motion, Equations of compatibility, Deformation in an arbitrary direction, Two-dimensional analysis of the strain tensor.

q4 – Constitutive law: Rheological behaviour – physical models, Generalized Hooke’s law (isotropic materials, monotropic, orthotropic, isotropic with linear visco-elastic behaviour), Newtonian liquid, Energy of deformation, Yielding and Rupture Laws (namely criteria of Mohr, Von Mises and Tresca)

Head Lecturer(s)

Vítor Dias da Silva

Assessment Methods

Final
Exam: 100.0%

Bibliography

Mecânica e Resistência dos Materiais, V. Dias da Silva, 2005.

Theory of Elasticity, Timoshenko, S.P., Goodier, J.N., McGraw-Hill, 1970

Continuum Mechanics, A. J. M. Spencer, DoverPublications.com, 1992

Introduction to Tensor Calculus and Continuum Mechanics, J.H.. Heinbockel, Trafford Pub., 2001.

An Introduction to Continuum Mechanics, M. Gurtin, Elsevier, 1981.

Principles of Continuum Mechanics, M.N.L. Narasimhan, John Wiley and Sons, 1993

Continuum Mechanics, W. Jaunzemis, The Macmillan Co, 1967.

Introduction to the Mechanics of Continuous Media, L.E. Malvern, Prentice Hall, 1969.

Tensor Analysis and Continuum Mechanics, W. Flugge, Springer-Verlag, 1972.

A First Course in Continuum Mechanics, Y.C. Fung, 3rd ed., Prentice Hall, 1994.