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Continuum Mechanics for Ph.D. Students - NDGF013

Title:	Mechanika kontinua pro doktorandy
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, 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. Zdeněk Martinec, DrSc.

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: T_KG (28.03.2008)

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 momemtum and angular momentum, energy conservation. Integral and differential forms. Interface conditions. Classical linear elasticity. Fluid dynamics. Weak motions of viscoelastic prestressed self-graviting body. Examples: Earth free oscillations, postglacial rebound, tidal and rotational deformation, convection in Earth mantle.

Aim of the course -

Last update: T_KG (28.03.2008)

The lecture provides application of theory of continuum mechanics to several geophysical phenomena.

Course completion requirements -

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

Oral exam

Literature - Czech

Last update: T_KG (18.01.2007)

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.

Teaching methods -

Last update: T_KG (11.04.2008)

Lecture + exercises

Syllabus -

Last update: T_KG (28.03.2008)

Small motions in a medium with a finite pre-stress
Total, initial and incremental fields, Lagrangian and Eulerian increments, material and local forms of the equations for the incremental fields, kinematic and dynamic interface conditions, increments in gravitation, linearized Poisson's equation for gravitational potential increments, linearized interface conditions for increments in gravitation.

Free elastic-gravitational oscillations of the Earth
Excitation of free oscillations, equations of motion, boundary and interface conditions, SNREI Earth model, toroidal and spheroidal oscillations, rotational and elliptical splitting, splitting due to the Earth's lateral heterogeneities, calculations of the eigenfrequencies.

Postglacial viscoelastic rebound
Maxwell solid, theory of initial and boundary-value viscoelastic problem for spherically symmetric sphere, the model of ice-load, implicit and explicit time integration, solution in the Laplace domain, Love numbers, effect of compressibility and gravitation, viscoelastic problem with 3-D viscosity, its numerical solution, synthetic test examples.

Thermal convection in the Earth's mantle
Formulation of the problem, methods of solution, review of the results.