Navigation

DG20RMK - Continuum mechanics

Course specification
Type of study Doctoral studies
Study programme
Course title Continuum mechanics
Acronym Status Semester Number of classes ECTS
DG20RMK elective 1 4L + E 10.0
Lecturers
Lecturer
Lecturer/Associate (practicals)
    Prerequisite Form of prerequisites
    - -
    Learning objectives
    To understand fundamental concepts of continuum mechanics and its applications in engineering. Develop ability and creativity to independently formulate and solve engineering problems: formulation of mechanical, mathematical, and calculation models, and discussion of results.
    Learning outcomes
    Student is able to analyze and solve basic problems of the continuum mechanics. Student is able to continue independent research work for the modeling of complex structures.
    Content
    Tensor calculus. Deformation of continuum. Material and spatial description. Deformation gradients, strain tensors (Green-Lagrange, Almansi-Euler). Principal directions, principal strains, invariants of strain tensors. Change of length, volume and area. Rotation tensor, left and right stretch tensor and polar decomposition theorem. Finite and infinitesimal strain, small and large rotations. Time derivatives, velocity and and acceleration. Strain rate tensor. Reynolds transport theorems. Continuum dynamics. Stress and pseudo stress. State of stress. General principles in continuum mechanics: mass balance, balance of momentum and angular momentum. The first and second Cauchy's law of motion. The principle of virtual displacements. Principle of objectivity.Objective quantities and objective derivatives. Introduction to continuum thermodynamics. The first and second laws of thermodynamics in global and local form. Constitutive equations - basics.
    Teaching Methods
    Auditory lectures and individual work with students
    Literature
    1. Finite elastoplastic strains
    2. Continuum mechanics
    3. C. Eringen, „Nonlinear theory of Continuos Media”, Mc Graw-Hill, 1967. (Original title)
    4. L. E. Malvern, „Introduction to the Mechanics of a Continuous Medium”, Prentice Hall, 1969. (Original title)
    5. J. Bonet, R. D. Wood: „Nonlinear Continuum Mechanics and Finite Element Analysis”, Cambridge University Press, 1997. (Original title)
    Evaluation and grading
    Calculation and defence of the semestral assignment (50%) Oral exam (50%)
    Specific remarks
    The course can be conducted in English.