Following the law of conservation of mass, we can write . We then convert the line integral to surface integral using Green’s theorem to obtain the following expression:

(27.6)

Since the integrand in the above equation should be zero, we obtain the following stress equilibrium equation

(27.7)

When we substitute the expressions for , and from equation 26.7 in 27.7, we obtain the expressions which are in terms of the initial stresses and the incremental stresses:

(27.8)

Writing the incremental body forces as,