We now establish the equations of equilibrium in incremental stress field.

Figure 27.1

In the  plane we consider a body outlined by a contour C. The initial stress on the body are . If X and Y are the components of body force per unit of mass and if ρ is the density of the medium before deformation, the initial stress components will satisfy the equilibrium relations,

(27.1)

A point P of the material originally of coordinates  moves to a point P' of coordinates  after deformation. We denote by the x and y components of the force  acting at a point P' of the boundary per unit area after deformation. This force is acting on the solid inside the contour C’.