Elements of Continuum Mechanics

Abstract

(1) The state of stress at a point is defined by a stress tensor with nine stress components. However only six of them, three normal stresses and three shear stresses, are independent due to moment equilibrium. These stresses need to satisfy three equations of equilibrium. (2) Deformation of a point can be described by strains. In three dimensions, there are also three normal strains and three shear strains. These strains are also linked by compatibility conditions. (3) The relationship between stresses and strains can be very complex and mainly depends on material types and loading conditions. For linear elastic materials, the relationship between stresses and strains is governed by Hooke's law.