Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Continuum Mechanics II - NGEO069

Title:	Mechanika kontinua II
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Ondřej Čadek, CSc. prof. RNDr. Zdeněk Martinec, DrSc.
Classification:	Physics > Geophysics
Pre-requisite :	NGEO111

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: T_KG (09.05.2013)

Deformation, deformation tensors, polar decomposition, volume and area deformation, geometric linearization. Kinematics, material time derivative, Reynold's theorem. Surface and volume forces, Cauchy traction principle, stress tensors. Basic axioms, mass conservation, balance of linear momentum and angular momentum, energy conservation. Integral and differential forms. Interface conditions. Classical linear elasticity. Fluid dynamics.

Aim of the course -

Last update: T_KG (09.05.2013)

The lecture helps students understand general principes of continuum mechanics with application to deformation of elastic solid and fluid flow.

Course completion requirements - Czech

Last update: prof. RNDr. František Gallovič, Ph.D. (10.06.2019)

Zkouška probíhá písemnou formou. Podmínkou k přistoupení ke zkoušce je udělení zápočtu za aktivní účast na cvičeních. Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.

Literature - Czech

Last update: T_KG (09.05.2013)

M. Brdička, Mechanika kontinua, ČSAV, Praha 1959.

F. Maršík, Termodynamika kontinua, Academia, Praha 1999.

A.C. Eringen: Nonlinear Theory of Continuous Media, McGraw-Hill Book Company, New York, 1962.

L.E. Malvern, Introduction of the Mechanics of a Continuous Medium, Prentice Hall, New York, 1969.

Z. Martinec, Continuum Mechanics, MFF UK Praha, elektronická skripta. http://geo.mff.cuni.cz/vyuka.htm#UcebniTexty

Teaching methods -

Last update: T_KG (09.05.2013)

Lecture + exercises

Syllabus -

Last update: T_KG (09.05.2013)

Strain

Reference and present configurations, Lagrangian and Eulerian descriptions of deformation, base vectors, shifters, axiom of continuity, deformation gradients and tensors, polar decomposition of deformation gradient, Jacobi's identities, displacement vector, length and angle changes, strain invariants and principal directions, area and volume changes, changes of an external normal, compatibility conditions, geometrical linearization, small deformations, orthogonal curvilinear coordinates.

Kinematics

Material and spatial time derivatives, material derivative of surface and volume integrals, Reynolds' transport theorem.

Stress

External and internal loads, volume and surface forces, Cauchy traction principle, Cauchy stress tensor, Cauchy stress formula, Piola-Kirchhoff stress tensors.

Fundamental axioms of Continuum Mechanics

Conservation of mass, balance of linear momentum, balance of angular momentum, conservation of energy, entropy inequality, local balance laws, jump and boundary conditions, local balance laws in the reference frame, interface and boundary conditions, Lagrangian and Eulerian form of Poisson's equation.

Classical linear elasticity

Anisotropic linear elastic solids, Hooke's law for isotropic solids, Lamé parameters, restriction on elastic coefficients, the equation of motion in anisotropic and isotropic medium, deformation of elastic plate by its own weight.

Fluid dynamics

Constitutive equations, Newtonian and Stokesian fluids, thermodynamic and hydrostatic pressures, experimental origin of viscosity, the Navier-Stokes equation, boundary conditions.