Course Details

The concept of a continuous material medium: definition of mass, density and volume. The notion of a material point (or marker) and its analogue in mathematics.

Kinematics in continuum mechanics: position of the material points, trajectory, velocity and acceleration. Definition and distinction between Lagrangian and Eulerian descriptions of kinematic fields in continuum mechanics. The displacement field and its analysis in terms of rigid and elastic motions. The kinematics of rigid bodies. Analysis of elastic kinematics. Definition of deformation and strain tensors. Linear and non-linear expressions of the strain tensors and alternative definitions of strains and deformations (Right and Left Cauchy-Green deformation tensors, Lagrangian and Eulerian Strain tensors). The notion of dilatation. Principal strain and maximum elongation. Compatibility conditions for strains and their rates. Polar decomposition theorem. Change of area and volume due to deformation.

Dynamics in continuum mechanics: equations of mass, momentum, moment of momentum and energy. The notion of stresses, definition of the stress tensor. Normal and shear stresses. Principal axes, maximum normal and shear stresses at a point. Formulation of the equations in Lagrangian and Eulerian descriptions with respect to the undeformed and deformed states.

Stress-strain relations: material properties, isotropic and anisotropic materials, homogeneous and non-homogeneous materials. Hooke’s law and elastic constants. Introduction to anisotropies and their effect on the stress-strain relations.

Basic example problems and applications of elastic solids: one dimensional tension, torsion and bending; simple beam theory (Euler-Bernoulli), bending and shear of beam structures and plane waves.