Continuum mechanics

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.

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.

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.

1. Finite elastoplastic strains

2. Continuum mechanics

3. C. Eringen, „Nonlinear theory of Continuos Media”, Mc Graw-Hill, 1967.

   (Original)

4. L. E. Malvern, „Introduction to the Mechanics of a Continuous Medium”, Prentice Hall, 1969.

   (Original)

5. J. Bonet, R. D. Wood: „Nonlinear Continuum Mechanics and Finite Element Analysis”, Cambridge University Press, 1997.

   (Original)

Calculation and defence of the semestral assignment (50%)
Oral exam (50%)

Auditory lectures and individual work with students