Stress integration schemes for unsaturated soils

The problem of stress integration arises every time numerical computations are performed with the displacement finite element method. Mathematically, the problem can be treated as a system of differential equations (explicit) or as a system of nonlinear equations (implicit). In either case, the equations may be solved analytically for simple constitutive laws, but in general need to be solved numerically. This paper initially introduces the stress integration problem and briefly describes two popular approaches to stress integration (i.e. the explicit and the implicit approach). It follows with a brief description of an implementation of the explicit scheme with use of the equivalent stress approach. Further on, special attention is given to the common problems that are encountered in the implementation of this stress integration algorithm. The paper also contains brief guidelines for choosing the right numerical integration scheme for a given problem.