Overall objectives:

1 - Master the most important basic concepts of Continuum Mechanics and knowing how to apply theoretical knowledge to solve simple problems.
2 - Apply mathematical models to the phenomena of everyday life, nature and technology, perform numerical estimates.
3 - Develop curiosity and critical thinking.

Syllabus:

1 - Introduction
1.1 - Subject of Continuum Mechanics
1.2 - Methods of Continuum Mechanics
1.3 - Assumption of continuum
2 - Elements of the theory of tensors
2.1 - The indicial notation
2.1.1 - Summation convention, dummy indices
2.1.2 - Free indices
2.1.3 - The Kronecker delta
2.1.4 - The Permutation symbol
2.1.5 - Indicial notation manipulations
2.2 - Tensors
2.2.1 - Tensor: a linear transformation
2.2.2 - Components of a tensor
2.2.3 - Sum of tensors
2.2.4 - Dyadic product of vectors
2.2.5 - Product of two tensors
2.2.6 - Indentity tensor and tensor inverse
2.2.7 - Transpose of a tensor
2.2.8 - Orthogonal tensor
2.2.9 - Transformation laws for Cartesian components of vectors and tensors
2.2.10 - Principal scalar invariants of a tensor
2.2.11 - Tensors of different orders
2.2.12 - Symmetric and antisymmetric tensors
2.2.13 - The dual vector of an antisymmetric tensor
2.2.14 - Eigenvalues and eigenvectors of a tensor
2.2.15 - Principal values and principal directions of real symmetric tensors
2.2.16 - Matrix of a tensor with respect to principal directions
2.2.17 - Gradient of a vector function
2.2.18 - Divergence of a tensor field
3 - Kinematics of a continuum
3.1 - Lagrangean description of motion of a continuum
3.2 - Eulerian description of motion of a continuum
3.3 - Material derivative
3.4 - Acceleration of a particle
3.5 - Displacement field
3.6 - Rate of deformation
3.7 - Equation of conservation of mass
3.8 - Compatibility conditions for components of the infinitesimal strain tensor
3.9 - Compatibility conditions for components of the rate of deformation tensor
4 - Stress
4.1 - Stress vector
4.2 - Stress tensor
4.3 - Symmetry of stress tensor
4.4 - Principal stresses
4.5 - Maximum shearing stresses
4.6 - Equations of motion
4.7 - Boundary conditions for the stress tensor
5 - Constitutive equations for simple models of continuum
5.1 - Ideal fluid
5.2 - Linear elastic solid
5.3 - Newtonian viscous fluid
6 - Linear elastic solid
6.1 - Equations of the infinitesimal theory of elasticity
6.2 - Principle of superposition
6.3 - Examples of elastodynamic problems
6.3.1 - Plane irrotational wave
6.3.2 - Plane equivoluminal wave
6.4 - Examples of elastostatic problems
6.4.1 - Equations of elastostatics
6.4.2 - Simple extension
6.4.3 - Torsion of circular cylinder
7 - Newtonean viscous fluid
7.1 - Boundary conditions
7.2 - Streamlines, pathline, steady and unsteady flows, laminar and turbulent flows
7.3 - Examples of hydrostatics
7.4 - Examples of steady flows of Newtonian incompressible fluid
7.4.1 - Plane Couette flow
7.4.2 - Plane Poiseuille flow
7.4.3 - Hagen-Poiseuille flow
7.4.4 - Plane Couette flow of two layers of incompressible fluids
7.4.5 - Cylindrical Couette flow
7.5 - Irrotational flow
7.6 - Irrotational flow of inviscid incompressible fluid
7.7 - Concept of a boundary layer
7.8 - Compressible Newtonean fluid
7.9 - Acoustic wave

Literature/Sources:

W. M. Lai, D. Rubin and E. Krempl , 1996 , Introduction to Continuum Mechanics , Pergamon
Y. C. Fung , 1994 , A First Course in Continuum Mechanics for Physical and Biological Scientists and Engineers , Prentice Hall
M. E. Gurtin , 1993 , An Introduction to Continuum Mechanics , Academic Press
Philip J. Pritchard, John C. Leylegian , 2011 , Fox and McDonald's Introduction to Fluid Mechanics , John Wiley & Sons, Inc

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Blackboard will be used in theoretical classes to present the contents. The video projector can be used to display figures, plots, and tables. In theoretical-practical classes, students will solve problems from the problem sheets prepared by the teacher. During the semester, students will do two tests, each one counts for 50% of the grade. The tests have as objective the assessment of theoretical and theoretical-practical knowledge. Each test covers several topics of the curricular unit and requires from students, in particular, the ability to inter-relate different parts of the subject. The student may, during the semester, evaluate his/her performance and change strategies if necessary. Students can repeat one or two tests during the re-sitting period. Assessment Model: A