Continuum Mechanics

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mechanics, Biomechanics and Mechatronics

Synopsis:

Elementar continuum mechanics-kinematics and fundamental laws. Mechanics of solids-thermoelasticity, hypoelasticity, objective rates. Inviscid and viscous fluids flow, shock waves. Examples.

Requirements:

Elementar courses of mechanics, elasticity and strength of materials, fluid dynamics and thermodynamics. Mathematics-analysis, tensor calculus.

Syllabus of lectures:

-Kinematics: Lagrangean and Eulerean descriptions, deformation gradient, multiplicative decomposition, strain tensors, material derivative, velocity gradient.

-Fundamental laws: mass conservation, balance of linear and angular momentum, balance of energy, entropy, Clausius-Duhem inequality, dissipation inequality.

-Mechanics of solids:coupled problem of thermo-elasticity and heat conduction under finite strains, hypo-elasticity, objective rates (Jaumann, Green-Naghdi, Oldroyd).

-Mechanics of fluids: inviscid flow (Euler), shock waves (Hugoniot), viscous flow (Newton-Stokes, Navier-Stokes, Reynolds).

-More than 120 worked out examples.

Syllabus of tutorials:

Introduction of continuum mechanics as general frame for description of mechanical response of bodies. Formulation of basic laws and their application on particular problems of solid and fluid dynamics.

Study Objective:

Study materials:

[1]Chandrasekharaiah, D.S., Lokenath Debnath: Continuum Mechanics. Academic Press, San Diego 1994.

[2] Gurtin, M.E.: An Introduction to Continuum Mechanics. Academic Press, San Diego 1981

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: