Faculty of Science

Objectives

To give a basic knowledge on solids or fluids viewed as continuous medium and related topics: description of continuous media, balance and conservation laws; transport equations, applications in linear elasticity and viscous fluids flows, have an ability to critically judge the content of mechanical discussions in literature and technical seminars, solid deformation, elasticity.

Contents

Modelling the continuum; Lagrangian and Eulerian descriptions; Deformation and strain: the homogeneous tangent map, expansion tensor, Green-Lagrange strain tensor, displacement field, polar factorisation and rigid body transformation, infinitesimal transformations; Motion and flow: convective transport and material derivative, rate of deformation and vorticity tensor, material derivative of a volume integral, conservation of mass; Balance equations: linear momentum and equations of motion, conservation of energy; Analysis of stress: Stress tensor symmetry, stress transformation laws, principal stresses, stress invariants, Mohr’s circles for stress; Linear elasticity; Fluids; Plasticity; Viscoelasticity, Piezoelectricity, Acoustic surface waves.